Dissertations / Theses on the topic 'Nonlinear robust optimization'

The goal of robust speech recognition is to maintain satisfactory recognition accuracy under mismatched operating conditions. This dissertation addresses the robustness issue from two directions. In the first part of the dissertation, we propose the Gauss-Newton method as a unified approach to estimating noise parameters for use in prevalent nonlinear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, we demonstrate that such approaches are variants of the Gauss-Newton method. Furthermore, we propose a novel noise variance estimation algorithm that is consistent with the Gauss-Newton principle. The formulation of the Gauss-Newton method reduces the noise estimation problem to determining the Jacobians of the corrupted speech parameters. For sampling-based compensations, we present two methods, sample Jacobian average (SJA) and cross-covariance (XCOV), to evaluate these Jacobians. The Gauss-Newton method is closely related to another noise estimation approach, which views the model compensation from a generative perspective, giving rise to an EM-based algorithm analogous to the ML estimation for factor analysis (EM-FA). We demonstrate a close connection between these two approaches: they belong to the family of gradient-based methods except with different convergence rates. Note that the convergence property can be crucial to the noise estimation in many applications where model compensation may have to be frequently carried out in changing noisy environments to retain desired performance. Furthermore, several techniques are explored to further improve the nonlinear compensation approaches. To overcome the demand of the clean speech data for training acoustic models, we integrate nonlinear compensation with adaptive training. We also investigate the fast VTS compensation to improve the noise estimation efficiency, and combine the VTS compensation with acoustic echo cancellation (AEC) to mitigate issues due to interfering background speech. The proposed noise estimation algorithm is evaluated for various compensation models on two tasks. The first is to fit a GMM model to artificially corrupted samples, the second is to perform speech recognition on the Aurora 2 database, and the third is on a speech corpus simulating the meeting of multiple competing speakers. The significant performance improvements confirm the efficacy of the Gauss-Newton method to estimating the noise parameters of the nonlinear compensation models. The second research work is devoted to developing more effective models to take full advantage of heterogeneous speech data, which are typically collected from thousands of speakers in various environments via different transducers. The proposed synchronous HMM, in contrast to the conventional HMMs, introduces an additional layer of substates between the HMM state and the Gaussian component variables. The substates have the capability to register long-span non-phonetic attributes, such as gender, speaker identity, and environmental condition, which are integrally called speech scenes in this study. The hierarchical modeling scheme allows an accurate description of probability distribution of speech units in different speech scenes. To address the data sparsity problem in estimating parameters of multiple speech scene sub-models, a decision-based clustering algorithm is presented to determine the set of speech scenes and to tie the substate parameters, allowing us to achieve an excellent balance between modeling accuracy and robustness. In addition, by exploiting the synchronous relationship among the speech scene sub-models, we propose the multiplex Viterbi algorithm to efficiently decode the synchronous HMM within a search space of the same size as for the standard HMM. The multiplex Viterbi can also be generalized to decode an ensemble of isomorphic HMM sets, a problem often arising in the multi-model systems. The experiments on the Aurora 2 task show that the synchronous HMMs produce a significant improvement in recognition performance over the HMM baseline at the expense of a moderate increase in the memory requirement and computational complexity.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 107-110).
A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These formulations can be solved numerically with computationally-effcient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the class of nonlinear systems representable as an interconnection of a linear system with bounded uncertainty blocks. Recently, stability and performance analyses of more general nonlinear deterministic systems, namely those with polynomial or rational dynamics, have been converted into an LMI framework using sum of squares (SOS) programming. SOS programming combines elements of computational algebra and convex optimization to provide e±cient convex relaxations for various computationally-hard problems. In this thesis we extend the class of systems that can be analyzed with LMI-based methods.
(cont.) We show how to analyze the robust stability properties of uncertain non-linear systems with polynomial or rational dynamics, as well as a class of systems with external inputs, via contraction analysis and SOS programming. Specifically, we show how contraction analysis, a stability theory for nonlinear dynamical systems in which stability is designed incrementally between two arbitrary trajectories via a contraction metric, provides a useful framework for analyzing the stability of uncertain systems. Then, using SOS programming we develop an algorithmic method to search for contraction metrics for these systems. The search process is made computationally tractable by relaxing matrix deniteness constraints, the feasibility of which indicates the existence of a contraction metric, to SOS constraints on polynomial matrices. We illustrate our results through examples from the literature and show how our contraction-based approach offers advantages when compared with traditional Lyapunov analysis.
by Erin M. Aylward.
S.M.

This thesis addresses the challenges in the efficient and robust generation and optimization of three-dimensional landing trajectories for fixed-wing aircraft subject to prescribed boundary conditions and constraints on maneuverability and collision avoidance. In particular, this thesis focuses on the airliner emergency landing scenario and the minimization of landing time. The main contribution of the thesis is two-fold. First, it provides a hierarchical scheme for integrating the complementary strength of a variety of methods in path planning and trajectory optimization for the improvement in efficiency and robustness of the overall landing trajectory optimization algorithm. The second contribution is the development of new techniques and results in mesh refinement for numerical optimal control, optimal path tracking, and smooth path generation, which are all integrated in a hierarchical scheme and applied to the landing trajectory optimization problem. A density function based grid generation method is developed for the mesh refinement process during numerical optimal control. A numerical algorithm is developed based on this technique for solving general optimal control problems, and is used for optimizing aircraft landing trajectories. A path smoothing technique is proposed for recovering feasibility of the path and improving the tracking performance by modifying the path geometry. The optimal aircraft path tracking problem is studied and analytical results are presented for both the minimum-time, and minimum-energy tracking with fixed time of arrival. The path smoothing and optimal path tracking methods work together with the geometric path planner to provide a set of feasible initial guess to the numerical optimal control algorithm. The trajectory optimization algorithm in this thesis was tested by simulation experiments using flight data from two previous airliner accidents under emergency landing scenarios.The real-time application of the landing trajectory optimization algorithm as part of the aircraft on-board automation avionics system has the potential to provide effective guidelines to the pilots for improving the fuel consumption during normal landing process, and help enhancing flight safety under emergency landing scenarios. The proposed algorithms can also help design optimal take-off and landing trajectories and procedures for airports.

