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1
Deshpande, Ameet Shridhar. "Efficient idempotent methods for optimal control". Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3389391.
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Thesis (Ph. D.)--University of California, San Diego, 2009.Title from first page of PDF file (viewed February 12, 2010). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 178-182).
2
Bassou, Leila. "Optimal control methods for systemic risk". Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAX041.
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Cette thèse porte sur l'étude des équilibres de Nash du jeu de détentions mutuelles dans différents cadres. Le modèle correspondant, qui a été introduit par M-F. Djete & N. Touzi en 2020, vise à capturer l'interdépendance entre différents agents économiques en tenant compte à la fois des détentions mutuelles de parts entre les entités et de leurs revenus qui peuvent être corrélés.- Dans la première partie, on a étudié le jeu à population finie dans le cadre du critère d'utilité exponentielle. Dans les cas statiques et dynamiques sous une dynamique de type Bachelier gaussienne, on obtient une caractérisation complète des équilibres de Nash et de leurs conditions d'existence.- La deuxième partie est dédiée à l'analyse du jeu à champ moyen avec bruit commun (les revenus sont corrélés), pour le critère moyenne-variance à une période. La résolution de ce problème a fait apparaître une structure liée à une condition de non--arbitrage. Dans ce cadre, on a déterminé une caractérisation explicite de cette condition, ainsi qu'une caractérisation complète des équilibres de Nash.- Dans la troisième partie, on a étendu le jeu à champ moyen avec bruit commun, au cadre du temps continu. Ici, on voit apparaître une condition plus faible de non--arbitrage. Sa caractérisation permet de réduire l'analyse des équilibres de Nash au problème classique d'optimisation de portefeuille avec des dotations aléatoiresThis thesis is dedicated to the study of cross-holding game's Nash equilibria in various frameworks. The related model, which was introduced by M-F. Djete & N. Touzi in 2020, aims to capture the interdependence between differenteconomic agents by taking into account, on the one hand, the mutual holding of sharesbetween the entities, and on the other hand, their incomes that can be correlated.- The first part is devoted to the finite population game within the framework of the exponential utility criterion. In the static and dynamic settings under gaussian Bachelier type dynamic, we completely characterize the Nash equilibria and their existence conditions.- The second part is dedicated to the one-period mean field game with common noise (the revenues are correlated), by considering the mean-variance criterion. The formulation of the problem reveals a No-arbitrage condition. In this framework, we characterized explicitly this condition, as well as the mean field equilibria.- In the third part, we extended the study of the mean-field game, with common noise, to the continuous time setting. Here, the problem reveals a weak notion of No-arbitrage condition. The characterization of this condition reduces the analysis of the mean field equilibria to the classical problem of optimal portfolio with random endowment
3
Goodwin, David L. "Advanced optimal control methods for spin systems". Thesis, University of Southampton, 2017. https://eprints.soton.ac.uk/423078/.
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Work within this thesis advances optimal control algorithms for application to magnetic resonance systems. Specifically, presenting a quadratically convergent version of the gradient ascent pulse engineering method. The work is formulated in a superoperator representation of the Liouville-von Neumann equation. A Newton-grape method is developed using efficient calculation of analytical second directional derivatives. The method is developed to scale with the same complexity as methods that use only first directional derivatives. Algorithms to ensure a well-conditioned and positive definite matrix of second directional derivatives are used so the sufficient conditions of gradient-based numerical optimisation are met. A number of applications of optimal control in magnetic resonance are investigated: solid-state nuclear magnetic resonance, magnetisation-to-singlet pulses, and electron spin resonance experiments.
4
Fabrini, Giulia. "Numerical methods for optimal control problems with biological applications". Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066096/document.
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Cette thèse se développe sur deux fronts: nous nous concentrons sur les méthodes numériques des problèmes de contrôle optimal, en particulier sur le Principe de la Programmation Dynamique et sur le Model Predictive Control (MPC) et nous présentons des applications de techniques de contrôle en biologie. Dans la première partie, nous considérons l'approximation d'un problème de contrôle optimal avec horizon infini, qui combine une première étape, basée sur MPC permettant d'obtenir rapidement une bonne approximation de la trajectoire optimal, et une seconde étape, dans la quelle l¿équation de Bellman est résolue dans un voisinage de la trajectoire de référence. De cette façon, on peux réduire une grande partie de la taille du domaine dans lequel on résout l¿équation de Bellman et diminuer la complexité du calcul. Le deuxième sujet est le contrôle des méthodes Level Set: on considère un problème de contrôle optimal, dans lequel la dynamique est donnée par la propagation d'un graphe à une dimension, contrôlé par la vitesse normale. Un état finale est fixé, l'objectif étant de le rejoindre en minimisant une fonction coût appropriée. On utilise la programmation dynamique grâce à une réduction d'ordre de l'équation utilisant la Proper Orthogonal Decomposition. La deuxième partie est dédiée à l'application des méthodes de contrôle en biologie. On présente un modèle décrit par une équation aux dérivées partielles qui modélise l'évolution d'une population de cellules tumorales. On analyse les caractéristiques du modèle et on formule et résout numériquement un problème de contrôle optimal concernant ce modèle, où le contrôle représente la quantité du médicament administréeThis thesis is divided in two parts: in the first part we focus on numerical methods for optimal control problems, in particular on the Dynamic Programming Principle and on Model Predictive Control (MPC), in the second part we present some applications of the control techniques in biology. In the first part of the thesis, we consider the approximation of an optimal control problem with an infinite horizon, which combines a first step based on MPC, to obtain a fast but rough approximation of the optimal trajectory and a second step where we solve the Bellman equation in a neighborhood of the reference trajectory. In this way, we can reduce the size of the domain in which the Bellman equation can be solved and so the computational complexity is reduced as well. The second topic of this thesis is the control of the Level Set methods: we consider an optimal control, in which the dynamics is given by the propagation of a one dimensional graph, which is controlled by the normal velocity. A final state is fixed and the aim is to reach the trajectory chosen as a target minimizing an appropriate cost functional. To apply the Dynamic Programming approach we firstly reduce the size of the system using the Proper Orthogonal Decomposition. The second part of the thesis is devoted to the application of control methods in biology. We present a model described by a partial differential equation that models the evolution of a population of tumor cells. We analyze the mathematical and biological features of the model. Then we formulate an optimal control problem for this model and we solve it numerically
5
Weiser, Martin. "Function space complementarity methods for optimal control problems". [S.l. : s.n.], 2001. http://www.diss.fu-berlin.de/2001/189/index.html.
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Teuber, Claus [Verfasser]. "Optimal Control Methods for Transmission Lines / Claus Teuber". München : Verlag Dr. Hut, 2017. http://d-nb.info/1147674663/34.
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Blanchard, Eunice Anita. "Exact penalty methods for nonlinear optimal control problems". Thesis, Curtin University, 2014. http://hdl.handle.net/20.500.11937/1805.
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Research comprised of developing solution techniques to three classes of non-standard optimal control problems, namely: optimal control problems with discontinuous objective functions arising in aquaculture operations; impulsive optimal control problems with minimum subsystem durations; optimal control problems involving dual-mode hybrid systems with state-dependent switching conditions. The numerical algorithms developed involved an exact penalty approach to transform the constrained problem into an unconstrained problem which was readily solvable by a standard optimal control software.
8
Yucel, Hamdullah. "Adaptive Discontinuous Galerkin Methods For Convectiondominated Optimal Control Problems". Phd thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614523/index.pdf.
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Many real-life applications such as the shape optimization of technological devices, the identification
of parameters in environmental processes and flow control problems lead to optimization
problems governed by systems of convection diusion partial dierential equations
(PDEs). When convection dominates diusion, the solutions of these PDEs typically exhibit
layers on small regions where the solution has large gradients. Hence, it requires special numerical
techniques, which take into account the structure of the convection. The integration
of discretization and optimization is important for the overall eciency of the solution process.
Discontinuous Galerkin (DG) methods became recently as an alternative to the finite
dierence, finite volume and continuous finite element methods for solving wave dominated
problems like convection diusion equations since they possess higher accuracy.
This thesis will focus on analysis and application of DG methods for linear-quadratic convection
dominated optimal control problems. Because of the inconsistencies of the standard stabilized
methods such as streamline upwind Petrov Galerkin (SUPG) on convection diusion
optimal control problems, the discretize-then-optimize and the optimize-then-discretize do not commute. However, the upwind symmetric interior penalty Galerkin (SIPG) method leads to
the same discrete optimality systems. The other DG methods such as nonsymmetric interior
penalty Galerkin (NIPG) and incomplete interior penalty Galerkin (IIPG) method also yield
the same discrete optimality systems when penalization constant is taken large enough. We
will study a posteriori error estimates of the upwind SIPG method for the distributed unconstrained
and control constrained optimal control problems. In convection dominated optimal
control problems with boundary and/or interior layers, the oscillations are propagated downwind
and upwind direction in the interior domain, due the opposite sign of convection terms in
state and adjoint equations. Hence, we will use residual based a posteriori error estimators to
reduce these oscillations around the boundary and/or interior layers. Finally, theoretical analysis
will be confirmed by several numerical examples with and without control constraints
9
Musser, Jonathan Wesley. "A comparison of optimal and suboptimal reservoir control methods". Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/19315.
