Algebraic, Computational, and Data-Driven Methods for Control-Theoretic Analysis and Learning of Ensemble Systems
Date of Award
Doctor of Philosophy (PhD)
In this thesis, we study a class of problems involving a population of dynamical systems under a common control signal, namely, ensemble systems, through both control-theoretic and data-driven perspectives. These problems are stemmed from the growing need to understand and manipulate large collections of dynamical systems in emerging scientific areas such as quantum control, neuroscience, and magnetic resonance imaging. We examine fundamental control-theoretic properties such as ensemble controllability of ensemble systems and ensemble reachability of ensemble states, and propose ensemble control design approaches to devise control signals that steer ensemble systems to desired profiles. We show that these control-theoretic properties of ensemble systems can be well-understood by customized algebraic and geometric approaches. Furthermore, we investigate the problem of manipulating ensemble systems using aggregated measurements, i.e., observations collected from the population level of the ensemble. We discuss observability of ensemble systems through aggregated measurements and apply data-driven approaches not only to recognize ensemble systems but also to cluster multiple ensemble systems with unknown systems dynamics. The new mathematical structures arising from these problems are excellent motivations for studying the control and learning of ensemble systems.
Bruno Sinopoli, Shen Zeng, Tao Ju, