Electrical & Computer Engineering Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2765
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Item Mean-field Approaches in Multi-agent Systems: Learning and Control(2023) Tirumalai, Amoolya; Baras, John S; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In many settings in physics, chemistry, biology, and sociology, when individuals (particles) interact in large collectives, they begin to behave in emergent ways. This is to say that their collective behavior is altogether different from their individual behavior. In physics and chemistry, particles interact through the various forces, and this results in the rich behavior of the phases of matter. A particularly interesting case arises in the dynamics of gaseous star formation. In models of star formation, the gases are subject to the attractive gravitational force, and perhaps viscosity, electromagnetism, or thermal fluctuations. Depending on initial conditions, and inclusion of additional forces in the models, a variety of interesting configurations can arise, from dense nodules of gas to swirling vortices. In biology and sociology, these interactions (forces) can be explicitly tied to chemical or physical phenomena, as in the case of microbial chemotaxis, or they can be more abstract or virtual, as in the case of bird flocking or human pedestrian traffic. We focus on the latter cases in this work. In collective animal or human traffic, we do not say that animals or humans are explicity subject to physical forces that causes them to move in alignment with each other, or whatever else. Rather, they behave as if there were such forces. In short, we use the language and notation of physics and forces as a convenient tool to build our understanding. We do so since natural phenomena are rich with sophisticated and adaptive behavior. Bird flocks rapidly adapt to avoid collisions, to fly around obstacles, and to confuse predators. Engineers today can only dream of building drone swarms with such plasticity. An important question to answer is how one takes a model of interacting individuals and builds a model of a collective. Once one answers this question, another immediately follows: how do we take these models of collectives and use them to discover representations of natural phenomena? Then, can we use these models to build methods to control such phenomena, assuming suitable actuation? Once these questions are answered, our understanding of collective dynamics will improve, broadening the applications we can tackle. In this thesis, we study collective dynamics via mean-field theory. In mean-field theory, an individual is totally anonymous, and so can be removed or permuted from a large collective without changing the collective dynamics significantly. More specifically, when any individual is excluded from the definition of the empirical measure of all the individuals, those empirical measures converge to the same measure, termed the mean-field measure. The mean-field measure is governed by the forward Kolmogorov equation. In certain scenarios where an analogy can be drawn to particle dynamics, these forward Kolmogorov equations can be converted to compressible Euler equations. When optimal control problems are posed on the particle dynamics, in the mean-field limit we obtain a forward Kolmogorov equation coupled to a backward Hamilton-Jacobi-Bellman (-Isaacs) equation (or a stationary analogue of these). This system of equations describes the solution to the mean-field game. The first two problems we explore in this thesis are focused on the system identification (inverse) problem: discover a model of collective dynamics from data. In these problems, we study a generalized hydrodynamic Cucker-Smale-type model of flocking in a bounded region of 3D space. We first prove existence of weak bounded energy solutions and a weak-strong uniqueness principle for our model. Then, we use the model to learn a representation of the dynamics of data associated to a synthetic bird flock. The second two problems we study focus on the control (forward) problem: learn an approximately optimal control for collective dynamics online. We study this first in a relatively simple state-and-control-constrained mean-field game on traffic. In this case, the mean-field term is contained only in the mean-field game's cost. We first numerically study a finite horizon version of this problem. The approach for the first problem is not online. Then, we take an infinite horizon version, and we form a system of approximate dynamic programming ODE-PDEs from the exact dynamic programming PDEs. This approach results in online learning and adapting of the control to the dynamics. We prove this ODE-PDE system has a unique weak solution via semigroup and successive approximation methods. We present a numerical example, and discuss the tradeoffs in this approach. We conclude the thesis by summarizing our results, and discussing future directions and applications in theoretical and practical settings.Item Control and Stabilization of Soft Inverted Pendulum on a Cart(2023) Ajithkumar, Ananth; Chopra, Nikhil Dr.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Underactuated systems are systems that cannot be controlled to track any arbitrary trajectories in their configuration space. In this work, we introduce a novel soft-robotic pendulum on a cart system. This is an underactuated soft-robotic system with two degrees of under-actuation. We model the system, derive the kinematics, and motivated by the control strategies for classical underactuated systems, we study the swing-up control and stabilization of this system around the vertical equilibrium point. The switching-based control law uses an energy-based control for swing-up and LQR for stabilization once the system is within the region of attraction of LQR. The simulation results depict the efficaciousness of the developed control scheme. Further, in this thesis, we discuss the viability and feasibility of feedback linearization, partially feedback-linearize the system, and analyze the zero dynamics of the system.Item Distributed