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Chai, Qinqin. "Computational methods for solving optimal industrial process control problems". Thesis, Curtin University, 2013. http://hdl.handle.net/20.500.11937/1227.
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In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem involving systems with both input and output delays, and subject to continuous inequality state constraints; and (iii) a max-min optimal control problem arising in gradient elution chromatography.In the first problem, we consider a parameter identification problem involving a general nonlinear time-delay system, where the unknown time delays and system parameters are to be identified. This problem is posed as a dynamic optimization problem, where its cost function is to measure the discrepancy between predicted output and observed system output. The aim is to find unknown time-delays and system parameters such that the cost function is minimized. We develop a gradient-based computational method for solving this dynamic optimization problem. We show that the gradients of the cost function with respect to these unknown parameters can be obtained via solving a set of auxiliary time-delay differential systems from t = 0 to t = T. On this basis, the parameter identification problem can be solved as a nonlinear optimization problem and existing optimization techniques can be used. Two numerical examples are solved using the proposed computational method. Simulation results show that the proposed computational method is highly effective. In particular, the convergence is very fast even when the initial guess of the parameter values is far away from the optimal values.Unlike the first problem, in the second problem, we consider a time delay identification problem, where the input function for the nonlinear time-delay system is piecewise-constant. We assume that the time-delays—one involving the state variables and the other involving the input variables—are unknown and need to be estimated using experimental data. We also formulate the problem of estimating the unknown delays as a nonlinear optimization problem in which the cost function measures the least-squares error between predicted output and measured system output. This estimation problem can be viewed as a switched system optimal control problem with time-delays. We show that the gradient of the cost function with respect to the unknown state delay can be obtained via solving a auxiliary time-delay differential system. Furthermore, the gradient of the cost function with respect to the unknown input delay can be obtained via solving an auxiliary time-delay differential system with jump conditions at the delayed control switching time points. On this basis, we develop a heuristic computational algorithm for solving this problem using gradient based optimization algorithms. Time-delays in two industrial processes are estimated using the proposed computational method. Simulation results show that the proposed computational method is highly effective.For the third problem, we consider a general optimal control problem governed by a system with input and output delays, and subject to continuous inequality constraints on the state and control. We focus on developing an effective computational method for solving this constrained time delay optimal control problem. For this, the control parameterization technique is used to approximate the time planning horizon [0, T] into N subintervals. Then, the control is approximated by a piecewise constant function with possible discontinuities at the pre-assigned partition points, which are also called the switching time points. The heights of the piecewise constant function are decision variables which are to be chosen such that a given cost function is minimized. For the continuous inequality constraints on the state, we construct approximating smooth functions in integral form. Then, the summation of these approximating smooth functions in integral form, which is called the constraint violation, is appended to the cost function to form a new augmented cost function. In this way, we obtain a sequence of approximate optimization problems subject to only boundedness constraints on the decision variables. Then, the gradient of the augmented cost function is derived. On this basis, we develop an effective computational method for solving the time-delay optimal control problem with continuous inequality constraints on the state and control via solving a sequence of approximate optimization problems, each of which can be solved as a nonlinear optimization problem by using existing gradient-based optimization techniques. This proposed method is then used to solve a practical optimal control problem arising in the study of a real evaporation process. The results obtained are highly satisfactory, showing that the proposed method is highly effective.The fourth problem that we consider is a max-min optimal control problem arising in the study of gradient elution chromatography, where the manipulative variables in the chromatographic process are to be chosen such that the separation efficiency is maximized. This problem has three non-standard characteristics: (i) The objective function is nonsmooth; (ii) each state variable is defined over a different time horizon; and (iii) the order of the final times for the state variable, the so-called retention times, are not fixed. To solve this problem, we first introduce a set of auxiliary decision variables to govern the ordering of the retention times. The integer constraints on these auxiliary decision variables are approximated by continuous boundedness constraints. Then, we approximate the control by a piecewise constant function, and apply a novel time-scaling transformation to map the retention times and control switching times to fixed points in a new time horizon. The retention times and control switching times become decision variables in the new time horizon. In addition, the max-min objective function is approximated by a minimization problem subject to an additional constraint. On this basis, the optimal control problem is reduced to an approximate nonlinear optimization problem subject to smooth constraints, which is then solved using a recently developed exact penalty function method. Numerical results obtained show that this approach is highly effective.Finally, some concluding remarks and suggestions for further study are made in the conclusion chapter.
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Sampathirao, Ajay Kumar. "Parallel methods for solving stochastic optimal control problems: control of drinking water networks". Thesis, IMT Alti Studi Lucca, 2016. http://e-theses.imtlucca.it/203/1/Sampathirao_phdthesis.pdf.
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This thesis is concerned with the development of
optimisation methods to solve stochastic Model Predictive
Control (MPC) problem and employ them in
the management of DrinkingWater Networks (DWNs).
DWNs are large-scale, complex both in topology and
dynamics, energy-intensive systems subjected to irregular
demands. Managing these networks play a
crucial role in the economic sustainability of urban
cities. The main challenge associated with such infrastructures
is to minimise the energy required for
pumping water while simultaneously maintaining
uninterrupted water supply. State-of-the-art control
methodologies as well as the current engineering
practices use predictive models to forecast upcoming
water demands but do not take into consideration
the inevitable forecasting error. This way, the
water network is operated in a deterministic fashion
disregarding its inherent stochastic behaviour
which accrues from the volatility of water demand
and, often, electricity prices. In this thesis, we address
two challenges namely: optimisation methods
for solving stochastic MPC problems and closedloop
feedback control for the management of drinking
water networks.
MPC is an advanced control technology that copes with complex control problem by repeatedly solving
a finite horizon constrained optimal control problem;
uses only the first decision as input and discards
the rest of the sequence. This methodology
decides the control action based on present state of
the system and thus provides an implicit feedback
to the system. Instead of historical demand profile,
time-series models were developed to forecast the
future water demand. The economic and the social
aspects involved in operation of the DWN were
captured in a cost function. Now the MPC controller
combined with online forecaster minimise the
cost function across a prediction horizon of 1 day
with sampling time equal to 1 hour and thus the
closed-loop strategy for DWN management is devised.
The forecasts are just nominal demands and differ
from the actual demands. There exist several approaches
when it comes to working with uncertain
forecasts: (i) to assume that forecast errors are negligible
and disregard them, (ii) to assume knowledge
of their worst-case values (maximum errors), (iii)
to assume knowledge of probabilistic information.
These three approaches lead to the three principal
flavours of MPC: the certainty-equivalent (CE), the
worst-case robust and the stochastic MPC. CE-MPC
is simple but not realistic (because the errors are not
negligible), worst-case MPC is more meaningful but
it is too conservative (because it is highly improbable
that the errors admit their worst-case values) and then we have stochastic MPC which is the approach
pursued in this thesis.
A stochastic MPC allows a systematic framework
as trade-off performance against constraint violation
by modelling the uncertainty as stochastic process
and quantifying its influence. However, this
formulation is an infinite dimensional optimisation
problem and its corresponding discrete approximation
is deemed to be a large-scale problem with millions
of decision variables. Therefore, the applicability
of stochastic MPC in control applications is
limited due to the unavailability of algorithms that
can solve them efficiently and within the sampling
time of the controlled system.
Here we developed optimisation algorithms that solve
stochastic MPC problem by exploiting their structure
and using parallelisation. These algorithms are
(i) accelerated proximal gradient algorithm also known
as forward-backward splitting and (ii) LBFGS
method for forward-backward envelope (FBE) function.
Both these algorithms employ decomposition
to solve the Fenchel dual and make them suitable
for parallel implementation. Graphics processing
units (GPUs) are capable of perform parallel computation
and are therefore perfect hardware to solve
the stochastic MPC problem with the accelerated
proximal gradient method.
The water network of the city Barcelona is considered
to study the validity of the proposed algorithm.
The GPU implementation is found to be 10 times faster than commercial solvers like Gurobi running
in multi-core environment and made the problem
computationally tractable in the sampling time. The
efficiency of the stochastic MPC to manage theDWN
is quantified in terms of key performance indicators
like economic utility, network utility and quality of
service.
The forward-backward splitting is a first-order method
and has slow convergence for ill-conditioned
problems. We constructed a continuously differentiable
real-valued forward-backward envelope function
that has the same set of minimisers as the actual
problem. Then we use quasi-Newton method,
in particular LBFGS method, that utilises secondorder
information to solve the FBE. The computations
with this algorithm are also parallelisable and
it demonstrated fast convergence compared to accelerated
dual proximal gradient algorithm.
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Kouzoupis, Dimitris [Verfasser] y Moritz [Akademischer Betreuer] Diehl. "Structure-exploiting numerical methods for tree-sparse optimal control problems". Freiburg : Universität, 2019. http://d-nb.info/1191689549/34.
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Liu, Jun. "NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS". OpenSIUC, 2015. https://opensiuc.lib.siu.edu/dissertations/1076.