SLAM (Simultaneous Localization And Mapping) has been a very active and almost ubiquitous problem in the field of mobile and autonomous robotics for over two decades. For many years, filter-based methods have dominated the SLAM literature, but a change of paradigms could be observed recently. Current state of the art solutions of the SLAM problem are based on efficient sparse least squares optimization techniques. However, it is commonly known that least squares methods are by default not robust against outliers . In SLAM, such outliers arise mostly from data association errors like false positive loop closures. Since the optimizers in current SLAM systems are not robust against outliers, they have to rely heavily on certain preprocessing steps to prevent or reject all data association errors. Especially false positive loop closures will lead to catastrophically wrong solutions with current solvers. The problem is commonly accepted in the literature, but no concise solution has been proposed so far. The main focus of this work is to develop a novel formulation of the optimization-based SLAM problem that is robust against such outliers. The developed approach allows the back-end part of the SLAM system to change parts of the topological structure of the problem’s factor graph representation during the optimization process. The back-end can thereby discard individual constraints and converge towards correct solutions even in the presence of many false positive loop closures. This largely increases the overall robustness of the SLAM system and closes a gap between the sensor-driven front-end and the back-end optimizers. The approach is evaluated on both large scale synthetic and real-world datasets. This work furthermore shows that the developed approach is versatile and can be applied beyond SLAM, in other domains where least squares optimization problems are solved and outliers have to be expected. This is successfully demonstrated in the domain of GPS-based vehicle localization in urban areas where multipath satellite observations often impede high-precision position estimates.

SLAM (Simultaneous Localization And Mapping) has been a very active and almost ubiquitous problem in the field of mobile and autonomous robotics for over two decades. For many years, filter-based methods have dominated the SLAM literature, but a change of paradigms could be observed recently. Current state of the art solutions of the SLAM problem are based on efficient sparse least squares optimization techniques. However, it is commonly known that least squares methods are by default not robust against outliers. In SLAM, such outliers arise mostly from data association errors like false positive loop closures. Since the optimizers in current SLAM systems are not robust against outliers, they have to rely heavily on certain preprocessing steps to prevent or reject all data association errors. Especially false positive loop closures will lead to catastrophically wrong solutions with current solvers. The problem is commonly accepted in the literature, but no concise solution has been proposed so far. The main focus of this work is to develop a novel formulation of the optimization-based SLAM problem that is robust against such outliers. The developed approach allows the back-end part of the SLAM system to change parts of the topological structure of the problem\'s factor graph representation during the optimization process. The back-end can thereby discard individual constraints and converge towards correct solutions even in the presence of many false positive loop closures. This largely increases the overall robustness of the SLAM system and closes a gap between the sensor-driven front-end and the back-end optimizers. The approach is evaluated on both large scale synthetic and real-world datasets. This work furthermore shows that the developed approach is versatile and can be applied beyond SLAM, in other domains where least squares optimization problems are solved and outliers have to be expected. This is successfully demonstrated in the domain of GPS-based vehicle localization in urban areas where multipath satellite observations often impede high-precision position estimates.

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality. We first briefly consider the reliability-constrained single-path problem, where we look for the lowest cost path that meets a reliability side constraint. This analysis enables us to then examine the reliability-constrained two-path problem, which seeks to establish two minimum-cost paths between a source and destination node wherein at least one path must remain fully operable with some threshold probability. We consider the case in which both paths must be arc-disjoint and the case in which arcs can be shared between the paths. We prove both problems to be NP-hard. We examine strategies for solving the resulting nonlinear integer program, including pruning, coefficient tightening, lifting, and branch-and-bound partitioning schemes. Next, we consider the reliable h-path routing problem, which seeks a minimum-cost set of h ≥ 2 arc-independent paths between a source and destination node, such that the probability that at least one path remains operational is sufficiently large. Our prior arc-based models and algorithms tailored for the case in which h = 2 do not extend well to the general h-path problem. Thus, we propose two alternative integer programming formulations for the h-path problem in which the variables correspond to origin-destination paths. We propose two branch-and-price-and-cut algorithms for solving these new formulations, and provide computational results to demonstrate the efficiency of these algorithms. Finally, we examine the robust design of an evacuation tree, in which evacuation is subject to capacity restrictions on arcs. Given a discrete set of disaster scenarios with varying network populations, arc capacities, transit times, and time-dependent penalty functions, we seek to establish an optimal a priori evacuation tree that minimizes the expected evacuation penalty. The solution strategy is based on Benders decomposition, and we provide effcient methods for obtaining primal and dual sub-problem solutions. We analyze techniques for strengthening the master problem formulation, thus reducing the number of master problem solutions required for the algorithm's convergence.

This thesis deals with the design of a robust and safe control algorithm to aim at an artificial pancreas. More precisely we will be interested in controlling the stabilizing part of a classical cure. To meet this objective, the design of a robust nonlinear model predictive controller based on the solution of a saddle point optimization problem is considered. Also, to test the controller performances in a realistic case, numerical simulations on a FDA validated testing platform are envisaged.In a first part, we present an extension of the usual nonlinear model predictive controller designed to robustly control, in a sampled-data framework, systems described by nonlinear ordinary differential equations. This controller, which computes the best control input by considering the solution of a constrained saddle point optimization problem, is called saddle point model predictive controller (SPMPC). Using this controller, it is proved that the closed-loop is Ultimately Bounded and, with some assumptions on the problem structure, Input-to State practically Stable. Then, we are interested in numerically solving the corresponding control problem. To do so, we propose an algorithm inspired from the augmented Lagrangian technique and which makes use of adjoint model.In a second part, we consider the application of this controller to the problem of artificial blood glucose control. After a modeling phase, two models are retained. A simple one will be used to design the controller and a complex one will be used to simulate realistic virtual patients. This latter is needed to validate our control approach. In order to compute a good control input, the SPMPC controller needs the full state value. However, the sensors can only provide the value of blood glucose. That is why the design of an adequate observer is envisaged. Then, numerical simulations are performed. The results show the interest of the approach. For all virtual patients, no hypoglycemia event occurs and the time spent in hyperglycemia is too short to induce damageable consequences. Finally, the interest of extending the SPMPC approach to consider the control of time delay systems in a sampled-data framework is numerically explored.