Control for Formula SAE-Type Electric Vehicle(2022) Falco, Samantha Rose; Khaligh, Alireza; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The recent trend in transportation electrification creates an enormous increase in demand for electric vehicles (EVs). Increasingly, electric cars have novel features like autonomous driving and fault tolerance, all of which require additional hardware and computation power. Changes to the electronic control unit (ECU) structure will be needed to make these advances scalable. This thesis examines the driving economic, technical, and societal factors behind needed changes to the existing control structures. It proposes a control platform design to address issues of complexity and scalability. A generic, modular control board structure using the TMS320F2837xS digital signal processor (DSP) is described with several input/output functionalities including a wide range of analog inputs, multiple logic levels for digital pins, CAN communication, and wireless communication capabilities. A distributed control network is built by interconnecting multiple implementations of the control board, each of which has distinct responsibilities dictated by software instead of hardware. A prototype electric vehicle control structure for a Formula SAE electric vehicle was built utilizing a network of three control boards and tested to prove the viability of the proposed concept. Results of these tests and future steps for the project are discussed.Item ESTIMATION AND CONTROL OF NONLINEAR SYSTEMS: MODEL-BASED AND MODEL-FREE APPROACHES(2020) Goswami, Debdipta; Paley, Derek A.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)State estimation and subsequent controller design for a general nonlinear system is an important problem that have been studied over the past decades. Many applications, e.g., atmospheric and oceanic sampling or lift control of an airfoil, display strongly nonlinear dynamics with very high dimensionality. Some of these applications use smaller underwater or aerial sensing platforms with insufficient on-board computation power to use a Monte-Carlo approach of particle filters. Hence, they need a computationally efficient filtering method for state-estimation without a severe penalty on the performance. On the other hand, the difficulty of obtaining a reliable model of the underlying system, e.g., a high-dimensional fluid dynamical environment or vehicle flow in a complex traffic network, calls for the design of a data-driven estimation and controller when abundant measurements are present from a variety of sensors. This dissertation places these problems in two broad categories: model-based and model-free estimation and output feedback. In the first part of the dissertation, a semi-parametric method with Gaussian mixture model (GMM) is used to approximate the unknown density of states. Then a Kalman filter and its nonlinear variants are employed to propagate and update each Gaussian mode with a Bayesian update rule. The linear observation model permits a Kalman filter covariance update for each Gaussian mode. The estimation error is shown to be stochastically bounded and this is illustrated numerically. The estimate is used in an observer-based feedback control to stabilize a general closed-loop system. A transferoperator- based approach is then proposed for the motion update for Bayesian filtering of a nonlinear system. A finite-dimensional approximation of the Perron-Frobenius (PF) operator yields a method called constrained Ulam dynamic mode decomposition (CUDMD). This algorithm is applied for output feedback of a pitching airfoil in unsteady flow. For the second part, an echo-state network (ESN) based approach equipped with an ensemble Kalman filter is proposed for data-driven estimation of a nonlinear system from a time series. A random reservoir of recurrent neural connections with the echo-state property (ESP) is trained from a time-series data. It is then used as a model-predictor for an ensemble Kalman filter for sparse estimation. The proposed data-driven estimation method is applied to predict the traffic flow from a set of mobility data of the UMD campus. A data-driven model-identification and controller design is also developed for control-affine nonlinear systems that are ubiquitous in several aerospace applications. We seek to find an approximate linear/bilinear representation of these nonlinear systems from data using the extended dynamic mode decomposition algorithm (EDMD) and apply Liealgebraic methods to analyze the controllability and design a controller. The proposed method utilizes the Koopman canonical transform (KCT) to approximate the dynamics into a bilinear system (Koopman bilinear form) under certain assumptions. The accuracy of this approximation is then analytically justified with the universal approximation property of the Koopman eigenfunctions. The resulting bilinear system is then subjected to controllability analysis using the Myhill semigroup and Lie algebraic structures, and a fixed endpoint optimal controller is designed using the Pontryagin’s principle.Item Optimality of Event-Based Policies for Decentralized Estimation over Shared Networks(2016) Vasconcelos, Marcos Muller; Martins, Nuno C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Cyber-physical systems often consist of multiple non-collocated components that sense, exchange information and act as a team through a network. Although this new paradigm provides convenience, flexibility and robustness to modern systems, design methods to achieve optimal performance are elusive as they must account for certain detrimental characteristics of the underlying network. These include constrained connectivity among agents, rate-limited communication links, physical noise at the antennas, packet drops and interference. We propose a new class of problems in optimal networked estimation where multiple sensors operating as a team communicate their measurements to a fusion center over an interference prone network modeled by a collision channel. Using a team decision theoretic approach, we characterize jointly optimal