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Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Optimal control of partial differential equations (PDEs) has tremendous applications in engineering and science, such as shape optimization, image processing, fluid dynamics, and chemical processes. In this thesis, we develop and analyze several efficient numerical methods for the optimal control problems governed by elliptic PDE, parabolic PDE, and wave PDE, respectively. The thesis consists of six chapters. In Chapter 1, we briefly introduce a few motivating applications and summarize some theoretical and computational foundations of our following developed approaches. In Chapter 2, we establish a new multigrid algorithm to accelerate the semi-smooth Newton method that is applied to the first-order necessary optimality system arising from semi-linear control-constrained elliptic optimal control problems. Under suitable assumptions, the discretized Jacobian matrix is proved to have a uniformly bounded inverse with respect to mesh size. Different from current available approaches, a new strategy that leads to a robust multigrid solver is employed to define the coarse grid operator. Numerical simulations are provided to illustrate the efficiency of the proposed method, which shows to be computationally more efficient than the popular full approximation storage (FAS) multigrid method. In particular, our proposed approach achieves a mesh-independent convergence and its performance is highly robust with respect to the regularization parameter. In Chaper 3, we present a new second-order leapfrog finite difference scheme in time for solving the first-order necessary optimality system of the linear parabolic optimal control problems. The new leapfrog scheme is shown to be unconditionally stable and it provides a second-order accuracy, while the classical leapfrog scheme usually is well-known to be unstable. A mathematical proof for the convergence of the proposed scheme is provided under a suitable norm. Moreover, the proposed leapfrog scheme gives a favorable structure that leads to an effective implementation of a fast solver under the multigrid framework. Numerical examples show that the proposed scheme significantly outperforms the widely used second-order backward time differentiation approach, and the resultant fast solver demonstrates a mesh-independent convergence as well as a linear time complexity. In Chapter 4, we develop a new semi-smooth Newton multigrid algorithm for solving the discretized first-order necessary optimality system that characterizes the optimal solution of semi-linear parabolic PDE optimal control problems with control constraints. A new leapfrog discretization scheme in time associated with the standard five-point stencil in space is established to achieve a second-order accuracy. The convergence (or unconditional stability) of the proposed scheme is proved when time-periodic solutions are considered. Moreover, the derived well-structured discretized Jacobian matrices greatly facilitate the development of an effective smoother in our multigrid algorithm. Numerical simulations are provided to illustrate the effectiveness of the proposed method, which validates the second-order accuracy in solution approximations as well as the optimal linear complexity of computing time. In Chapter 5, we offer a new implicit finite difference scheme in time for solving the first-order necessary optimality system arising in optimal control of wave equations. With a five-point central finite difference scheme in space, the full discretization is proved to be unconditionally convergent with a second-order accuracy, which is not restricted by the classical Courant-Friedrichs-Lewy (CFL) stability condition on the spatial and temporal step sizes. Moreover, based on its advantageous developed structure, an efficient preconditioned Krylov subspace method is provided and analyzed for solving the discretized sparse linear system. Numerical examples are presented to confirm our theoretical conclusions and demonstrate the promising performance of proposed preconditioned iterative solver. Finally, brief summaries and future research perspectives are given in Chapter 6.
14
Mohammadi, Seyed A. "A numerical study of some hybrid conjugate gradient methods in optimal control". Thesis, Loughborough University, 1995. https://dspace.lboro.ac.uk/2134/27361.
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The main work of this thesis is concerned with the comparison of conjugate gradient with hybrid conjugate gradient methods when they are applied to optimal control problems. Descriptions of the conjugate gradient. and hybrid conjugate gradient methods, for general optimisation, in finite and infinite dimensions are also given. The numerical methods for solving the differential equations and the line searches required in the optimisation are discussed next.
15
Antoine, Olivier. "Contrôle optimal et robuste de l'attitude d'un lanceur. Aspects théoriques et numériques". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS196/document.
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L'objectif premier de cette thèse est d'étudier certains aspects du contrôle d'attitude d'un corps rigide, afin d'optimiser la trajectoire d'un lanceur au cours de sa phase balistique. Nous y développons un cadre mathématique permettant de formuler ce problème comme un problème de contrôle optimal avec des contraintes intermédiaires sur l'état. En parallèle de l'étude théorique de ce problème, nous avons mené l'implémentation d'un logiciel d'optimisation basé sur la combinaison d'une méthode directe et d'un algorithme de point intérieur, permettant à l'utilisateur de traiter une phase balistique quelconque. Nous entendons par là qu'il est possible de spécifier un nombre quelconque de contraintes intermédiaires, correspondant à un nombre quelconque de largages de charges utiles. En outre, nous avons appliqué les méthodes dites indirectes, exploitant le principe du maximum de Pontryagin, à la résolution de ce problème de contrôle optimal. On cherche dans ce travail à trouver des trajectoires optimales du point de vue de la consommation en ergols, ce qui correspond à un coût L 1 . Réputé difficile numériquement, ce critère peut être atteint grâce à une méthode de continuation, en se servant d'un coût L 2 comme intermédiaire de calcul et en déformant progressivement ce problème L 2 . Nous verrons également d'autres exemples d'application des méthodes de continuation. Enfin, nous présenterons également un algorithme de contrôle robuste, permettant de rejoindre un état cible à partir d'un état perturbé, en suivant une trajectoire de référence tout en conservant la structure bang-bang des contrôles. La robustesse d'un contrôle peut également être améliorée par l'ajout de variations aiguilles, et un critère qualifiant la robustesse d'une trajectoire à partir des valeurs singulières d'une certaine application entrée-sortie est déduitThe first objective of this work is to study some aspects of the attitude control problem of a rigid body, in order to optimize the trajectory of a launcher during a ballistic flight. We state this problem in a general mathematical setting, as an optimal control problem with intermediate constraints on the state. Meanwhile, we also implement an optimization software that relies on the combination of a direct method and of an interior-point algorithm to optimize any given ballistic flight, with any number of intermediate constraints, corresponding to any number of satellite separations. Besides, we applied the so-called indirect methods, exploiting Pontryagin maximum principle, to the resolution of this optimal control problem. In this work, optimal trajectories with respect to the consumption are looked after, which corresponds to a L 1 cost. Known to be numerically challenging, this criterion can be reached by performing a continuation procedure, starting from a L 2 cost, for which it is easier to provide a good initialization of the underlying optimization algorithm. We shall also study other examples of applications for continuation procedures. Eventually, we will present a robust control algorithm, allowing to reach a target point from a perturbed initial point, following a nominal trajectory while preserving its bang-bang structure. The robustness of a control can be improved introducing needle-like variations, and a criterion to measure the robustness of a trajectory is designed, involving the singular value decomposition of some end-point mapping
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Huschto, Tony [Verfasser] y Sebastian [Akademischer Betreuer] Sager. "Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations / Tony Huschto ; Betreuer: Sebastian Sager". Heidelberg : Universitätsbibliothek Heidelberg, 2014. http://d-nb.info/118030067X/34.
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Akman, Tugba. "Discontinuous Galerkin Methods For Time-dependent Convection Dominated Optimal Control Problems". Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613394/index.pdf.
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Distributed optimal control problems with transient convection dominated diffusion convection reaction equations are considered. The problem is discretized in space by using three types of discontinuous Galerkin (DG) method: symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), incomplete interior penalty Galerkin (IIPG). For time discretization, Crank-Nicolson and backward Euler methods are used. The discretize-then-optimize approach is used to obtain the finite dimensional problem. For one-dimensional unconstrained problem, Newton-Conjugate Gradient method with Armijo line-search. For two-dimensional control constrained problem, active-set method is applied. A priori error estimates are derived for full discretized optimal control problem. Numerical results for one and two-dimensional distributed optimal control problems for diffusion convection equations with boundary layers confirm the predicted orders derived by a priori error estimates.
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Biehn, Neil David. "Implicit Runge-Kutta Methods for Stiff and Constrained Optimal Control Problems". NCSU, 2001. http://www.lib.ncsu.edu/theses/available/etd-20010322-165913.
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The purpose of the research presented in this thesis is to better understand and improve direct transcription methods for stiff and state constrained optimal control problems. When some implicit Runge-Kutta methods are implemented as approximations to the dynamics of an optimal control problem, a loss of accuracy occurs when the dynamics are stiff or constrained. A new grid refinement strategy which exploits the variation of accuracy is discussed. In addition, the use of a residual function in place of classical error estimation techniques is proven to work well for stiff systems. Computational experience reveals the improvement in efficiency and reliability when the new strategies are incorporated as part of a direct transcription algorithm. For index three differential-algebraic equations, the solutions of some implicit Runge-Kutta methods may not converge. However, computational experience reveals apparent convergence for the same methods used when index three state inequality constraints become active. It is shown that the solution chatters along the constraint boundary allowing for better approximations. Moreover, the consistency of the nonlinear programming problem formed by a direct transcription algorithm using an implicit Runge-Kutta approximation is proven for state constraints of arbitrary index.
19
Clever, Debora [Verfasser]. "Adaptive Multilevel Methods for PDAE-Constrained Optimal Control Problems / Debora Clever". München : Verlag Dr. Hut, 2013. http://d-nb.info/1031845267/34.
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Anthony, David Keith. "Robust optimal design using passive and active methods of vibration control". Thesis, University of Southampton, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312863.
