Electrical & Computer Engineering Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2765
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Item Optimality, Synthesis and a Continuum Model for Collective Motion(2019) Halder, Udit; Krishnaprasad, Perinkulam S.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)It is of importance to study biological collectives and apply the wisdom so accrued to modern day engineering problems. In this dissertation we attempt to gain insight into collective behavior where the main contribution is twofold. First, a `bottom-up' approach is employed to study individual level control law synthesis and emergence thereby of collective behavior. Three different problems, involving single and multiple agents, are studied by both analytical and experimental means. These problems arise from either a practical viewpoint or from attempts at describing biologically plausible feedback mechanisms. One result obtained in this context for a double agent scenario is that under a particular constant bearing pursuit strategy, the problem exhibits certain features common with the Kepler two body problem. Laboratory demonstrations of the solutions to these problems are presented. It is to be noted that these types of individual level control problems can help understand and construct building blocks for group level behaviors. The second approach is `top-down' in nature. It treats a collective as a whole and asks if its movement minimizes some kind of energy functional. A key goal of this work is to develop wave equations and their solutions for a natural class of optimal control problems with which one can analyze information transfer in flocks. Controllability arguments in infinite dimensional spaces give strong support to construct solutions for such optimal control problems. Since the optimal control problems are infinite dimensional in the state space and one cannot simply expect Pontryagin's Maximum Principle (PMP) to apply in such a setting, the work has required care and attention to functional analytic considerations. In this work, it is shown that under a certain assumption on finite co-dimensionality of a reachable set, PMP remains valid. This assumption is then shown to hold true for the case of a specific ensemble of agents, each with state space as the Heisenberg group H(3). Moreover, analysis of optimal controls demonstrates the existence of traveling wave solutions in that setting. Synchronization results are obtained in a high coupling limit where deviation from neighbors is too costly for every agent. The combination of approaches based on PMP and calculus of variations have been fruitful in developing a solid new understanding of wave phenomena in collectives. We provide partial results along these lines for the case of a continuum of planar agents (SE(2) case). Finally, a different top-down and data-driven approach to analyze collective behavior is also put forward in this thesis. It is known that the total kinetic energy of a flock can be divided into several modes attributed to rigid-body translations, rotations, volume changes, etc. Flight recordings of multiple events of European starling flocks yield time-signals of these different energy modes. This approach then seeks an explanation of kinetic energy mode distributions (viewed as flock-scale decisions) by appealing to techniques from evolutionary game theory and optimal control theory. We propose the notion of cognitive cost that calculates a suitably defined action functional and measures the cost to an event, resulting from temporal variations of energy mode distributions.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.