Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Learning in Large Multi-Agent Systems(2024) Kara, Semih; Martins, Nuno C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we study a framework of large-scale multi-agent strategic interactions. The agents are nondescript and use a learning rule to repeatedly revise their strategies based on their payoffs. Within this setting, our results are structured around three main themes: (i) Guaranteed learning of Nash equilibria, (ii) The inverse problem, i.e. estimating the payoff mechanism from the agents' strategy choices, and (iii) Applications to the placement of electric vehicle charging stations. In the traditional setup, the agents' inter-revision times follow identical and independent exponential distributions. We expand on this by allowing these intervals to depend on the agents' strategies or have Erlang distributions. These extensions enhance the framework's modeling capabilities, enabling it to address problems such as task allocation with varying service times or multiple stages. We also explore a third generalization, concerning the accessibility among strategies. Majority of the existing literature assume that the agents can transition between any two strategies, whereas we allow only certain alternatives to be accessible from certain others. This adjustment further improves the framework's modeling capabilities, such as by incorporating constraints on strategy switching related to spatial and informational factors. For all of these extensions, we use Lyapunov's method and passivity-based techniques to find conditions on the revision rates, learning rule, and payoff mechanism that ensure the agents learn to play a Nash equilibrium of the payoff mechanism. For our second class of problems, we adopt a multi-agent inverse reinforcement learning perspective. Here, we assume that the learning rule is known but, unlike in existing work, the payoff mechanism is unknown. We propose a method to estimate the unknown payoff mechanism from sample path observations of the populations' strategy profile. Our approach is two-fold: We estimate the agents' strategy transitioning probabilities, which we then use - along with the known learning rule - to obtain a payoff mechanism estimate. Our findings regarding the estimation of transitioning probabilities are general, while for the second step, we focus on linear payoff mechanisms and three well-known learning rules (Smith, replicator, and Brown-von Neumann-Nash). Additionally, under certain assumptions, we show that we can use the payoff mechanism estimate to predict the Nash equilibria of the unknown mechanism and forecast the strategy profile induced by other rules. Lastly, we contribute to a traffic simulation tool by integrating electric vehicles, their charging behaviors, and charging stations. This simulation tool is based on spatial-queueing principles and, although less detailed than some microscopic simulators, it runs much faster and accurately represents traffic rules. Using this tool, we identify optimal charging station locations (on real roadway networks) that minimize the overall traffic.Item Optimization-based Robustness and Stabilization in Decentralized Control(2017) Alavian, Alborz; Rotkowitz, Michael C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation pertains to the stabilization, robustness, and optimization of Finite Dimensional Linear Time Invariant (FDLTI) decentralized control systems. We study these concepts for FDLTI systems subject to decentralizations that emerge from imposing sparsity constraints on the controller. While these concepts are well-understood in absence of an information structure, they continue to raise fundamental interesting questions regarding an optimal controller, or on suitable notions of robustness in presence of information structures. Two notions of stabilizability with respect to decentralized controllers are considered. First, the seminal result of Wang & Davison in 1973 regarding internal stabilizability of perfectly decentralized system and its connection to the decentralized fixed-modes of the plant is revisited. This seminal result would be generalized to any arbitrary sparsity-induced information structure by providing an inductive proof that verifies and shows that those mode of the plant that are fixed with respect to the static controllers would remain fixed with respect to the dynamic ones. A constructive proof is also provided to show that one can move any non-fixed mode of the plant to any arbitrary location within desired accuracy provided that they remain symmetric in the complex plane. A synthesizing algorithm would then be derived from the inductive proof. A second stronger notion of stability referred to as "non-overshooting stability" is then addressed. A key property called "feedthrough consistency" is derived, that when satisfied, makes extension of the centralized results to the decentralized case possible. Synthesis of decentralized controllers to optimize an H_Infinity norm for model-matching problems is considered next. This model-matching problem corresponds to an infinite-dimensional convex optimization problem. We study a finite-dimensional parametrization, and show that once the poles are chosen for this parametrization, the remaining problem of coefficient optimization can be cast as a semidefinite program (SDP). We further demonstrate how to use first-order methods when the SDP is too large or when a first-order method is otherwise desired. This leaves the remaining choice of poles, for which we develop and discuss several methods to better select the most effective poles among many candidates, and to systematically improve their location using convex optimization techniques. Controllability of LTI systems with decentralized controllers is then studied. Whether an LTI system is controllable (by LTI controllers) with respect to a given information structure can be determined by testing for fixed modes, but this gives a binary answer with no information about robustness. Measures have already been developed to determine how far a system is from having a fixed mode when one considers complex or real perturbations to the state-space matrices. These measures involve intractable minimizations of a non-convex singular value over a power-set, and hence cannot be computed except for the smallest of the plants. We replace these problem by equivalent optimization problems that involve a binary vector rather than the power-set minimization and prove their equality. Approximate forms are also provided that would upper bound the original metrics, and enable us to utilize MINLP techniques to derive scalable upper bounds. We also show that we can formulate lower bounds for these measures as polynomial optimization problems,and then use sum-of-squares methods to obtain a sequence of SDPs, whose solutions would lower bound these metrics.Item Optimal Control with Information Pattern Constraints(2011) Sabau, Serban; Martins, Nuno C.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Despite the abundance of available literature that starts with the seminal paper of Wang and Davison almost forty years ago, when dealing with the problem of decentralized control for linear dynamical systems, one faces a surprising lack of general design methods, implementable via computationally tractable algorithms. This is mainly due to the fact that for decentralized control configurations, the classical control theoretical framework falls short in providing a systematic analysis of the stabilization problem, let alone cope with additional optimality criteria. Recently, a significant leap occurred through the theoretical machinery developed in Rotkowitz and Lall, IEEE-TAC, vol. 51, 2006, pp. 274-286 which unifies and consolidates many previous results, pinpoints certain tractable decentralized control structures, and outlines the most general known class of convex problems in decentralized control. The decentralized setting is modeled via the structured sparsity constraints paradigm, which proves to be a simple and effective way to formalize many decentralized configurations where the controller feature a given sparsity pattern. Rotkowitz and Lall propose a computationally tractable algorithm for the design of H2 optimal, decentralized controllers for linear and time invariant systems, provided that the plant is strongly stabilizable. The method is built on the assumption that the sparsity constraints imposed on the controller satisfy a certain condition (named quadratic invariance) with respect to the plant and that some decentralized, strongly stablizable, stabilizing controller is available beforehand. For this class of decentralized feedback configurations modeled via sparsity constraints, so called quadratically invariant, we provided complete solutions to several open problems. Firstly, the strong stabilizability assumption was removed via the so called coordinate free parametrization of all, sparsity constrained controllers. Next we have addressed the unsolved problem of stabilizability/stabilization via sparse controllers, using a particular form of the celebrated Youla parametrization. Finally, a new result related to the optimal disturbance attenuation problem in the presence of stable plant perturbations is presented. This result is also valid for quadratically invariant, decentralized feedback configurations. Each result provides a computational, numerically tractable algorithm which is meaningful in the synthesis of sparsity constrained optimal controllers.