With the increased performance and reduced cost of cameras, the robotics community has taken great interest in estimation and control algorithms that fuse camera data with other sensor data.In response to this interest, this dissertation investigates the algorithms needed for robust guidance, navigation, and control of fixed-wing and multirotor aircraft applied to target estimation and circumnavigation.This work begins with the development of a method to estimate target position relative to static landmarks, deriving and using a state-of-the-art EKF that estimates static landmarks in its state.Following this estimator, improvements are made to a nonlinear observer solving part of the SLAM problem.These improvements include a moving origin process to keep the coordinate origin within the camera field of view and a sliding window iteration algorithm to drastically improve convergence speed of the observer.Next, observers to directly estimate relative target position are created with a circumnavigation guidance law for a multirotor aircraft.Taking a look at fixed-wing aircraft, a state-dependent LQR controller with inputs based on vector fields is developed, in addition to an EKF derived from error state and Lie group theory to estimate aircraft state and inertial wind velocity.The robustness of this controller/estimator combination is demonstrated through Monte Carlo simulations.Next, the accuracy, robustness, and consistency of a state-of-the-art EKF are improved for multirotors by augmenting the filter with a drag coefficient, partial updates, and keyframe resets.Monte Carlo simulations demonstrate the improved accuracy and consistency of the augmented filter.Lastly, a visual-inertial EKF using image coordinates is derived, as well as an offline calibration tool to estimate the transforms needed for accurate, visual-inertial estimation algorithms.The imaged-based EKF and calibrator are also shown to be robust under various conditions through numerical simulation.

Multivariate adaptive regression spline (MARS) denotes a modern methodology from statistical learning which is very important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. MARS is very useful for high dimensional problems and shows a great promise for fitting nonlinear multivariate functions. MARS technique does not impose any particular class of relationship between the predictor variables and outcome variable of interest. In other words, a special advantage of MARS lies in its ability to estimate the contribution of the basis functions so that both the additive and interaction effects of the predictors are allowed to determine the response variable. The function fitted by MARS is continuous, whereas the one fitted by classical classification methods (CART) is not. Herewith, MARS becomes an alternative to CART. The MARS algorithm for estimating the model function consists of two complementary algorithms: the forward and backward stepwise algorithms. In the first step, the model is built by adding basis functions until a maximum level of complexity is reached. On the other hand, the backward stepwise algorithm is began by removing the least significant basis functions from the model. In this study, we propose not to use the backward stepwise algorithm. Instead, we construct a penalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization problem, which is also known as ridge regression. We treat this problem using continuous optimization techniques which we consider to become an important complementary technology and alternative to the concept of the backward stepwise algorithm. In particular, we apply the elegant framework of conic quadratic programming which is an area of convex optimization that is very well-structured, herewith, resembling linear programming and, hence, permitting the use of interior point methods. The boundaries of this optimization problem are determined by the multiobjective optimization approach which provides us many alternative solutions. Based on these theoretical and algorithmical studies, this MSc thesis work also contains applications on the data investigated in a TÜ
BiTAK project on quality control. By these applications, MARS and our new method are compared.

Dans cette Thèse, la conception robuste avec un modèle incertain d'un système électromécanique avec vibro-impact est fait. Le système électromécanique est constitué d'un chariot, dont le mouvement est excité par un moteur à courant continu et un marteau embarqué dans ce chariot. Le marteau est relié au chariot par un ressort non linéaire et par un amortisseur linéaire, de façon qu'un mouvement relatif existe entre eux. Une barrière flexible linéaire, placé à l'extérieur du chariot limite les mouvements de marteau. En raison du mouvement relatif entre le marteau et la barrière, impacts peuvent se produire entre ces deux éléments. Le modèle du système développé prend en compte l'influence du courant continu moteur dans le comportement dynamique du système. Certains paramètres du système sont incertains, tels comme les coefficients de rigidité et d'amortissement de la barrière flexible. L'objectif de la Thèse est de réaliser une optimisation de ce système électromécanique par rapport aux paramètres de conception afin de maximiser l'impact puissance sous la contrainte que la puissance électrique consommée par le moteur à courant continu est inférieure à une valeur maximale. Pour choisir les paramètres de conception dans le problème d'optimisation, une analyse de sensibilité a été réalisée afin de définir les paramètres du système les plus sensibles. L'optimisation est formulée dans le cadre de la conception robuste en raison de la présence d'incertitudes dans le modèle. Les lois de probabilités liées aux variables aléatoires du problème sont construites en utilisant le Principe du Maximum l'Entropie et les statistiques de la réponse stochastique du système sont calculées en utilisant la méthode de Monte Carlo. L'ensemble d'équations non linéaires sont présentés, et un solveur temporel adapté est développé. Le problème d'optimisation non linéaire stochastique est résolu pour différents niveaux d'incertitudes, et aussi pour le cas déterministe. Les résultats sont différents, ce qui montre l'importance de la modélisation stochastique
In this Thesis, the robust design with an uncertain model of a vibro-impact electromechanical system is done. The electromechanical system is composed of a cart, whose motion is excited by a DC motor (motor with continuous current), and an embarked hammer into this cart. The hammer is connected to the cart by a nonlinear spring component and by a linear damper, so that a relative motion exists between them. A linear flexible barrier, placed outside of the cart, constrains the hammer movements. Due to the relative movement between the hammer and the barrier, impacts can occur between these two elements. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. Some system parameters are uncertain, such as the stiffness and the damping coefficients of the flexible barrier. The objective of the Thesis is to perform an optimization of this electromechanical system with respect to design parameters in order to maximize the impact power under the constraint that the electric power consumed by the DC motor is lower than a maximum value. To chose the design parameters in the optimization problem, an sensitivity analysis was performed in order to define the most sensitive system parameters. The optimization is formulated in the framework of robust design due to the presence of uncertainties in the model. The probability distributions of random variables are constructed using the Maximum Entropy Principle and statistics of the stochastic response of the system are computed using the Monte Carlo method. The set of nonlinear equations are presented, and an adapted time domain solver is developed. The stochastic nonlinear constrained design optimization problem is solved for different levels of uncertainties, and also for the deterministic case. The results are different and this show the importance of the stochastic modeling

The thesis focuses on a mixed integer linear programming (MILP) formulation for a bi-level mathematical program with equilibrium constraints (MPEC) considering chance constraints. The particular MPEC problem relates to a power producer’s bidding strategy: maximize its total benefit through determining bidding price and bidding power output while considering an electricity pool’s operation and guessing the rival producer’s bidding price. The entire decision-making process can be described by a bi-level optimization problem. The contribution of our thesis is the MILP formulation of this problem considering the use of chance constrained mathematical program for handling the uncertainties. First, the lower-level poor operation problem is replaced by Karush-Kuhn-Tucker (KKT) optimality condition, which is further converted to an MILP formulation except a bilinear item in the objective function. Secondly, duality theory is implemented to replace the bilinear item by linear items. Finally, two types of chance constraints are examined and modeled in MILP formulation. With the MILP formulation, the entire MPEC problem considering randomness in price guessing can be solved using off-shelf MIP solvers, e.g., Gurobi. A few examples and a case study are given to illustrate the formulation and show the case study results.

Dissertation (Ph.D.)--Worcester Polytechnic Institute.
Keywords: Parametric optimization; nonlinear dynamics; functional equations; chemical reaction system dynamics; time scale multiplicity; robust control; nonlinear observers; invariant manifold; process monitoring; Lyapunov stability. Includes bibliographical references (leaves 92-98).

In automatic speech recognition systems (ASRs), training is a critical phase to the system?s success. Communication media, either analog (such as analog landline phones) or digital (VoIP) distort the speaker?s speech signal often in very complex ways: linear distortion occurs in all channels, either in the magnitude or phase spectrum. Non-linear but time-invariant distortion will always appear in all real systems. In digital systems we also have network effects which will produce packet losses and delays and repeated packets. Finally, one cannot really assert what path a signal will take, and so having error or distortion in between is almost a certainty. The channel introduces an acoustical mismatch between the speaker's signal and the trained data in the ASR, which results in poor recognition performance. The approach so far, has been to try to undo the havoc produced by the channels, i.e. compensate for the channel's behavior. In this thesis, we try to characterize the effects of different transmission media and use that as an inexpensive and repeatable way to train ASR systems.

This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost.
Ph. D.

This research aims at solving an engineering design problem encountered in the field of robotics using mathematical programming techniques. The problem addressed is an indispensable part of designing the operation of Ursula, an underwater mobile robot, and involves finding its location as it moves along the circumference of a nuclear reactor vessel. The study has been conducted with an intent to aid a laser based global positioning system to make this determination. The physical nature of this problem enables it to be conceptualized as a position and orientation determination problem. Ursula tests the weldments in the reactor vessel, and its position and orientation needs to be found continuously in real-time. The kinematic errors in the setup and the use of a laser based positioning system distinguish this from traditional position and orientation determination problems. The aim of this research effort is to construct a suitable representative mathematical model for this problem, and to design and compare various solution methodologies that are computationally competitive, numerically stable, and accurate.
Master of Science

Face à l’augmentation des exigences à la fois économiques et de santé publique, les industriels sont dans la nécessité de concevoir des systèmes mécaniques de plus en plus performants et respectant un certain niveau de confort acoustique. En mécanique ou en acoustique, le contrôle de vibrations est un champ de recherche très actif. Trois grands types de technologie sont majoritairement utilisées dans l’industrie : le contrôle passif par dissipation, le contrôle passif à l’aide d’absorbeurs linéaires accordées et le contrôle actif, chacune de ses techniques possédant ses avantages et ses inconvénients. Depuis une quinzaine d’années, l’utilisation d’absorbeurs non linéaires de type NES (« Nonlinear Energy Sink » en anglais), typiquement un système masse-ressort-amortisseur à raideur purement non linéaire, a montré son efficacité comme solution alternative de contrôle passif des vibrations en conciliant les avantages des technologies existantes. Cependant, le comportement dynamique du système couplé constitué du NES et du système primaire à protéger peut s’avérer très sensible aux paramètres qui admettent une dispersion importante. Notamment, lorsqu’il s’agit d’atténuer une instabilité dynamique (comme c’est le cas dans cette thèse) une discontinuité dans le profil de l’amplitude vibratoire du système peut s’observer, ce dernier passant brutalement d’un régime atténué (où le NES agit) à un régime non atténué (où le NES n’agit pas). Un régime non atténué étant potentiellement dangereux, il est important d’être en mesure, en prenant en compte les incertitudes paramétriques auxquelles le système primaire peut être confronté, de concevoir un NES qui soit robuste, c’est-à-dire fonctionnant au maximum dans l’espace des paramètres incertains correspondant à des régimes non atténués du système primaire.Dans la première partie, des méthodes basées sur le formalisme du chaos polynomial sont proposées pour la localisation, dans l’espace des paramètres incertains du système primaire, de la frontière entre la région correspondant aux régimes atténués et celle correspondant aux régimes non atténués, permettant ainsi le calcul de la propension du système couplé à être dans un régime atténué. Ces méthodes sont ensuite appliquées aux cas d’un système frottant à deux degrés de liberté (le modèle dit de Hultèn) couplé à deux NES identiques. Les résultats montrent d’une part que les méthodes basées sur le chaos polynomial permettent de réduire significativement le cout de calcul par rapport à la méthode de référence en conservant une bonne précision et d’autre part que la méthode basée sur le chaos polynomial multi-éléments (appelée méthode ME-gPC) est la plus efficace.Dans la deuxième partie, une méthodologie d'optimisation des NES sous incertitudes est développée. Deux approches sont proposées, à chaque fois basées sur la maximisation, sous incertitudes des paramètres du système primaire, de la propension du système couplé à être dans un régime atténué. La première approche considère que les paramètre des NES sont déterministes et sont donc les variables de conception à optimiser. La seconde méthode considère que les paramètres des NES sont également incertains mais avec une loi de probabilité connue. Ainsi, les variables de conception à optimiser ne sont plus directement les paramètres des NES mais l’une de leurs statistiques (la moyenne ou l’écart-type par exemple) appelées hyper-paramètres. Les résultats obtenus sont comparés à une optimisation déterministe de référence. L’efficacité des méthodes proposée, basées sur le chaos polynomial, à réduire significativement le cout de calcul en gardant une bonne précision est mise en évidence
Faced with increasing economic and public health requirements, industrialists are faced with the need to design increasingly efficient mechanical systems that respect a certain level of acoustic comfort. In mechanics or acoustics, vibration control is a very active field of research. Three main types of technology are mainly used in industry: passive control by dissipation, passive control using tuned linear absorbers and active control, each of these techniques having its advantages and disadvantages. Over the past 15 years, the use of NES (Nonlinear Energy Sink) non-linear absorbers, typically a purely non-linear stiffness mass-spring-damper system, has proven its effectiveness as an alternative solution for passive vibration control by combining the advantages of existing technologies. However, the dynamic behaviour of the coupled system consisting of the NES and the primary system to be protected can be very sensitive to parameters that allow for high dispersion. In particular, when attenuating dynamic instability (as is the case in this thesis) a discontinuity in the vibration amplitude profile of the system can be observed, as the system suddenly switches from an attenuated regime (where the NES acts) to an unattenuated regime (where the NES does not act). Since an unattenuated regime is potentially dangerous, it is important to be able, taking into account the parameter uncertainties that the primary system may face, to design an NES that is robust, i.e. operating at maximum within the space of the uncertain parameters corresponding to unattenuated regimes of the primary system.In the first part, methods based on the formalism of polynomial chaos are proposed for locating, in the space of the uncertain parameters of the primary system, the boundary between the region corresponding to attenuated regimes and that corresponding to non-attenuated regimes, thus allowing the calculation of the propensity of the coupled system to be in an attenuated regime. These methods are then applied to the cases of a two-degree-of-freedom friction system (the so-called Hultèn model) coupled to two identical NES. The results show, on the one hand, that the methods based on polynomial chaos allow a significant reduction of the calculation cost compared to the reference method while maintaining a good accuracy and, on the other hand, that the method based on multi-element polynomial chaos (called ME-gPC method) is the most efficient.In the second part, a methodology for optimizing NES under uncertainty is developed. Two approaches are proposed, each based on maximizing, under uncertainties of the primary system parameters, the propensity of the coupled system to be in a mitigated regime. The first approach considers that the SNF parameters are deterministic and are therefore the design variables to be optimized. The second approach considers that the SEL parameters are also uncertain but with a known probability distribution. Thus, the design variables to be optimized are no longer directly the parameters of the NES but one of their statistics (the mean or the standard deviation for example) called hyper-parameters. The results obtained are compared with a reference deterministic optimization. The effectiveness of the proposed methods, based on polynomial chaos, to significantly reduce the cost of calculation while maintaining good precision is highlighted

Les travaux de cette thèse portent sur l’estimation et la commande décentralisée des systèmes de grande dimension. L’objectif est de développer des capteurs logiciels pouvant produire une estimation fiable des variables nécessaires pour la stabilisation des systèmes non linéaires interconnectés. Une décomposition d’un tel système de grande dimension en un ensemble de n sous-systèmes interconnectés est primordiale. Ensuite, en tenant compte de la nature du sous-système ainsi que les fonctions d’interconnexions, des lois de commande décentralisées basées observateurs ont été synthétisées. Chaque loi de commande est associée à un sous-système qui permet de le stabiliser localement, ainsi la stabilité du système global est assurée. L’existence d’un observateur et d’un contrôleur stabilisant le système dépend de la faisabilité d’un problème d’optimisation LMI. La formulation LMI, basée sur l’approche de Lyapunov, est élaborée par l’utilisation de principe de DMVT sur la fonction d’interconnexion non linéaire supposée bornée et incertaine. Ainsi des conditions de synthèse non restrictives sont obtenues. Des méthodes de synthèse de loi de commande décentralisée basée observateur ont été proposées pour les systèmes non linéaires interconnectés dans le cas continu et dans le cas discret. Des lois de commande robuste H1 décentralisées sont élaborées pour les systèmes non linéaires interconnectés en présence de perturbations et des incertitudes paramétriques. L’efficacité et la validation des approches présentées sont testées sur un modèle de réseaux électriques composé de trois générateurs interconnectés
This thesis focuses on the decentralized estimation and control for large scale systems. The objective is to develop software sensors that can produce a reliable estimate of the variables necessary for the interconnected nonlinear systems stability analysis. A decomposition of a such large system into a set of n interconnected subsystems is paramount for model simplification. Then, taking into account the nature of the subsystem as well as the interconnected functions, observer-based decentralized control laws have been synthesized. Each control law is associated with a subsystem which allows it to be locally stable, thus the stability of the overall system is ensured. The existence of an observer and a controller gain matrix stabilizing the system depends on the feasibility of an LMI optimization problem. The LMI formulation, based on Lyapunov approach, is elaborated by applying the DMVT technique on the nonlinear interconnection function, assumed to be bounded and uncertain. Thus, non-restrictive synthesis conditions are obtained. Observer-based decentralized control schemes have been proposed for nonlinear interconnected systems in the continuous and discrete time. Robust Hinfini decentralized controllers are provided for interconnected nonlinear systems in the presence of perturbations and parametric uncertainties. Effectiveness of the proposed schemes are verified through simulation results on a power systems with interconnected machines

D'un point de vue énergétique, les robots marcheurs sont moins performants que les humains. Face à ce défi, cette thèse propose une approche pour contrôler et optimiser les allures de marche des robots bipèdes à la fois en 2D et 3D en considérant les fréquences propres du robot et par ajout de ressorts. L'étude porte essentiellement sur un robot bipède 2D à 5 corps et des pieds ponctuels ainsi qu'un robot bipède 3D à 8 corps avec des pieds sans masse à contact linéique. La commande en boucle fermée considérée est basée sur la méthode des contraintes virtuelles et la linéarisation par retour d'état. Suite à des études précédentes, la stabilité du robot bipède 2D est vérifiée par une section de Poincaré unidimensionnelle et étendue au robot bipède 3D à contact linéique avec le sol. L'optimisation est effectuée en utilisant la programmation quadratique séquentielle. Les paramètres optimisés incluent des coefficients de polynômes de Bézier et des paramètres posturaux. Des contraintes d'optimisation sont imposées pour assurer la validité de l'allure de marche. Pour le robot bipède 2D, deux configurations différentes de ressorts placés aux hanches sont étudiées. Ces deux configurations ont permis de réduire le coût énergétique. Pour le robot bipède 3D, les paramètres d'optimisation sont séparés en deux parties : ceux décrivant le mouvement dans le plan sagittal et ceux du plan frontal. Les résultats de l'optimisation montrent que ces deux types de paramètres doivent être optimisés. Ensuite, des ressorts sont ajoutés respectivement par rapport au plan sagittal, par rapport au plan frontal puis dans les deux plans. Les résultats montrent que l'ajout des ressorts dans le plan sagittal permet de réduire significativement le coût énergétique et que l'association de ressorts dans le plan frontal améliore encore plus la consommation d'énergie
From an energy standpoint, walking robots are less efficient than humans. In facing this challenge, this study aims to provide an approach for controlling and optimizing the gaits of both 2D and 3D bipedal robots with consideration for exploiting natural dynamics and elastic couplings. A 5-link 2D biped with point feet and an 8-link 3D biped with massless line feet are studied. The control method is based on virtual constraints and feedback linearization. Following previous studies, the stability of the 2D biped is verified by computing scalar Poincaré map in closed form, and now this method also applies to the 3D biped because of its line-foot configuration. The optimization is performed using sequential quadratic programming. The optimization parameters include postural parameters and Bézier coefficients, and the optimization constraints are used to ensure gait validity. For the 2D biped, two different configurations of hip joint springs are investigated and both configurations successfully reduce the energy cost. For the 3D biped, the optimization parameters are further divided into sagittal parameters and coronal parameters, and the optimization results indicate that both these parameters should be optimized. After that, hip joint springs are added respectively to the sagittal plane, the coronal plane and both these planes. The results demonstrate that the elastic couplings in the sagittal plane should be considered first and that the additional couplings in the coronal plane reduce the energy cost even further

In this thesis, we consider problems connected to navigation and tracking for autonomousrobots under the assumption of constraints on sensors and kinematics. We study formation controlas well as techniques for filtering and smoothing of noise contaminated input. The scientific contributions of the thesis comprise five papers.In Paper A, we propose three cascaded, stabilizing formation controls for multi-agent systems.We consider platforms with non-holonomic kinematic constraints and directional rangesensors. The resulting formation is a leader-follower system, where each follower agent tracksits leader agent at a specified angle and distance. No inter-agent communication is required toexecute the controls. A switching Kalman filter is introduced for active sensing, and robustnessis demonstrated in experiments and simulations with Khepera II robots.In Paper B, an optimization-based adaptive Kalman filteringmethod is proposed. The methodproduces an estimate of the process noise covariance matrix Q by solving an optimization problemover a short window of data. The algorithm recovers the observations h(x) from a system˙ x = f (x), y = h(x)+v without a priori knowledge of system dynamics. The algorithm is evaluatedin simulations and a tracking example is included, for a target with coupled and nonlinearkinematics. In Paper C, we consider the problem of estimating a closed curve in R2 based on noisecontaminated samples. A recursive control theoretic smoothing spline approach is proposed, thatyields an initial estimate of the curve and subsequently computes refinements of the estimateiteratively. Periodic splines are generated by minimizing a cost function subject to constraintsimposed by a linear control system. The optimal control problem is shown to be proper, andsufficient optimality conditions are derived for a special case of the problem using Hamilton-Jacobi-Bellman theory.Paper D continues the study of recursive control theoretic smoothing splines. A discretizationof the problem is derived, yielding an unconstrained quadratic programming problem. Aproof of convexity for the discretized problem is provided, and the recursive algorithm is evaluatedin simulations and experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics. Finally, in Paper E we explore the issue of optimal smoothing for control theoretic smoothingsplines. The output of the control theoretic smoothing spline problem is essentially a tradeoff between faithfulness to measurement data and smoothness. This tradeoff is regulated by the socalled smoothing parameter. In Paper E, a method is developed for estimating the optimal valueof this smoothing parameter. The procedure is based on general cross validation and requires noa priori information about the underlying curve or level of noise in the measurements.
QC 20100722

