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Dissertations / Theses on the topic 'Optimal control theory'

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Published: 4 June 2021

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1

Bellon, James. "Riccati Equations in Optimal Control Theory." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/46.

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It is often desired to have control over a process or a physical system, to cause it to behave optimally. Optimal control theory deals with analyzing and finding solutions for optimal control for a system that can be represented by a set of differential equations. This thesis examines such a system in the form of a set of matrix differential equations known as a continuous linear time-invariant system. Conditions on the system, such as linearity, allow one to find an explicit closed form finite solution that can be more efficiently computed compared to other known types of solutions. This is done by optimizing a quadratic cost function. The optimization leads to solving a Riccati equation. Conditions are discussed for which solutions are possible. In particular, we will obtain a solution for a stable and controllable system. Numerical examples are given for a simple system with 2x2 matrix coefficients.

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2

Yiu, Ka Fai Cedric. "Aerodynamic design via optimal control theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317867.

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3

Zenios, Stefanos A. (Stefanos Andrea). "Health care applications of optimal control theory." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/11042.

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4

Silva, Francisco Jose. "Interior penalty approximation for optimal control problems. Optimality conditions in stochastic optimal control theory." Palaiseau, Ecole polytechnique, 2010. http://pastel.archives-ouvertes.fr/docs/00/54/22/95/PDF/tesisfjsilva.pdf.

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Résumé français : Cette thèse est divisée en deux parties. Dans la première partie on s'intéresse aux problèmes de commande optimale déterministes et on étudie des approximations intérieures pour deux problèmes modèles avec des contraintes de non-négativité sur la commande. Le premier modèle est un problème de commande optimale dont la fonction de coût est quadratique et dont la dynamique est régie par une équation différentielle ordinaire. Pour une classe générale de fonctions de pénalité intérieure, on montre comment calculer le terme principal du développement ponctuel de l'état et de l'état adjoint. Notre argument principal se fonde sur le fait suivant: si la commande optimale pour le problème initial satisfait les conditions de complémentarité stricte pour le Hamiltonien sauf en un nombre fini d'instants, les estimations pour le problème de commande optimale pénalisé peuvent être obtenues à partir des estimations pour un problème stationnaire associé. Nos résultats fournissent plusieurs types de mesures de qualité de l'approximation pour la technique de pénalisation: estimations des erreurs de la commande , estimations des erreurs pour l'état et l'état adjoint et aussi estimations de erreurs pour la fonction valeur. Le second modèle est le problème de commande optimale d'une équation semi-linéaire elliptique avec conditions de Dirichlet homogène au bord, la commande étant distribuée sur le domaine et positive. L'approche est la même que pour le premier modèle, c'est-à-dire que l'on considère une famille de problèmes pénalisés, dont la solution définit une trajectoire centrale qui converge vers la solution du problème initial. De cette manière, on peut étendre les résultats, obtenus dans le cadre d'équations différentielles, au contrôle optimal d'équations elliptiques semi-linéaires. Dans la deuxième partie on s'intéresse aux problèmes de commande optimale stochastiques. Dans un premier temps, on considère un problème linéaire quadratique stochastique avec des contraintes de non-negativité sur la commande et on étend les estimations d'erreur pour l'approximation par pénalisation logarithmique. La preuve s'appuie sur le principe de Pontriaguine stochastique et un argument de dualité. Ensuite, on considère un problème de commande stochastique général avec des contraintes convexes sur la commande. L'approche dite variationnelle nous permet d'obtenir un développement au premier et au second ordre pour l'état et la fonction de coût, autour d'un minimum local. Avec ces développements on peut montrer des conditions générales d'optimalité de premier ordre et, sous une hypothèse géométrique sur l'ensemble des contraintes, des conditions nécessaires du second ordre sont aussi établies
Résumé anglais : This thesis is divided in two parts. In the first one we consider deterministic optimal control problems and we study interior approximations for two model problems with non-negativity constraints. The first model is a quadratic optimal control problem governed by a nonautonomous affine ordinary differential equation. We provide a first-order expansion for the penalized state an adjoint state (around the corresponding state and adjoint state of the original problem), for a general class of penalty functions. Our main argument relies on the following fact: if the optimal control satisfies strict complementarity conditions for its Hamiltonian, except for a set of times with null Lebesgue measure, the functional estimates of the penalized optimal control problem can be derived from the estimates of a related finite dimensional problem. Our results provide three types of measure to analyze the penalization technique: error estimates of the control, error estimates of the state and the adjoint state and also error estimates for the value function. The second model we study is the optimal control problem of a semilinear elliptic PDE with a Dirichlet boundary condition, where the control variable is distributed over the domain and is constrained to be non-negative. Following the same approach as in the first model, we consider an associated family of penalized problems, whose solutions define a central path converging to the solution of the original one. In this fashion, we are able to extend the results obtained in the ODE framework to the case of semilinear elliptic PDE constraints. In the second part of the thesis we consider stochastic optimal control problems. We begin withthe study of a stochastic linear quadratic problem with non-negativity control constraints and we extend the error estimates for the approximation by logarithmic penalization. The proof is based is the stochastic Pontryagin's principle and a duality argument. Next, we deal with a general stochastic optimal control problem with convex control constraints. Using the variational approach, we are able to obtain first and second-order expansions for the state and cost function, around a local minimum. This analysis allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second-order necessary conditions are also established