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Chen, Haisong. "Methods and algorithms for optimal control of fed-batch fermentation processes". Thesis, Cape Peninsula University of Technology, 2005. http://hdl.handle.net/20.500.11838/1151.
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Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2005Fennentation is the process that results in the fonnation ofalcohol or organic acids on the basis of growth of bacteria, moulds or fungi on different nutritional media (Ahmed et al., 1982). Fennentation process have three modes of operation i.e. batch, fed-batch and continuous ones. The process that interests a lot of control engineers is the fed-batch fennentation process (Johnson, 1989). The Fed-batch process for the production ofyeast is considered in the study. The fennentation is based on the Saccharomyces cerevisiae yeast. It grows in both aerobic and anaerobic environmental conditions with maximum product in the aerobic conditions, also at high concentration of glucose (Njodzi, 200I). Complexity of fed-batch fennentation process, non-linearity, time varying characteristics, application of conventional analogue controllers provides poor control due to problems in tuning individual loops and the process characteristics. The problem for control of the fed-batch process for the production of yeast is further complicated by the lack of on-line sensors, lack ofadequate models as a result ofpoorly understood dynamics. The lack of on-line sensors results in the impossibility oftuning the analogue controllers in real time. The process for propagation of yeast in aerobic conditions is considered in the dissertation. The experiments are conducted at the University of Cape Town (DCT), Department of Chemical Engineering with a bioreactor and bio-controller combined in a Biostat ® C lab scale plant (H. Braun Biotech International, 1996). The bio-controller has built in Pill controller loops for control variables, with the ability to adjust the controller parameters i.e. P, D and I through the serial interface (SeidIer, 1996).
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Schamel, George C. "Experimental and theoretical investigation of optimal control methods with model reduction". Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54412.
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In this study three types of optimized controllers are developed and tested on two laboratory structures. The two structures represented a progression in complexity and challenge to the controllers. The first structure was simple enough to be accurately modeled so the analytical frequencies and mode shapes agreed with the experimental measurements. The second structure being more complex was more difficult to model so differences between the analytical results and experimental measurements were present. These differences required the application a correction method to the reduced models developed for the second structure. The correction method was shown to work with good results on one reduced model and with poor results on the second reduced model.
Two direct rate feedback control laws and a linear quadratic regulator with state estimation (LQG controller) were designed and implemented on both structures. It was shown that the performance of the LQG controller can be approached with a much simpler direct rate feedback controller with better analytical-experimental agreement. The best analytical-experimental agreement occurred with the simplest controller applied analytically to the corrected reduced model demonstrating the validity of the correction method as well as giving a strong reason to use simpler controller designs.Ph. D.
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Pooseh, Shakoor. "Computational methods in the fractional calculus of variations and optimal control". Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/11510.
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Doutoramento em MatemáticaThe fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.
O cálculo das variações e controlo óptimo fraccionais são generalizações das correspondentes teorias clássicas, que permitem formulações e modelar problemas com derivadas e integrais de ordem arbitrária. Devido à carência de métodos analíticos para resolver tais problemas fraccionais, técnicas numéricas são desenvolvidas. Nesta tese, investigamos a aproximação de operadores fraccionais recorrendo a séries de derivadas de ordem inteira e diferenças finitas generalizadas. Obtemos majorantes para o erro das aproximações propostas e estudamos a sua eficiência. Métodos directos e indirectos para a resolução de problemas variacionais fraccionais são estudados em detalhe. Discutimos também condições de optimalidade para diferentes tipos de problemas variacionais, sem e com restrições, e para problemas de controlo óptimo fraccionais. As técnicas numéricas introduzidas são ilustradas recorrendo a exemplos.
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Ng, Chi Kong. "Globally convergent and efficient methods for unconstrained discrete-time optimal control". HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/149.
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Frego, Marco. "Numerical Methods for Optimal Control Problems with Application to Autonomous Vehicles". Doctoral thesis, Università degli studi di Trento, 2014. https://hdl.handle.net/11572/368533.
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In the present PhD thesis an optimal problem suite is proposed as benchmark for the test of numerical solvers. The problems are divided in four categories, classic, singular, constrained and hard problems. Apart from the hard problems, where it is not possible to give the analytical solution but only some details, all other problems are supplied with the derivation of the solution. The exact solution allows a precise comparison of the performance of the considered software. All of the proposed problems were taken from published papers or books, but it turned out that an analytic exact solution was only rarely provided, thus a true and reliable comparison among numerical solvers could not be done before. A typical wrong conclusion when a solver obtains a lower value of the target functional with respect to other solvers is to claim it better than the others, but it is not recognized that it has only underestimated the true value.
In this thesis, a cutting edge application of optimal control to vehicles is showed: the optimization of the lap time in a race circuit track considering a number of realistic constraints. A new algorithm for path planning is completely described for the construction of a quasi G2 fitting of the GPS data with a clothoid spline in terms of the G1 Hermite interpolation problem. In particular the present algorithm is proved to work better than state of the art algorithms in terms of both efficiency and precision.
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Frego, Marco. "Numerical Methods for Optimal Control Problems with Application to Autonomous Vehicles". Doctoral thesis, University of Trento, 2014. http://eprints-phd.biblio.unitn.it/1227/1/MFT.pdf.
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In the present PhD thesis an optimal problem suite is proposed as benchmark for the test of numerical solvers. The problems are divided in four categories, classic, singular, constrained and hard problems. Apart from the hard problems, where it is not possible to give the analytical solution but only some details, all other problems are supplied with the derivation of the solution. The exact solution allows a precise comparison of the performance of the considered software. All of the proposed problems were taken from published papers or books, but it turned out that an analytic exact solution was only rarely provided, thus a true and reliable comparison among numerical solvers could not be done before. A typical wrong conclusion when a solver obtains a lower value of the target functional with respect to other solvers is to claim it better than the others, but it is not recognized that it has only underestimated the true value.
In this thesis, a cutting edge application of optimal control to vehicles is showed: the optimization of the lap time in a race circuit track considering a number of realistic constraints. A new algorithm for path planning is completely described for the construction of a quasi G2 fitting of the GPS data with a clothoid spline in terms of the G1 Hermite interpolation problem. In particular the present algorithm is proved to work better than state of the art algorithms in terms of both efficiency and precision.
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Kang, Bei. "STATISTICAL CONTROL USING NEURAL NETWORK METHODS WITH HIERARCHICAL HYBRID SYSTEMS". Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/122303.
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Electrical EngineeringPh.D.
The goal of an optimal control algorithm is to improve the performance of a system. For a stochastic system, a typical optimal control method minimizes the mean (first cumulant) of the cost function. However, there are other statistical properties of the cost function, such as variance (second cumulant) and skewness (third cumulant), which will affect the system performance. In this dissertation, the work on the statistical optimal control are presented, which extends the traditional optimal control method using cost cumulants to shape the system performance. Statistical optimal control will allow more design freedom to achieve better performance. The solutions of statistical control involve solving partial differential equations known as Hamilton-Jacobi-Bellman equation. A numerical method based on neural networks is employed to find the solutions of the Hamilton-Jacobi-Bellman partial differential equation. Furthermore, a complex problem such as multiple satellite control, has both continuous and discrete dynamics. Thus, a hierarchical hybrid architecture is developed in this dissertation where the discrete event system is applied to discrete dynamics, and the statistical control is applied to continuous dynamics. Then, the application of a multiple satellite navigation system is analyzed using the hierarchical hybrid architecture. Through this dissertation, it is shown that statistical control theory is a flexible optimal control method which improves the performance; and hierarchical hybrid architecture allows control and navigation of a complex system which contains continuous and discrete dynamics.
Temple University--Theses
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Sharp, Jesse A. "Numerical methods for optimal control and parameter estimation in the life sciences". Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/230762/1/Jesse_Sharp_Thesis.pdf.
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This thesis concerns numerical methods in mathematical optimisation and inference; with a focus on techniques for optimal control, and for parameter estimation and uncertainty quantification. Novel methodological and computational developments are presented, with a view to improving the efficiency, effectiveness and accessibility of these techniques for practitioners. The numerical methods considered in this work are widely applied throughout the life sciences; in areas including ecology, epidemiology and oncology, and beyond the life sciences; in engineering, economics, aeronautics and other disciplines.
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Reig, Bernad Alberto. "Optimal Control for Automotive Powertrain Applications". Doctoral thesis, Universitat Politècnica de València, 2017. http://hdl.handle.net/10251/90624.
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Optimal Control (OC) is essentially a mathematical extremal problem. The procedure consists on the definition of a criterion to minimize (or maximize), some constraints that must be fulfilled and boundary conditions or disturbances affecting to the system behavior. The OC theory supplies methods to derive a control trajectory that minimizes (or maximizes) that criterion.
This dissertation addresses the application of OC to automotive control problems at the powertrain level, with emphasis on the internal combustion engine. The necessary tools are an optimization method and a mathematical representation of the powertrain. Thus, the OC theory is reviewed with a quantitative analysis of the advantages and drawbacks of the three optimization methods available in literature: dynamic programming, Pontryagin minimum principle and direct methods. Implementation algorithms for these three methods are developed and described in detail. In addition to that, an experimentally validated dynamic powertrain model is developed, comprising longitudinal vehicle dynamics, electrical motor and battery models, and a mean value engine model.