Cette thèse étudie l'approche LPV pour la commande robuste des systèmes non linéaires. Son originalité est de proposer pour la première fois un cadre rigoureux permettant de résoudre efficacement des problèmes de synthèse non linéaire. L'approche LPV a été proposée comme une extension de l'approche H-infini dans le contexte des systèmes LPV (« Linéaires à Paramètres Variant dans le temps »), voire non linéaires. Quoique prometteuse, cette approche pour la commande des systèmes non linéaires restait peu utilisée. En effet, au-delà même de certaines limitations théoriques, la nature des solutions obtenues semblait inadéquate. Cette question ouverte est notre point de départ. Nous montrons tout d'abord que la faible variation des correcteurs constatée est due avant tout à la nature du schéma informationnel utilisé traditionnellement lors de la synthèse LPV, et que sous des hypothèses raisonnables, le cadre LPV peut permettre de recouvrir des stratégies de type « linéarisation par bouclage ». Ce point étant acquis, une deuxième difficulté réside dans l'obtention effective de correcteurs non linéaires donnant des garanties de performance. Nous proposons un cadre rigoureux permettant de résoudre efficacement un problème de synthèse incrémentale pondérée, par la résolution d'un problème LPV associé à un schéma informationnel spécifique compatible avec celui identifié dans la première partie. Cette étude et son aboutissement à la définition d'un cadre formel et d'une procédure complète d'obtention de correcteurs, incluant des méthodes de réduction de complexité, donnent des arguments puissants en faveur de l'approche LPV pour la commande robuste de systèmes non linéaires
This thesis studies the LPV approach for the robust control of nonlinear systems. Its originality is to propose for the first time a rigorous framework allowing to solve efficiently nonlinear synthesis problems.The LPV approach was proposed as an extension of the H-infinity approach in the context of LPV (Linear Parameter-Varying) systems and nonlinear systems. Although this approach seemed promising, it was not much used in practise. Indeed, beyond certain theoretical limitations, the nature itself of the obtained solutions did not seem adequate. This open question constitutes the starting point of our work.We first prove that the observed weak variation of the controllers is in fact mostly due to the information structure traditionally used for LPV synthesis, and that under reasonable assumptions, the LPV framework can overlap feedback linearization strategies. This point having been resolved, a second difficulty lies in the actual achievement of nonlinear controllers yielding performance guarantees. We propose a rigorous framework allowing to solve efficiently an incremental synthesis problem, through the resolution of an LPV problem associated to a specific information structure compatible with the one identified in the first part.This study and its corollary description of a formal framework and of a complete controller synthesis procedure, including complexity reduction methods, provide powerful arguments in favor of the LPV approach for the robust control of nonlinear systems

Un robot humanoïde est un système complexe doté de nombreux degrés de liberté, et dont le comportement est sujet aux équations non linéaires du mouvement. Par conséquent, la planification de mouvement pour un tel système est une tâche difficile d'un point de vue calculatoire. Dans ce mémoire, nous avons pour objectif de développer une méthode permettant d'utiliser la puissance de calcul des GPUs dans le contexte de la planification de mouvement corps-complet basée sur de l'optimisation. Nous montrons dans un premier temps les propriétés du problème d'optimisation, et des pistes d'étude pour la parallélisation de ce dernier. Ensuite, nous présentons notre approche du calcul de la dynamique, adaptée aux architectures de calcul parallèle. Cela nous permet de proposer une implémentation de notre problème de planification de mouvement sur GPU: contraintes et gradients sont calculés en parallèle, tandis que la résolution du problème même se déroule sur le CPU. Nous proposons en outre une nouvelle paramétrisation des forces de contact adaptée à notre problème d'optimisation. Enfin, nous étudions l'extension de notre travail au contrôle prédictif
A humanoid robot is a complex system with numerous degrees of freedom, whose behavior is subject to the nonlinear equations of motion. As a result, planning its motion is a difficult task from a computational perspective.In this thesis, we aim at developing a method that can leverage the computing power of GPUs in the context of optimization-based whole-body motion planning. We first exhibit the properties of the optimization problem, and show that several avenues can be exploited in the context of parallel computing. Then, we present our approach of the dynamics computation, suitable for highly-parallel processing architectures. Next, we propose a many-core GPU implementation of the motion planning problem. Our approach computes the constraints and their gradients in parallel, and feeds the result to a nonlinear optimization solver running on the CPU. Because each constraint and its gradient can be evaluated independently for each time interval, we end up with a highly parallelizable problem that can take advantage of GPUs. We also propose a new parametrization of contact forces adapted to our optimization problem. Finally, we investigate the extension of our work to model predictive control

Un robot humanoïde est un système polyarticulé complexe dont la cinématique et la dynamique sont gouvernées par des équations non linéaires. Trouver des postures viables qui minimisent une tâche objectif tout en satisfaisant un ensemble de contraintes (intrinsèques ou extrinsèques) est un problème central pour la planification de mouvement robotique et est une fonctionnalité importante de tout logiciel de robotique. Le générateur de posture (PG) a pour rôle de trouver une posture viable en formulant puis résolvant un problème d’optimisation non linéaire. Nous étendons l’état de l’art en proposant de nouvelles formulations et méthodes de résolution de problèmes de génération de postures. Nous enrichissons la formulation de contraintes de contact par ajout de variables au problème d’optimisation, ce qui permet au solveur de décider automatiquement de la zone d’intersection entre deux polygones en contact ou encore de décider du lieu de contact sur une surface non plane. Nous présentons une reformulation du PG qui gère nativement les variétés non Euclidiennes et nous permet de formuler des problèmes mathématiques plus élégants et efficaces. Pour résoudre de tels problèmes, nous avons développé un solveur non linéaire par SQP qui supporte nativement les variables sur variétés. Ainsi, nous avons une meilleure maîtrise de notre solveur et pouvons le spécialiser pour la résolution de problèmes de robotique
Humanoid robots are complex poly-articulated structures whose kinematics and dynamics are governed by nonlinear equations. Finding viable postures to realize set-point task objectives under a set of constraints (intrinsic and extrinsic limitations) is a key issue in the planning of robot motion and an important feature of any robotics framework. It is handled by the so called posture generator (PG) that consists in formalizing the viable posture as the solution to a nonlinear optimization problem. We present several extensions to the state-of-the-art by exploring new formulations and resolution methods for the posture generation problems. We reformulate the notion of contact constraints by adding variables to enrich our optimization problem and allow the solver to decide on the shape of the intersection of contact polygons or of the location of a contact point on a non-flat surface. We present a reformulation of the PG problem that encompasses non-Euclidean manifolds natively for a more elegant and efficient mathematical formulation of the problems. To solve such problems, we decided to implement a new SQP solver that is most suited to non-Euclidean manifolds structural objects. By doing so, we have a better mastering in the way to tune and specialize our solver for robotics problems