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5

Hunt, K. J. "Stochastic optimal control theory with application in self-tuning control." Thesis, University of Strathclyde, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382399.

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6

Shaikh, Mohammad Shahid. "Optimal control of hybrid systems : theory and algorithms." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85095.

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Many complex systems are hybrid in the sense that: (i) the state set possesses continuous and discrete components, and (ii) system evolution may occur in both continuous and discrete time. One important class of hybrid systems is that characterized by a feedback configuration of a set of continuous controlled low level systems and a high level discrete controller; such systems appear frequently in engineering and are particularly evident when a system is required to operate in a number of distinct modes. Other classes of hybrid systems are found in such diverse areas as (i) air traffic management systems, (ii) chemical process control, (iii) automotive engine-transmission systems, and (iv) intelligent vehicle-highway systems.
In this thesis we first formulate a class of hybrid optimal control problems (HOCPs) for systems with controlled and autonomous location transitions and then present necessary conditions for hybrid system trajectory optimality. These necessary conditions constitute generalizations of the standard Minimum Principle (MP) and are presented for the cases of open bounded control value sets and compact control value sets. These conditions give information about the behaviour of the Hamiltonian and the adjoint process at both autonomous and controlled switching times.
Such proofs of the necessary conditions for hybrid systems optimality which can be found in the literature are sufficiently complex that they are difficult to verify and use; in contrast, the formulation of the HOCP given in Chapter 2 of this thesis, together with the use of (i) classical variational methods and more recent needle variation techniques, and (ii) a local controllability condition, called the small time tubular fountain (STTF) condition, make the proofs in that chapter comparatively accessible. We note that the STTF condition is used to establish the adjoint and Hamiltonian jump conditions in the autonomous switchings case.
A hybrid Dynamic Programming Principle (HDPP) generalizing the standard dynamic programming principle to hybrid systems is also derived and this leads to hybrid Hamilton-Jacobi-Bellman (HJB) equation which is then used to establish a verification theorem within this framework. (Abstract shortened by UMI.)

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7

Nedeljković, Nikola. "The LORE computational method in optimal control theory." Thesis, Nedeljković, Nikola (1985) The LORE computational method in optimal control theory. PhD thesis, Murdoch University, 1985. https://researchrepository.murdoch.edu.au/id/eprint/51530/.

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A number of iterative algorithms for solving unconstrained continuous-time optimal control problems is developed. The method, named LORE is modelled locally on the linear quadratic problem and treats a whole family of algorithms in a unified manner, proposed approach is similar to the philosophy underlying Newton's, the Conjugate gradient and the quasi- Newton methods in the function minimization theory, The where the function being minimized is approximated locally by a quadratic function. In addition to the development of a unified theory of algorithms, the thesis contains several first-order implementable algorithms, the convergence speed of which is comparable to that of second-order methods. A proof of the reduction of the cost at each iterative step of the LORE algorithms, a convergence analysis in the Lm∞ space and a proof of the convergence in the space of relaxed controls are included. The power of the adopted approach lies in the use of the Riccati matrix differential equation which within the context of the LQRE method always has a bounded solution. Within the general framework of the analysis it is possible to obtain both first-order and second-order algorithms. The emphasis is however placed on the first-order LORE algorithms which are simpler and computationally less demanding per iterative step; their computational effectiveness is compared with the performance of known methods. There is a noticeable degree of similarity in the form of the differential equations used by the LORE algorithms and the differential equations in the well-known second order methods; in fact, it is possible to derive LORE variants of the second variation and differential dynamic programming methods. The LORE algorithms converge in one step on the linear quadratic problem and are well suited for solving nonlinear problems with linear constraints via the penalty Their application in the computation of the singular optimal control, by adding and subtracting a quadratic term to the cost, is suggested. function methods. The method has been extended to handle problems with terminal equality constraints, control constraints (LORE projection technique) and a class of state and control equality constraints (sequential LORE-restoration algorithm). The LORE method of discrete-time unconstrained systems has also been developed.

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8

Dal, Bianco Nicola. "Optimal control of road vehicles: theory and applications." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3424690.

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In this thesis Optimal Control (OC) of road vehicles is studied especially focusing on minimum lap time simulations. The theory underlying the most used optimal control solving techniques is described, including both the Pontryagin Maximum Principle and the reduction to Nonlinear Programming. Direct and indirect methods for optimal control problems are presented and compared against minimum lap time simulations (LTS). Modelling of vehicles for OC-LTSs is studied in order to understand how different design choices can affect simulation outcomes. Novel multibody models of four wheeled vehicles - a GP2 car and a go-kart - for OC-LTSs are developed and validated thorough comparison with experimental data. Particular attention is dedicated to the simulation of tyre load dynamics, that is achieved by a proper modelling of the chassis and suspension motions and of the aerodynamic forces. OC-LTSs are applied to electric vehicles too, specifically to optimise the design of an electric motorbike taking part at the Tourist Trophy Zero competition. A concise yet effective model is proposed in order to perform reliable simulations on a 60km long road in a reasonable amount of time. Experimental data is used to validate the model. A direct full collocation transcription method for OCPs dealing with implicit differential equations and control derivatives is presented, moreover the structure of the resulting NLP problem is accurately described. The relationship between the first order necessary conditions and the Lagrange multipliers of the NLP and OC problems are derived under the adopted discretisation scheme. The presented transcription method is implemented into a software which is currently in use at the University of Padova to solve OC-LTSs.
In this thesis Optimal Control (OC) of road vehicles is studied especially focusing on minimum lap time simulations. The theory underlying the most used optimal control solving techniques is described, including both the Pontryagin Maximum Principle and the reduction to Nonlinear Programming. Direct and indirect methods for optimal control problems are presented and compared against minimum lap time simulations (LTS). Modelling of vehicles for OC-LTSs is studied in order to understand how different design choices can affect simulation outcomes. Novel multibody models of four wheeled vehicles - a GP2 car and a go-kart - for OC-LTSs are developed and validated thorough comparison with experimental data. Particular attention is dedicated to the simulation of tyre load dynamics, that is achieved by a proper modelling of the chassis and suspension motions and of the aerodynamic forces. OC-LTSs are applied to electric vehicles too, specifically to optimise the design of an electric motorbike taking part at the Tourist Trophy Zero competition. A concise yet effective model is proposed in order to perform reliable simulations on a 60km long road in a reasonable amount of time. Experimental data is used to validate the model. A direct full collocation transcription method for OCPs dealing with implicit differential equations and control derivatives is presented, moreover the structure of the resulting NLP problem is accurately described. The relationship between the first order necessary conditions and the Lagrange multipliers of the NLP and OC problems are derived under the adopted discretisation scheme. The presented transcription method is implemented into a software which is currently in use at the University of Padova to solve OC-LTSs.

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9

Seywald, Hans. "Optimal control problems with switching points." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-07282008-135220/.

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10

Guo, Chaoyang. "Some optimal control problems in mathematical finance." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0022/NQ39269.pdf.

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11

Amann, Notker. "Optimal algorithms for iterative learning control." Thesis, University of Exeter, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337751.