OC can be utilized for three different purposes:
1. Applied control, when all boundaries can be accurately defined. The engine control is addressed with this approach assuming that a the driving cycle is known in advance, translating into a large mathematical problem. Two specific cases are studied: the management of a dual-loop EGR system, and the full control of engine actuators, namely fueling rate, SOI, EGR and VGT settings.
2. Derivation of near-optimal control rules, to be used if some disturbances are unknown. In this context, cycle-specific engine calibrations calculation, and a stochastic feedback control for power-split management in hybrid vehicles are analyzed.
3. Use of OC trajectories as a benchmark or base line to improve the system design and efficiency with an objective criterion. OC is used to optimize the heat release law of a diesel engine and to size a hybrid powertrain with a further cost analysis.
OC strategies have been applied experimentally in the works related to the internal combustion engine, showing significant improvements but non-negligible difficulties, which are analyzed and discussed. The methods developed in this dissertation are general and can be extended to other criteria if appropriate models are available.El Control Óptimo (CO) es esencialmente un problema matemático de búsqueda de extremos, consistente en la definición de un criterio a minimizar (o maximizar), restricciones que deben satisfacerse y condiciones de contorno que afectan al sistema. La teoría de CO ofrece métodos para derivar una trayectoria de control que minimiza (o maximiza) ese criterio. Esta Tesis trata la aplicación del CO en automoción, y especialmente en el motor de combustión interna. Las herramientas necesarias son un método de optimización y una representación matemática de la planta motriz. Para ello, se realiza un análisis cuantitativo de las ventajas e inconvenientes de los tres métodos de optimización existentes en la literatura: programación dinámica, principio mínimo de Pontryagin y métodos directos. Se desarrollan y describen los algoritmos para implementar estos métodos así como un modelo de planta motriz, validado experimentalmente, que incluye la dinámica longitudinal del vehículo, modelos para el motor eléctrico y las baterías, y un modelo de motor de combustión de valores medios. El CO puede utilizarse para tres objetivos distintos: 1. Control aplicado, en caso de que las condiciones de contorno estén definidas. Puede aplicarse al control del motor de combustión para un ciclo de conducción dado, traduciéndose en un problema matemático de grandes dimensiones. Se estudian dos casos particulares: la gestión de un sistema de EGR de doble lazo, y el control completo del motor, en particular de las consignas de inyección, SOI, EGR y VGT. 2. Obtención de reglas de control cuasi-óptimas, aplicables en casos en los que no todas las perturbaciones se conocen. A este respecto, se analizan el cálculo de calibraciones de motor específicas para un ciclo, y la gestión energética de un vehículo híbrido mediante un control estocástico en bucle cerrado. 3. Empleo de trayectorias de CO como comparativa o referencia para tareas de diseño y mejora, ofreciendo un criterio objetivo. La ley de combustión así como el dimensionado de una planta motriz híbrida se optimizan mediante el uso de CO. Las estrategias de CO han sido aplicadas experimentalmente en los trabajos referentes al motor de combustión, poniendo de manifiesto sus ventajas sustanciales, pero también analizando dificultades y líneas de actuación para superarlas. Los métodos desarrollados en esta Tesis Doctoral son generales y aplicables a otros criterios si se dispone de los modelos adecuados.
El Control Òptim (CO) és essencialment un problema matemàtic de cerca d'extrems, que consisteix en la definició d'un criteri a minimitzar (o maximitzar), restriccions que es deuen satisfer i condicions de contorn que afecten el sistema. La teoria de CO ofereix mètodes per a derivar una trajectòria de control que minimitza (o maximitza) aquest criteri. Aquesta Tesi tracta l'aplicació del CO en automoció i especialment al motor de combustió interna. Les ferramentes necessàries són un mètode d'optimització i una representació matemàtica de la planta motriu. Per a això, es realitza una anàlisi quantitatiu dels avantatges i inconvenients dels tres mètodes d'optimització existents a la literatura: programació dinàmica, principi mínim de Pontryagin i mètodes directes. Es desenvolupen i descriuen els algoritmes per a implementar aquests mètodes així com un model de planta motriu, validat experimentalment, que inclou la dinàmica longitudinal del vehicle, models per al motor elèctric i les bateries, i un model de motor de combustió de valors mitjans. El CO es pot utilitzar per a tres objectius diferents: 1. Control aplicat, en cas que les condicions de contorn estiguen definides. Es pot aplicar al control del motor de combustió per a un cicle de conducció particular, traduint-se en un problema matemàtic de grans dimensions. S'estudien dos casos particulars: la gestió d'un sistema d'EGR de doble llaç, i el control complet del motor, particularment de les consignes d'injecció, SOI, EGR i VGT. 2. Obtenció de regles de control quasi-òptimes, aplicables als casos on no totes les pertorbacions són conegudes. A aquest respecte, s'analitzen el càlcul de calibratges específics de motor per a un cicle, i la gestió energètica d'un vehicle híbrid mitjançant un control estocàstic en bucle tancat. 3. Utilització de trajectòries de CO com comparativa o referència per a tasques de disseny i millora, oferint un criteri objectiu. La llei de combustió així com el dimensionament d'una planta motriu híbrida s'optimitzen mitjançant l'ús de CO. Les estratègies de CO han sigut aplicades experimentalment als treballs referents al motor de combustió, manifestant els seus substancials avantatges, però també analitzant dificultats i línies d'actuació per superar-les. Els mètodes desenvolupats a aquesta Tesi Doctoral són generals i aplicables a uns altres criteris si es disposen dels models adequats.
Reig Bernad, A. (2017). Optimal Control for Automotive Powertrain Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90624
TESIS
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FLINT, MATTHEW D. "COOPERATIVE UNMANNED AERIAL VEHICLE (UAV) SEARCH IN DYNAMIC ENVIRONMENTS USING STOCHASTIC METHODS". University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1105553725.
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Li, Bin. "Optimal control problems with constraints on the state and control and their applications". Thesis, Curtin University, 2011. http://hdl.handle.net/20.500.11937/2123.
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In this thesis, we consider several types of optimal control problems with constraints on the state and control variables. These problems have many engineering applications. Our aim is to develop efficient numerical methods for solving these optimal control problems.In the first problem, we consider a class of discrete time nonlinear optimal control problems with time delay and subject to constraints on states and controls at each time point. These constraints are called all-time-step constraints. A constraint transcription technique in conjunction with a local smoothing method is used to construct a sequence of approximate discrete time optimal control problems involving time delay in states and controls and subject to nonlinear inequality constraints in canonical form. These approximate optimal control problems are special cases of a general discrete time optimal control problems with time delay appearing in the state and control and subject to nonlinear inequality constraints in canonical form. Thus, we devise an efficient gradient-based computational method for solving this general optimal control problem.The gradient formulas needed for the cost and the canonical constraint functions are derived. With these gradient formulas, the discrete time optimal control problem with time delay appearing in states and controls and subject to nonlinear inequality constraints in canonical form is solvable as an optimization problem with inequality constraints by the Sequential Quadratic Programming (SQP) method. With this computational method, each of the approximate problems constructed from the original optimal control problem can be solved. A practical problem arising from the study of a tactical logistic decision analysis problem is considered and solved by using the computational method that we have developed.In the second problem, we consider a general class of maximin optimal control problems, where the violation avoidance of the continuous state inequality constraints is to be maximized. An efficient computational method is developed for solving this general maximin optimal control problem. In this computational method, the constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints, where the accuracy of the approximation is controlled by an accuracy parameter. We then obtain a sequence of smooth approximate optimal control problems, where the integral of the summation of these smooth approximate functions is taken as its cost function.A necessary condition and a sufficient condition are derived showing the relationship between the original maximin problem and the sequence of the smooth approximate problems. We then construct a violation avoidance function from the solution of each of the smooth approximate optimal control problems and the original continuous state inequality constraints in such a way that the problem of finding an optimal control of the maximin optimal control problem is equivalent to the problem of finding the largest root of the violation avoidance function. The control parameterization technique and a time scaling transform are applied to these smooth approximate optimal control problems. Two practical problems are considered as applications. The first one is an obstacle avoidance problem of an autonomous mobile robot, while the second one is the abort landing of an aircraft in a windshear downburst. The proposed computational method is then applied to solve these problems.In the third problem, we consider a class of optimal PID control problems subject to continuous inequality constraints and terminal equality constraint. By applying the constraint transcription method and a local smoothing technique to these continuous inequality constraint functions, we construct the corresponding smooth approximate functions. We use the concept of the penalty function to append these smooth approximate functions to the cost function, forming a new cost function. Then, the constrained optimal PID control problem is approximated by a sequence of optimal parameter selection problems subject to only terminal equality constraint. Each of these optimal parameter selection problems can be viewed and hence solved as a nonlinear optimization problem. The gradient formulas of the new appended cost function and the terminal equality constraint function are derived, and a reliable computation algorithm is given. The method proposed is used to solve a ship steering control problem.In the fourth problem, we consider a class of optimal control problems subject to equality terminal state constraints and continuous inequality constraints on the state and/or control variables. After the control parameterization together with a time scaling transformation, the problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constraints and continuous inequality constraints on the state and/or control. An exact penalty function is constructed for these terminal equality constraints and continuous inequality constraints. It is appended to the cost function to form a new cost function, giving rise to an unconstrained optimal parameter selection problem. The convergence analysis shows that, for a sufficiently large penalty parameter, a local minimizer of the unconstrained optimization problem is a local minimizer of the optimal parameter selection problem with terminal equality constraints and continuous inequality constraints. The relationships between the approximate optimal parameter selection problems and the original optimal control problem are also discussed. Finally, the method proposed is applied to solve three nontrivial optimal control problems.