communication policies for one-shot problems under different performance criteria. First we study the problem of estimating two independent continuous random variables observed by two different sensors communicating with a fusion center over a collision channel. For a minimum mean squared estimation error criterion, we show that there exist team-optimal strategies where each sensor uses a threshold policy. This result is independent of the distribution of the observations and, can be extended to vector observations and to any number of sensors. Consequently, the existence of team-optimal threshold policies is a result of practical significance, because it can be applied to a wide class of systems without requiring collision avoidance protocols. Next we study the problem of estimating independent discrete random variables over a collision channel. Using two different criteria involving the probability of estimation error, we show the existence of team-optimal strategies where the sensors either transmit all but the most likely observation; transmit only the second most likely observation; or remain always silent. These results are also independent of the distributions and are valid for any number of sensors. In our analysis, the proof of the structural result involves the minimization of a concave functional, which is an evidence of the inherent complexity of team decision problems with nonclassical information structure. In the last part of the dissertation, the assumption on the cooperation among sensors is relaxed, and we show that similar structural results can also be obtained for systems with one or more selfish sensors. Finally the assumption of the independence is lifted by introducing the observation of a common random variable in addition to the private observations of each sensor. The structural result obtained provides valuable insights on the characterization of team-optimal policies for a general correlation structure between the observed random variables.Item DISTRIBUTED ESTIMATION OVER NETWORKS WITH COMMUNICATION COSTS(2010) Lipsa, Gabriel-Mihai; Martins, Nuno C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We analyze how distributed or decentralized estimation can be performed over networks, when there is a price to be paid whenever nodes in the network communicate with each other. The work here has application especially in the network control systems. Assume that different nodes in the network can track perfectly or with imperfectly some stochastic processes, while other nodes in the network need to estimate these stochastic processes. The nodes which can observe the stochastic processes can send information directly to the nodes which need to estimate the processes, or information can be sent to intermediate nodes. When each transmission is performed a cost for communication is paid. The goal of the network is to optimize jointly a cost which consists both of a function of the estimation error and a function of the transmission cost. We show here that for some simple topologies the decision to send information over the network is a threshold policy, while the estimators are linear estimators which resemble with the Kalman-filter. For the result dealing with simple topologies we have proved the results using majorization theory. It is also shown here both analytically and numerically that things can immediately become quite complicated. If we take into consideration multidimensional problems or problems with multiple agents and/or transmission noise, the optimal strategies can no longer be found analytically and it can be quite difficult to compute numerically the optimal strategies.Item Application of Chaotic Synchronization and Controlling Chaos to Communications(2005-04-19) Dronov, Vasily; Ott, Edward; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis addresses two important issues that are applicable to chaotic communication systems: synchronization of chaos and controlling chaos. Synchronization of chaos is a naturally occurring phenomenon where one chaotic dynamical system mimics dynamical behavior of another chaotic system. The phenomenon of chaotic synchronization is a popular topic of research, in general, and has attracted much attention within the scientific community. Controlling chaos is another potential engineering application. A unique property of controlling chaos is the ability to cause large long-term impact on the dynamics using arbitrarily small perturbations. This thesis is broken up into three chapters. The first chapter contains a brief introduction to the areas of research of the thesis work, as well as the summaries the work itself. The second chapter is dedicated to the study of a particular situation of chaotic synchronization which leads to a novel structure of the basin of attraction. This chapter also develops theoretical scalings applicable to these systems and compares results of our numerical simulations on three different chaotic systems. The third chapter consists or two logically connected parts (both of them study chaotic systems that can be modeled with delayed differential equations). The first and the main part presents a study of a chaotically behaving traveling wave tube, or TWT, with the objective of improving efficiency of satellite communication systems. In this work we go through an almost complete design cycle, where, given an objective, we begin with developing a nonlinear model for a generic TWT; we then study numerically the dynamics of the proposed model; we find conditions where chaotic behavior occurs (we argue that TWT in chaotic mode could be more power efficient); then we use the idea of controlling chaos for information encoding; we support the concept with numerical simulations; and finally analyze the performance of the proposed chaotic communication system. The second part of this chapter describes an experiment with a pair of electronic circuits modeling the well-known Mackey-Glass equation. An experiment where human voice was encoded into chaotic signal had been conducted which showed a possibility of engineering application of chaos to secure communications.