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12

Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/368036.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on the introduction of the bundle of affine scalars over the configuration manifold, is then presented. The analysis includes a revisitation of Pontryagin Maximum Principle and of the Erdmann-Weierstrass corner conditions, a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system and a generalization of the classical criteria of Legendre and Bliss for the characterization of the minima of the action functional to the case of piecewise-differentiable extremals with asynchronous variation of the corners.

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13

Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, University of Trento, 2010. http://eprints-phd.biblio.unitn.it/170/1/Constrained_Calculus_of_Variations_and_Geometric_Optimal_Control_Theory.pdf.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on the introduction of the bundle of affine scalars over the configuration manifold, is then presented. The analysis includes a revisitation of Pontryagin Maximum Principle and of the Erdmann-Weierstrass corner conditions, a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system and a generalization of the classical criteria of Legendre and Bliss for the characterization of the minima of the action functional to the case of piecewise-differentiable extremals with asynchronous variation of the corners.

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14

Spjøtvold, Jørgen. "Parametric Programming in Control Theory." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-2198.

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The main contributions in this thesis are advances in parametric programming. The thesis is divided into three parts; theoretical advances, application areas and constrained control allocation. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear programming in control theory. The third part deals with constrained control allocation and how parametric programming can be used to obtain explicit solutions to this problem.

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15

Abou, El-Nasr Mohamad. "Timing control of manufacturing systems an optimal control perspective." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/14847.

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16

Huang, Hui. "Optimal control of piecewise continuous stochastic processes." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/23831217.html.

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17

姚濬帆 and Chun-fan Yiu. "Evolutionary synthesis of time-optimal control policies." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B29866170.

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18

Cheng, Tak Sum. "Stochastic optimal control in randomly-branching environments." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/713.

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19

Goebel, Rafal. "Convexity, convergence and feedback in optimal control /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/5792.

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Yiu, Chun-fan. "Evolutionary synthesis of time-optimal control policies /." Hong Kong : University of Hong Kong, 2002. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25151058.

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21

Achmatowicz, Richard L. (Richard Leon). "Optimal control problems on an infinite time horizon." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66052.

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22

Pavlic, Theodore P. "Optimal Foraging Theory Revisited." Connect to resource, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1181936683.

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23

Tsai, Mi-Ching. "Super-optimal control system design for multivariable plants." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238170.

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24

Ranga, Mithun Kumar. "Fixed order optimal control using genetic algorithms /." free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p1426097.

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25

Andrews, Timothy Paul. "An existence theory for optimal control problems with time delays." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47332.

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26

Thomas, Brian S. S. M. Massachusetts Institute of Technology. "Optimal control theory applied to ship maneuvering in restricted waters." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33591.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.
Includes bibliographical references (leaves 70-71).
Ship drivers have long understood that powerful interaction forces exist when ships operate in close proximity to rigid boundaries or other vessels. Controlling the effects of these forces has been traditionally handled by experienced helmsmen. The purpose of this research is to apply modern optimal control theory to these maneuvering scenarios in order to show that helmsman may some day be replaced by modern controllers. The maneuvering equations of motion are cast in a linear state space framework, permitting the design of a linear quadratic (LQ) controller. In addition, the hydrodynamic effects are modeled using potential flow theory in order to simulate the interaction forces and test the efficacy of the controller. This research demonstrates that the linear quadratic regulator effectively controls ship motions due to the presence of a boundary or other vessel over a broad range of speeds and separation distances. Furthermore, the method proposed provides stable control in the presence of additional. stochastic disturbances.
by Brian S. Thomas.
S.M.

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Paião, Ana Pedro Lemos. "Introduction to optimal control theory and its application to diabetes." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16806.