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Schröder, Dirk [Verfasser], Jens Akademischer Betreuer] Lang y Stefan [Akademischer Betreuer] [Ulbrich. "Peer Methods in Optimal Control / Dirk Schröder. Betreuer: Jens Lang ; Stefan Ulbrich". Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2016. http://d-nb.info/1112269215/34.
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Tan, Xiaolu. "Stochastic control methods for optimal transportation and probabilistic numerical schemes for PDEs". Palaiseau, Ecole polytechnique, 2011. https://theses.hal.science/docs/00/66/10/86/PDF/These_TanXiaolu.pdf.
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Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) non-linéaires dégénérées, ainsi que pour des problèmes de contrôle d'EDP non-linéaires résultants d'un nouveau problème de transport optimal. Toutes ces questions sont motivées par des applications en mathématiques financières. La thèse est divisée en quatre parties. Dans une première partie, nous nous intéressons à la condition nécessaire et suffisante de la monotonie du thêta-schéma de différences finies pour l'équation de diffusion en dimension un. Nous donnons la formule explicite dans le cas de l'équation de la chaleur, qui est plus faible que la condition classique de Courant-Friedrichs-Lewy (CFL). Dans une seconde partie, nous considérons une EDP parabolique non-linéaire dégénérée et proposons un schéma de type ''splitting'' pour la résoudre. Ce schéma réunit un schéma probabiliste et un schéma semi-lagrangien. Au final, il peut être considéré comme un schéma Monte-Carlo. Nous donnons un résultat de convergence et également un taux de convergence du schéma. Dans une troisième partie, nous étudions un problème de transport optimal, où la masse est transportée par un processus d'état type ''drift-diffusion'' controllé. Le coût associé est dépendant des trajectoires de processus d'état, de son drift et de son coefficient de diffusion. Le problème de transport consiste à minimiser le coût parmi toutes les dynamiques vérifiant les contraintes initiales et terminales sur les distributions marginales. Nous prouvons une formule de dualité pour ce problème de transport, étendant ainsi la dualité de Kantorovich à notre contexte. La formulation duale maximise une fonction valeur sur l'espace des fonctions continues bornées, et la fonction valeur correspondante à chaque fonction continue bornée est la solution d'un problème de contrôle stochastique optimal. Dans le cas markovien, nous prouvons un principe de programmation dynamique pour ces problèmes de contrôle optimal, proposons un algorithme de gradient projeté pour la résolution numérique du problème dual, et en démontrons la convergence. Enfin dans une quatrième partie, nous continuons à développer l'approche duale pour le problème de transport optimal avec une application à la recherche de bornes de prix sans arbitrage des options sur variance étant donnés les prix des options européennes. Après une première approximation analytique, nous proposons un algorithme de gradient projeté pour approcher la borne et la stratégie statique correspondante en options vanillesThis thesis deals with the numerical methods for a fully nonlinear degenerate parabolic partial differential equations (PDEs), and for a controlled nonlinear PDEs problem which results from a mass transportation problem. The manuscript is divided into four parts. In a first part of the thesis, we are interested in the necessary and sufficient condition of the monotonicity of finite difference thêta-scheme for a one-dimensional diffusion equations. An explicit formula is given in case of the heat equation, which is weaker than the classical Courant-Friedrichs-Lewy (CFL) condition. In a second part, we consider a fully nonlinear degenerate parabolic PDE and propose a splitting scheme for its numerical resolution. The splitting scheme combines a probabilistic scheme and the semi-Lagrangian scheme, and in total, it can be viewed as a Monte-Carlo scheme for PDEs. We provide a convergence result as well as a rate of convergence. In the third part of the thesis, we study an optimal mass transportation problem. The mass is transported by the controlled drift-diffusion dynamics, and the associated cost depends on the trajectories, the drift as well as the diffusion coefficient of the dynamics. We prove a strong duality result for the transportation problem, thus extending the Kantorovich duality to our context. The dual formulation maximizes a value function on the space of all bounded continuous functions, and every value function corresponding to a bounded continuous function is the solution to a stochastic control problem. In the Markovian cases, we prove the dynamic programming principle of the optimal control problems, and we propose a gradient-projection algorithm for the numerical resolution of the dual problem, and provide a convergence result. Finally, in a fourth part, we continue to develop the dual approach of mass transportation problem with its applications in the computation of the model-independent no-arbitrage price bound of the variance option in a vanilla-liquid market. After a first analytic approximation, we propose a gradient-projection algorithm to approximate the bound as well as the corresponding static strategy in vanilla options
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Mbangeni, Litha. "Development of methods for parallel computation of the solution of the problem for optimal control". Thesis, Cape Peninsula University of Technology, 2010. http://hdl.handle.net/20.500.11838/1110.
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Thesis (MTech(Electrical Engineering))--Cape Peninsula University of Technology, 2010Optimal control of fermentation processes is necessary for better behaviour of the process in order to achieve maximum production of product and biomass. The problem for optimal control is a very complex nonlinear, dynamic problem requiring long time for calculation Application of decomposition-coordinating methods for the solution of this type of problems simplifies the solution if it is implemented in a parallel way in a cluster of computers. Parallel computing can reduce tremendously the time of calculation through process of distribution and parallelization of the computation algorithm. These processes can be achieved in different ways using the characteristics of the problem for optimal control. Problem for optimal control of a fed-batch, batch and continuous fermentation processes for production of biomass and product are formulated. The problems are based on a criterion for maximum production of biomass at the end of the fermentation process for the fed-batch process, maximum production of metabolite at the end of the fermentation for the batch fermentation process and minimum time for achieving steady state fermentor behavior for the continuous process and on unstructured mass balance biological models incorporating in the kinetic coefficients, the physiochemical variables considered as control inputs. An augmented functional of Lagrange is applied and its decomposition in time domain is used with a new coordinating vector. Parallel computing in a Matlab cluster is used to solve the above optimal control problems. The calculations and tasks allocation to the cluster workers are based on a shared memory architecture. Real-time control implementation of calculation algorithms using a cluster of computers allows quick and simpler solutions to the optimal control problems.
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Kujane, Koketso Portia. "Investigation and development of methods for optimal control of the activated sludge process". Thesis, Cape Peninsula University of Technology, 2009. http://hdl.handle.net/20.500.11838/1099.
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Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2009This project was started as a result of strict environmental and health regulations together with a demand tor cost effective operation of wastewater treatment plants (VVWTPs). The main aim of this project is how to keep effluent concentration below a prescribed limit at the lowest possible cost. Due to large fluctuations in the quality and quantity of the influent concentrations, traditional control methods are not adequate to achieve this aim The major drawback with these methods is that the disturbances affect the process before the controller has time to correct the error (Olsson and Newell, 1999: 454). This problem is addressed through the use of modern control systems. Modern control systems are model based predictive algorithms arranged as feed-forward controllers (Olsson and Newell. 1999: 454). Normally a controller is equipped with a constant set point; the goal In this project is to calculate an optimal DO trajectory that may be sampled to provide a varying optimal set-point for the Activated Sludge Process, In this project an optimal control problem Is formulated using DO concentration as a control variable. This requires a model of the process to be controlled a mathematical expressions of the limitations on the process input and output variables and finally the objective functional. which consists of the objectives of the control. The structures of the Benchmark plant (developed within the COST 682 working group) and the Athlone WWTPs are used to implement this opt.mat control strategy in MATLAB. The plant's full models are developed based on the mass balance principle incorporating the activated sludge biological models: ,ASM1, ASM2, ASM2d and ASM3 (developed by the IWA working groups). To be able to develop a method that may later on be used for online control, the full models are reduced based on the technique In Lukasse (1996). To ensure that the reduced models keep the same prediction capabilities as the full models, parameters of the reduced models are calculated based on the Least Squares principle, The formulated optimal control problem is solved based on the decompostion-coorcdination method that involves time decomposition in a two layer structure. MATLAB software [5 developed to solve the problems for parameter estimation. fun and reduced mode! simulation. and optimal control calculation for the considered different cases of plant structures and biological models. The obtained optimal 00 trajectories produced the effluent state trajectories within prescribed requirements. These DO trajectories may be implemented in different SCADA systems to be tracked as set points or desired trajectories by different types of controllers.
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Sassi, Achille. "Numerical methods for hybrid control and chance-constrained optimization problems". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY005/document.