This dissertation attempts to address two important problems in systems engineering, namely, multicriteria optimization and robustness optimization. In fields ranging from engineering to the social sciences designers are very often required to make decisions that attempt to optimize several criteria or objectives at once. Mathematically this amounts to finding the Pareto optimal set of points for these constrained multiple criteria optimization problems which happen to be nonlinear in many realistic situations, particularly in engineering design. Traditional techniques for nonlinear multicriteria optimization suffer from various drawbacks. The popular method of minimizing weighted sums of the multiple objectives suffers from the deficiency that choosing an even spread of 'weights' does not yield an even spread of points on the Pareto surface and further this spread is often quite sensitive to the relative scales of the functions. A continuation/homotopy based strategy for tracing out the Pareto curve tries to make up for this deficiency, but unfortunately requires exact second derivative information and further cannot be applied to problems with more than two objectives in general. Another technique, goal programming, requires prior knowledge of feasible goals which may not be easily available for more than two objectives. Normal-Boundary Intersection (NBI), a new technique introduced in this dissertation, overcomes all of the difficulties inherent in the existing techniques by introducing a better parametrization of the Pareto set. It is rigorously proved that NBI is completely independent of the relative scales of the functions and is quite successful in producing an evenly distributed set of points on the Pareto set given an evenly distributed set of 'NBI parameters' (comparable to the 'weights' in minimizing weighted sums of objectives). Further, this method can easily handle more than two objectives while retaining the computational efficiency of continuation-type algorithms, which is an improvement over homotopy techniques for tracing the trade-off curve. Various aspects of NBI including computational issues and its relationships with minimizing convex combinations and goal programming are discussed in this dissertation. Finally some case studies from engineering disciplines are performed using NBI. The other facet of this dissertation deals with robustness optimization, a concept useful in quantifying the stability of an optimum in the face of random fluctuations in the design variables. This robustness optimization problem is presented as an application of multicriteria optimization since it essentially involves the simultaneous minimization of two criteria, the objective function value at a point and the dispersion in the function values in a neighborhood of the point. Moreover, a formulation of the robustness optimization problem is presented so that it fits the framework of constrained, nonlinear optimization problems, which is an improvement on existing formulations that deal with either unconstrained nonlinear formulations or constrained linear formulations.

Research Doctorate - Doctor of Philosophy (PhD)
Efficient wind turbine control can enhance the performance of the wind turbine operation by increasing the energy yield and reducing the mechanical loads on the turbine components and subsequently reducing maintenance costs. This thesis contributes to this stream of research by investigating the performance of a nonlinear model predictive controller in reducing long-term stress and fatigue on the tower structure of wind turbines. The proposed NMPC incorporates preview wind information (obtained by a LIDAR; LIght Detection and Ranging) in the control problem formulation. The control and state constraints are included in the formulation of the controller yielding smooth handling of loads especially in non-normal operating conditions (e.g., extreme gusts). Furthermore, a specialized cost function that incorporates the classic wind turbine control objectives is implemented. Finally, the continuous-time infinite optimization problem is piece-wise discretized based on the direct single shooting method. The resulting sampled-data finite optimization problem is solved using sequential quadratic programming technique. Comprehensive simulations and analysis in this thesis demonstrate that the proposed NMPC is an effective controller in achieving wind turbine control goals. Furthermore, as the performance and efficiency of the MPC controller is strongly dependent on the accuracy of the prediction model and the quality of the measurements, a robust NMPC controller, based on the scenario-based multi-stage approach, is also proposed. Here, uncertainty in the LIDAR wind measurements is considered. Various simulations are performed and and it is demonstrated that the proposed robust NMPC is capable of handling the uncertainties caused by errors in measuring the wind propagation times.

Over the last few decades, many factors, including increased electrification, have led to a critical need for fast and efficient transient cooling. Thermal management systems (TMSs) are typically designed using steady-state assumptions and to accommodate the most extreme operating conditions that could be encountered, such as maximum expected heat loads. Unfortunately, by designing systems in this manner, closed-loop transient performance is neglected and often constrained. If not constrained, conventional design approaches result in oversized systems that are less efficient under nominal operation. Therefore, it is imperative that \emph{transient} component modeling and subsystem interactions be considered at the design stage to avoid costly future redesigns. Simply put, as technological advances create the need for rapid transient cooling, a new design paradigm is needed to realize next generation systems to meet these demands.

In this thesis, I develop a new design approach for TMSs called hierarchical control co-design (HCCD). More specifically, I develop a HCCD algorithm aimed at optimizing high-fidelity design and control for a TMS across a system hierarchy. This is accomplished in part by integrating system level (SL) CCD with detailed component level (CL) design optimization. The lower-fidelity SL CCD algorithm incorporates feedback control into the design of a TMS to ensure controllability and robust transient response to exogenous disturbances, and the higher-fidelity CL design optimization algorithms provide a way of designing detailed components to achieve the desired performance needed at the SL. Key specifications are passed back and forth between levels of the hierarchy at each iteration to converge on an optimal design that is responsive to desired objectives at each level. The resulting HCCD algorithm permits the design and control of a TMS that is not only optimized for steady-state efficiency, but that can be designed for robustness to transient disturbances while achieving said disturbance rejection with minimal compromise to system efficiency. Several case studies are used to demonstrate the utility of the algorithm in designing systems with different objectives. Additionally, high-fidelity thermal modeling software is used to validate a solution to the proposed model-based design process.