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Mestrado em Matemática e Aplicações
O Cálculo das Variações e o Controlo Ótimo são dois ramos da Matemática que estão muito interligados entre si e também com outras áreas. Como exemplo, podemos citar a Geometria, a Física, a Mecânica, a Economia, a Biologia, bem como a Medicina. Nesta tese estudamos vários tipos de problemas variacionais e de Controlo Ótimo, estabelecendo a ligação entre alguns destes. Fazemos uma breve introdução sobre a Diabetes Mellitus, uma vez que estudamos um modelo matemático que traduz a interação entre a glicose e a insulina no sangue por forma a otimizar o estado de uma pessoa com diabetes tipo 1.
The Calculus of Variations and the Optimal Control are two branches of Mathematics that are very interconnected with each other and with other areas. As example, we can mention Geometry, Physics, Mechanics, Economics, Biology and Medicine. In this thesis we study various types of variational problems and of Optimal Control, establishing the connection between some of these. We make a brief introduction to the Diabetes Mellitus, because we study a mathematical model that reflects the interaction between glucose and insulin in the blood in order to optimize the state of a person with diabetes type 1.

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Whittle, Andrew John. "Gypsy moth modelling with an application of optimal control theory." Thesis, University of Bath, 2004. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.412345.

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Davies, I. "Optimal control of functional differential systems with application to transmission lines." Thesis, Coventry University, 2015. http://curve.coventry.ac.uk/open/items/11749285-3b9a-44cf-bc72-0d02c27141bc/1.

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Robust control is an aspect of control theory which explicitly considers uncertainties and how they affect robust stability in the analysis and design of control decisions. A basic requirement for optimal robust guaranteed control in a real life scenario is the stabilization of systems in the presence of uncertainties or perturbations. In this thesis, the system uncertainties are embedded into a norm bounded uncertainty elements. The perturbation function is modelled as a class of nonlinear uncertainty influencing a neutral system with infinite delay. It is assumed to have delay in state and is input dependent; which implies the effect of control action can directly or indirectly influence the nonlinear perturbation function. In recognition of the fact that stability and controllability are fundamental in obtaining the optimal robust guaranteed cost control design for neutral functional integro-differential systems with infinite delays (NFDSID), total asymptotic stability results were developed using Razumikhin technique, unique properties of eigenvalues, and the uniform stability properties of the functional difference operator for neutral systems. The new results, obtained using Razumikhin’s technique, extend and complement basic stability results in neutral systems to NFDSID. Novel sufficient conditions were developed for the null controllability of nonlinear NFDSID when the controls are constrained. By exploring the knowledge gained through other controllability results; conditions are placed on the perturbation function. This guaranteed that, if the uncontrolled system is uniformly asymptotically stable, and the controlled system satisfies a full rank condition, then the control system is null controllable with constraint if it satisfies some algebraic conditions. The investigation of optimal robust guaranteed cost control method has resulted in a novel delay dependent stability criterion for a nonlinear NFDSID with a given quadratic cost function. The new design is based on a model transformation technique, Lyapunov matrix equation and Lyapunov-Razumikhin stability approach. The Lyapunov-Razumikhin technique is adopted for this investigation because it is considered more scalable for optimal robust guaranteed cost control design for NFDSID. It is demonstrated that a memory less feedback control can be synthesized appropriately to ensure: (i) the closed-loop systems robust stability, and (ii) guarantee that the closed-loop cost function value remains within a specified bound. The problem of designing the optimal guaranteed cost controller is also realized in terms of inequalities. The Lyapunov-Krasovskii method is used to obtain stability conditions in comparison to the Razumikhin method. This method leads to linear matrix inequality (LMI) for the delay-independent case which is known to be conservative. To illustrate the potential practical applicability of the theoretical results; a cascade connection of two fully filled chemical solution mixers, and an integrated lossless transmission line which has a capacitance, inductance, resistance and terminated by a nonlinear function are modelled. A neutral control system model for NFDSID is derived from each of these systems. Simulation studies on the transmission line system confirm the theoretical robust stability results. The new results and methods of analysis expounded in this thesis are explicit, computationally more effective than existing ones and will serve as a working document for the present and future generations in the comity of researchers and industries alike.

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30

Axelsson, Henrik. "Optimal Control of Switched Autonomous Systems: Theory, Algorithms, and Robotic Applications." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-04052006-131248/.

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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2006.
Ashraf Saad, Committee Member ; Spyros Reveliotis, Committee Member ; Anthony Yezzi, Committee Member ; Erik Verriest, Committee Member ; Yorai Wardi, Committee Co-Chair ; Magnus Egerstedt, Committee Chair.