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Cette thèse est dediée à l'alanyse numérique de méthodes numériques dans le domaine du contrôle optimal, et est composée de deux parties. La première partie est consacrée à des nouveaux résultats concernant des méthodes numériques pour le contrôle optimal de systèmes hybrides, qui peuvent être contrôlés simultanément par des fonctions mesurables et des sauts discontinus dans la variable d'état. La deuxième partie est dédiée è l'étude d'une application spécifique surl'optimisation de trajectoires pour des lanceurs spatiaux avec contraintes en probabilité. Ici, on utilise des méthodes d'optimisation nonlineaires couplées avec des techniques de statistique non parametrique. Le problème traité dans cette partie appartient à la famille des problèmes d'optimisation stochastique et il comporte la minimisation d'une fonction de coût en présence d'une contrainte qui doit être satisfaite dans les limites d'un seuil de probabilité souhaitéThis thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold
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Mehta, Tejas R. "Optimal, Multi-Modal Control with Applications in Robotics". Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/14628.
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The objective of this dissertation is to incorporate the concept of optimality to multi-modal control and apply the theoretical results to obtain successful navigation strategies for autonomous mobile robots. The main idea in multi-modal control is to breakup a complex control task into simpler tasks. In particular, number of control modes are constructed, each with respect to a particular task, and these modes are combined according to some supervisory control logic in order to complete the overall control task. This way of modularizing the control task lends itself particularly well to the control of autonomous mobile robot, as evidenced by the success of behavior-based robotics. Many challenging and interesting research issues arise when employing multi-modal control. This thesis aims to address these issues within an optimal control framework.
In particular, the contributions of this dissertation are as follows: We first addressed the problem of inferring global behaviors from a collection of local rules (i.e., feedback control laws). Next, we addressed the issue of adaptively varying the multi-modal control system to further improve performance. Inspired by adaptive multi-modal control, we presented a constructivist framework for the learning from example problem. This framework was applied to the DARPA sponsored Learning Applied to Ground Robots (LAGR) project. Next, we addressed the optimal control of multi-modal systems with infinite dimensional constraints. These constraints are formulated as multi-modal, multi-dimensional (M3D) systems, where the dimensions of the state and control spaces change between modes to account for the constraints, to ease the computational burdens associated with traditional methods. Finally, we used multi-modal control strategies to develop effective navigation strategies for autonomous mobile robots. The theoretical results presented in this thesis are verified by conducting simulated experiments using Matlab and actual experiments using the Magellan Pro robot platform and the LAGR robot.
In closing, the main strength of multi-modal control lies in breaking up complex control task into simpler tasks. This divide-and-conquer approach helps modularize the control system. This has the same effect on complex control systems that object-oriented programming has for large-scale computer programs, namely it allows greater simplicity, flexibility, and adaptability.
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Rabi, Maben, Karl Henrik Johansson y Mikael Johansson. "Optimal stopping for event-triggered sensing and actuation". KTH, Reglerteknik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-80709.
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Novel event-triggered sensing and actuation strategies are presented for networked control systems with limited communication resources. Two architectures are considered: one with the controller co-located with the sensor and one with the control co-located with the actuator. A stochastic control problem with an optimal stopping rule is shown to capture two interesting instances of these architectures. The solution of the problem leads to a parametrization of the control alphabet as piecewise constant commands. The execution of the control commands is triggered by stopping rules for the sensor. In simple situations, it is possible to analytically derive the optimal controller. Examples illustrate how the new event-based control and sensing strategies outperform conventional time-triggered schemes.© 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Qc 20120220
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Winkelmann, Beate Maria. "Finite dimensional optimization methods and their application to optimal control with PDE constraints /". Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2005. http://wwwlib.umi.com/cr/ucsd/fullcit?p3205376.
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Tran, Hong-Thai. "Numerical methods for parameter estimation and optimal control of the Red River network". [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975808583.
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Ingalls, Brian Paul. "Conflict resolution in air traffic management using the methods of optimal control theory". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/mq24857.pdf.
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Hasan, Basri Mundzir. "Two new methods for optimal design of subsurface barrier to control seawater intrusion". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ62638.pdf.
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Gong, Bo. "Numerical methods for backward stochastic differential equations with applications to stochastic optimal control". HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/462.
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The concept of backward stochastic differential equation (BSDE) was initially brought up by Bismut when studying the stochastic optimal control problem. And it has been applied to describe various problems particularly to those in finance. After the fundamental work by Pardoux and Peng who proved the well-posedness of the nonlinear BSDE, the BSDE has been investigated intensively for both theoretical and practical purposes. In this thesis, we are concerned with a class of numerical methods for solving BSDEs, especially the one proposed by Zhao et al.. For this method, the convergence theory of the semi-discrete scheme (the scheme that discretizes the equation only in time) was already established, we shall further provide the analysis for the fully discrete scheme (the scheme that discretizes in both time and space). Moreover, using the BSDE as the adjoint equation, we shall construct the numerical method for solving the stochastic optimal control problem. We will discuss the situation when the control is deterministic as well as when the control is feedback.
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Heng, Jeremy. "On the use of transport and optimal control methods for Monte Carlo simulation". Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:6cbc7690-ac54-4a6a-b235-57fa62e5b2fc.
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This thesis explores ideas from transport theory and optimal control to develop novel Monte Carlo methods to perform efficient statistical computation. The first project considers the problem of constructing a transport map between two given probability measures. In the Bayesian formalism, this approach is natural when one introduces a curve of probability measures connecting the prior to posterior by tempering the likelihood function. The main idea is to move samples from the prior using an ordinary differential equation (ODE), constructed by solving the Liouville partial differential equation (PDE) which governs the time evolution of measures along the curve. In this work, we first study the regularity solutions of Liouville equation should satisfy to guarantee validity of this construction. We place an emphasis on understanding these issues as it explains the difficulties associated with solutions that have been previously reported. After ensuring that the flow transport problem is well-defined, we give a constructive solution. However, this result is only formal as the representation is given in terms of integrals which are intractable. For computational tractability, we proposed a novel approximation of the PDE which yields an ODE whose drift depends on the full conditional distributions of the intermediate distributions. Even when the ODE is time-discretized and the full conditional distributions are approximated numerically, the resulting distribution of mapped samples can be evaluated and used as a proposal within Markov chain Monte Carlo and sequential Monte Carlo (SMC) schemes. We then illustrate experimentally that the resulting algorithm can outperform state-of-the-art SMC methods at a fixed computational complexity. The second project aims to exploit ideas from optimal control to design more efficient SMC methods. The key idea is to control the proposal distribution induced by a time-discretized Langevin dynamics so as to minimize the Kullback-Leibler divergence of the extended target distribution from the proposal. The optimal value functions of the resulting optimal control problem can then be approximated using algorithms developed in the approximate dynamic programming (ADP) literature. We introduce a novel iterative scheme to perform ADP, provide a theoretical analysis of the proposed algorithm and demonstrate that the latter can provide significant gains over state-of-the-art methods at a fixed computational complexity.
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Boukheddimi, Melya. "Human gait simulation using motion generation methods from robotics". Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30105.
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Le corps humain est un système complexe composé de plus de 600 muscles, qui contribuent à l'actionnement de plus de 200 degrés de liberté (DDL) [35]. Il s'agit donc d'un système hautement redondant pour la plupart des tâches. De nombreux auteurs ont suggéré que le système nerveux central ne contrôle pas indépendamment en temps réel chaque muscle et DDL [54]. Bien que le nombre élevé de muscles et de DDL rende difficile le problème du contrôle moteur, il offre de grandes capacités d'adaptation au corps pour l'exécution de plusieurs tâches simultanément si nécessaire [54]. Parmi ces tâches qui requièrent un haut niveau de coordination motrice, la marche bipède est cruciale. La marche bipède est le moyen naturel de locomotion de l'être humain. Bien que ce mouvement soit assez stéréotypé entre les individus, on ne sait toujours pas comment le système nerveux central coordonne-t-il le système musculo-squelettique complexe afin de générer la marche, ni comment les différentes séquences du cycle de la marche sont régulées. Afin de répondre à ces problématiques, nous avons proposé de simuler la démarche semblable à celle de l'être- humain en utilisant un modèle simplifié de corps rigides poly-articulés (modèle squelettique 3D du corps entier comprenant 42 degrés de liberté), sur lequel nous avons appliqué deux méthodes différentes de génération de mouvement. Cette thèse s'inscrit donc dans le cadre de la génération de la démarche humaine, en utilisant des méthodes de génération de mouvement issues de la robotique. La première contribution de cette thèse, montre qu'il suffit de contrôler un petit nombre de tâches soigneusement sélectionnées pour reproduire fidèlement la cinématique de la démarche humaine. Pour cela, un contrôleur de tâches Hiérarchiques est appliqué au modèle du corps complet en utilisant uniquement 3 tâches hiérarchiques afin de générer neuf différentes allures de type humain. L'analyse des allures simulées montre l'émergence de propriétés significatives de la marche humaine. Afin de valider nos résultats, une comparaison entre les rotations articulaires des mouvements simulés et des mouvements de référence humaine est effectuée. Enfin, une discussion est fournie pour illustrer l'intérêt de l'approche choisie en comparaison à des travaux connexes. La deuxième contribution de cette thèse est basée sur l'hypothèse bien connue stipulant que le mouvement humain est le résultat d'un processus d'optimisation. Nous considérons ici un ensemble réduit de critères, qui semblent être optimisés pendant la marche humaine, issues de l'observation de la marche humaine et de l'état de l'art correspondant. Le Contrôle Optimal direct basé sur l'algorithme de Programmation Dynamique Différentielle est appliqué sur ces critères avec le modèle corps complet afin de générer neuf mouvements de marche différents. Les mouvements de marche simulés sont ensuite analysés et comparés à la référence humaine pour démontrer la qualité de la méthode de génération de la marche sélectionnée. L'intérêt de cette approche d'optimisation pour la génération de mouvements de type humain est enfin discuté. Finalement, une comparaison entre les deux méthodes issues de la robotique est présentée et discutée, en impliquant une analyse de la qualité des mouvements obtenusThe human body is a complex system made of more than 600 muscles, which contribute to the actuation of more than 200 Degrees of Freedom (DoFs) [35]. It is therefore a highly redundant system for most kinematic tasks. Many authors have suggested that the central nervous system does not independently control in real-time each muscle and DoFs [54]. Though the high number of muscles and DoFs makes motor control problems difficult, it offers high adaptation capabilities to the body for executing multiple tasks simultaneously when necessary [54]. Among the tasks that require a high level of motor coordination, bipedal gait is a crucial one. The bipedal gait is the natural means of human locomotion. Despite the fact that this movement is quite stereotyped across individuals, it is still unclear how the central nervous system coordinates the complex musculo-skeletal system for gait generation, and how the different sequences of the gait cycle are regulated. In order to address these issues, we proposed to simulate the human-like gait using a simplified model of poly- articulated rigid bodies (3D whole-body skeletal model including 42 degrees of freedom), on which we applied two different motion generation methods. Hence, this thesis is part of the human-like gait generation problem, using motion generation methods from robotics. The first contribution shows that controlling only a small set of adequately selected tasks is sufficient to closely reproduce the human gait kinematics. To this aim, a Hierarchical task controller is applied to the whole-body model with only 3 hierarchical tasks, to generate nine different human-like gaits. The analysis of the simulated gaits shows the emergence of significant human-like properties in walking. In order to validate our results, a comparison between the simulated and human reference joint rotations is conducted. In the end, a discussion is given to illustrate the interest of this approach comparing to related works.The second contribution is based on the well-known hypothesis that human motion is the result of an optimization process. We consider a reduced set of criteria, which seem to be optimized during the human gait, taken from the observation of human walking and the study of the related literature. Direct Optimal Control based on the Differential Dynamic Programming algorithm is applied following these criteria with the whole-body model to generate nine different walking motions. The simulated walking motions are then analyzed and compared to the human reference to show the quality of the gait generation process. The interest of this optimization approach for human-like motion generation is finally discussed. Finally, a comparison between the two methods from robotics is presented and discussed, involving an analysis of the obtained movements' quality
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Sassi, Achille. "Numerical methods for hybrid control and chance-constrained optimization problems". Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY005.
Texto completoResumen
Cette thèse est dediée à l'alanyse numérique de méthodes numériques dans le domaine du contrôle optimal, et est composée de deux parties. La première partie est consacrée à des nouveaux résultats concernant des méthodes numériques pour le contrôle optimal de systèmes hybrides, qui peuvent être contrôlés simultanément par des fonctions mesurables et des sauts discontinus dans la variable d'état. La deuxième partie est dédiée è l'étude d'une application spécifique surl'optimisation de trajectoires pour des lanceurs spatiaux avec contraintes en probabilité. Ici, on utilise des méthodes d'optimisation nonlineaires couplées avec des techniques de statistique non parametrique. Le problème traité dans cette partie appartient à la famille des problèmes d'optimisation stochastique et il comporte la minimisation d'une fonction de coût en présence d'une contrainte qui doit être satisfaite dans les limites d'un seuil de probabilité souhaitéThis thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold
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Loxton, Ryan Christopher. "Optimal control problems involving constrained, switched, and delay systems". Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/1479.
Texto completoResumen
In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming problem. The decision variables in this nonlinear programming problem influence its cost function (and constraints, if it has any) implicitly through the dynamic system. Hence, deriving the gradient of the cost and the constraint functions is a difficult task. A major focus of this thesis is on developing methods for computing these gradients. These methods can then be used in conjunction with a gradient-based optimization technique to solve the optimal control problem efficiently.The first optimal control problem that we consider has nonlinear inequality constraints that depend on the state at two or more discrete time points. These time points are decision variables that, together with a control function, should be chosen in an optimal manner. To tackle this problem, we first approximate the control by a piecewise constant function whose values and switching times (the times at which it changes value) are decision variables. We then apply a novel time-scaling transformation that maps the switching times to fixed points in a new time horizon. This yields an approximate dynamic optimization problem with a finite number of decision variables. We develop a new algorithm, which involves integrating an auxiliary dynamic system forward in time, for computing the gradient of the cost and constraints in this approximate problem.The second optimal control problem that we consider has nonlinear continuous inequality constraints. These constraints restrict both the state and the control at every point in the time horizon. As with the first problem, we approximate the control by a piecewise constant function and then transform the time variable. This yields an approximate semi-infinite programming problem, which can be solved using a penalty function algorithm. A solution of this problem immediately furnishes a suboptimal control for the original optimal control problem. By repeatedly increasing the number of parameters used in the approximation, we can generate a sequence of suboptimal controls. Our main result shows that the cost of these suboptimal controls converges to the minimum cost.The third optimal control problem that we consider is an applied problem from electrical engineering. Its aim is to determine an optimal operating scheme for a switchedcapacitor DC-DC power converter—an electronic device that transforms one DC voltage into another by periodically switching between several circuit topologies. Specifically, the optimal control problem is to choose the times at which the topology switches occur so that the output voltage ripple is minimized and the load regulation is maximized. This problem is governed by a switched system with linear subsystems (each subsystem models one of the power converter’s topologies). Moreover, its cost function is non-smooth. By introducing an auxiliary dynamic system and transforming the time variable (so that the topology switching times become fixed), we derive an equivalent semi-infinite programming problem. This semi-infinite programming problem, like the one that approximates the continuously-constrained optimal control problem, can be solved using a penalty function algorithm.The fourth optimal control problem that we consider involves a general switched system, which includes the model of a switched-capacitor DC-DC power converter as a special case. This switched system evolves by switching between several subsystems of nonlinear ordinary differential equations. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantaneous changes—so-called state jumps—are influenced by control variables that, together with the subsystem switching times, should be selected in an optimal manner. As with the previous optimal control problems, we tackle this problem by transforming the time variable to obtain an equivalent problem in which the switching times are fixed. However, the functions governing the state jumps in this new problem are discontinuous. To overcome this difficulty, we introduce an approximate problem whose state jumps are governed by smooth functions. This approximate problem can be solved using a nonlinear programming algorithm. We prove an important convergence result that links the approximate problem’s solution with the original problem’s solution.The final optimal control problem that we consider is a parameter identification problem. The aim of this problem is to use given experimental data to identify unknown state-delays in a nonlinear delay-differential system. More precisely, the optimal control problem involves choosing the state-delays to minimize a cost function measuring the discrepancy between predicted and observed system output. We show that the gradient of this cost function can be computed by solving an auxiliary delay-differential system. On the basis of this result, the optimal control problem can be formulated—and hence solved—as a standard nonlinear programming problem.
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Yan, Hui. "Dynamics and real-time optimal control of satellite attitude and satellite formation systems". Texas A&M University, 2006. http://hdl.handle.net/1969.1/4283.
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In this dissertation the solutions of the dynamics and real-time optimal control of
magnetic attitude control and formation flying systems are presented. In magnetic
attitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with a
pseudospectral algorithm are examined. The time-optimal magnetic control is bang-bang
and the optimal slew time is about 232.7 seconds. The start time occurs when the
maneuver is symmetric about the maximum field strength. For real-time computations,
all the tested samples converge to optimal solutions or feasible solutions. We find the
average computation time is about 0.45 seconds with the warm start and 19 seconds with
the cold start, which is a great potential for real-time computations. Three-axis magnetic
attitude stabilization is achieved by using a pseudospectral control law via the receding
horizon control for satellites in eccentric low Earth orbits. The solutions from the
pseudospectral control law are in excellent agreement with those obtained from the
Riccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitude
motion is in the steady state.
Approximate models are often used for the study of relative motion of formation
flying satellites. A modeling error index is introduced for evaluating and comparing the
accuracy of various theories of the relative motion of satellites in order to determine the
effect of modeling errors on the various theories. The numerical results show the
sequence of the index from high to low should be Hill's equation, non- J2, small
eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach
and the Yan-Alfriend nonlinear method having the lowest index and equivalent
performance. A higher order state transition matrix is developed using unit sphere
approach in the mean elements space. Based on the state transition matrix analytical
control laws for formation flying maintenance and reconfiguration are proposed using
low-thrust and impulsive scheme. The control laws are easily derived with high
accuracy. Numerical solutions show the control law works well in real-time
computations.
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Häfner, Stefan [Verfasser] y Mikhail [Akademischer Betreuer] Urusov. "Regression-based Monte Carlo methods with optimal control variates / Stefan Häfner ; Betreuer: Mikhail Urusov". Duisburg, 2017. http://d-nb.info/1136270337/34.
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Halimic, Mirsad Kjazim. "Performance improvement of dynamic weighing systems using optimal control and advanced signal processing methods". Thesis, Brunel University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249791.
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