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Tsang, Siu Chung. "Preconditioners for linear parabolic optimal control problems." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.

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In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and All-time problems. Our major contribution in this research is that we developed a preconditioner for each kind of problems, so our iterative method is accelerated. In chapter 1, we gave a brief introduction to our problems with a literature review. In chapter 2, we demonstrated how to derive the first-order optimality conditions from the parabolic optimal control problems. Afterwards, we showed how to use the shooting method along with the flexible generalized minimal residual to find the solution. In chapter 3, we offered three preconditioners to enhance our shooting method for the problems with symmetric differential operator. Next, in chapter 4, we proposed another three preconditioners to speed up our scheme for the problems with non-symmetric differential operator. Lastly, we have the conclusion and the future development in chapter 5.

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32

Safi, Samghabadi Pedram. "Kinematic analysis and control design of a retractable wheel mechanism using optimal control theory." Thesis, California State University, Long Beach, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1527340.

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Mobile robots are un-manned systems and must be able to overcome the obstacles they face without human intervention. In this research we have proposed a novel retractable mechanism which converts a linear hydraulic motion into expansion of six claws at each wheel. In order to control the expansion, optimal control theory was applied and a constrained optimization problem was defined using different Simulink toolboxes and applied to the mechanism modeled in SimHydraulics/SimMechanics. The main benefit of performing both hydraulic and mechanical system simulation and also control design in the same environment is to eliminate mathematical approximation of the model and using existing Simulink simulation tools for simulation and control. Systems were modeled and controller optimization was performed. Simulation results are illustrated at the end, which show the method's versatility and reliability for controlling the mechanism operation.

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33

Buckingham, N. J. "Aspects of feedback stabilisation and optimal control of bilinear systems." Thesis, University of Bath, 1986. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373389.

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34

Zhang, Lei. "Stochastic optimal control and regime switching : applications in economics." Thesis, University of Warwick, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387250.

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35

Iourtchenko, Daniil V. "Optimal bounded control and relevant response analysis for random vibrations." Link to electronic thesis, 2001. http://www.wpi.edu/Pubs/ETD/Available/etd-0525101-111407.

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Thesis (Ph. D.)--Worcester Polytechnic Institute.
Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration. Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration; energy balance method. Includes bibliographical references (p. 86-89).

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36

Lin, Yiing-Yuh. "Nonlinear optimal control and near-optimal guidance strategies in spacecraft general attitude maneuvers." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/53572.

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Solving the optimal open-loop control problems for spacecraft large-angle attitude maneuvers generally requires the use of numerical techniques whose reliability is strongly case dependent. The primary goal of this dissertation is to increase the solution reliability of the associated nonlinear two-point boundary-value problems as derived from Pontryagin’s Principle. Major emphasis is placed upon the formulation of the best possible starting or nominal solution. Constraint relationships among the state and costate variables are utilized. A hybrid approach which begins with the direct gradient method and ends with the indirect method of particular solutions is proposed. Test case results which indicate improved reliability are presented. The nonlinear optimal control law derived from iterative procedures cannot adjust itself in accordance with state deviations measured during the control period. A real-time near-optimal guidance scheme which takes the perturbed states to the desired manifold by tracking a given optimal trajectory is also proposed. Numerical simulations are presented which show that highly accurate tracking results can be achieved.
Ph. D.

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37

Kim, Eulgon. "Optimal helicopter trajectory planning for terrain following flight." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/12932.

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38

李澤康 and Chak-hong Lee. "Nonlinear time-delay optimal control problem: optimality conditions and duality." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31212475.

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39

Lee, Chak-hong. "Nonlinear time-delay optimal control problem : optimality conditions and duality /." [Hong Kong] : University of Hong Kong, 1995. http://sunzi.lib.hku.hk/hkuto/record.jsp?B16391640.

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40

Grigorenko, Ilia A. "Theory for ultrafast dynamics and optimal control of electrons in nanostructures." [S.l. : s.n.], 2002. http://www.diss.fu-berlin.de/2003/37/index.html.

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41

Wong, Man-kwun, and 黃文冠. "Some sensitivity results for time-delay optimal control problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223655.

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42

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.

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43

Dinesh, K. "An approximation method for the finite-time optimal control for nonlinear systems." Thesis, University of Sheffield, 1999. http://etheses.whiterose.ac.uk/14781/.

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44

Morris, Russell A. "Optimal state estimation for the optimal control of far-field acoustic radiation pressure from submerged plates." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-06232009-063036/.

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45

Zhang, Xiaohong. "Optimal feedback control for nonlinear discrete systems and applications to optimal control of nonlinear periodic ordinary differential equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40185.

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46

Pokrud, Boonyarit. "H∞ optimal control : general solution by interpolation and design with multiple objective functions." Thesis, University of Surrey, 1989. http://epubs.surrey.ac.uk/847911/.

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A new method for solving Hinfinity control problems is developed. The method makes use of the Youla parametrization to characterize the set of all stabilizing controllers K(s) in terms of a stable function Q(s). and also to transform the Hinfinity control problem into a model-matching problem with an objective function E(s) being linear in Q(s). The model-matching problem is then solved by using the interpolation results of Hung. In the general case (i.e. problems of the 3rd kind) closed-form state-space characterizations of optimal and suboptimal solutions for Q(s) and E(s) are given. Furthermore, the solutions generally only require to solve two standard algebraic Riccati equations of smaller size than the McMillan degree of the (generalized) plant. This has an advantage of alleviating the computation burden associated with the ?-iteration required for determining the attainable minimum of ||E(s)||[infinity]. The Hinfinity approach to feedback design with multiple objective functions is studied in this thesis. For a system with two objective functions T[i](s), (i = 1, 2) a design criterion of minimizing the function max (||T[1](s)||[infinity], ||T[2](s)||[infinity]) subject to internal stability of the closed-loop system is proposed. The problem is formulated as an Hinfinity control problem and an iterative algorithm for obtaining a solution is given. A numerical example is given to illustrate the effectiveness of the proposed design technique for tightly bounding and shaping the frequency responses of two objective functions. The application of Hinfinity feedback design techniques to the control of flexible structures is investigated. Experiments are conducted in order to evaluate the use of the Hinfinity approach to the control of flexible structures. An Hinfinity optimal controller is designed and implemented in a laboratory system to manoeuvre a cantilever flexible beam and simultaneously control its vibrations. The controller performance is then assessed. The results obtained are shown to be satisfactory and encouraging.

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47

Wingard, Philip A. (Philip Allen). "Improving the rowing process with a computer model and optimal control theory." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13423.

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Thesis (Ocean. E.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1991.
Title as it appears in the June, 1991 M.I.T. Graduate List: Rowing optimization using a computer.
by Philip A. Wingard.
Ocean.E.

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48

Borneman, Troy W., David G. Cory, and Martin D. Hürlimann. "Signal optimization in inhomogeneous fields: application of quantum optimal control theory troy." Diffusion fundamentals 10 (2009) 12, S. 1-3, 2009. https://ul.qucosa.de/id/qucosa%3A14103.

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We demonstrate that pulses derived using Optimal Control Theory (OCT) techniques can be used to significantly enhance the robustness of the Carr-Purcell-Meiboom-Gill sequence (CPMG) [1,2] to inhomogeneities in the static BB0 field. By numerically inverting the Liouville - von Neumann equation, OCT pulses were derived that can be used directly in place of hard pulses in the CPMG sequence to greatly improve the bandwidth of refocusing. To retain the echo stability achieved by the Meiboom-Gill correction to the Carr-Purcell sequence, the refocusing pulses were designed to perform a unitary π-rotation as opposed to just a state inversion transfer. To illustrate this approach we present an example of optimized pulses that show an improved CPMG-like behavior with complete excitation and multiple refocusing over a bandwidth of +/- 2.6 γB1,max B with a pulse duration limited to 10 t180.

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Riffer, Jennifer Lynn. "Time-optimal control of discrete-time systems with known waveform disturbances." [Milwaukee, Wis.] : e-Publications@Marquette, 2009. http://epublications.marquette.edu/theses_open/18.

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Hamzavi-Rad, S. "The optimal control of energy consumption in the United States Economy." Thesis, University of Essex, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381927.

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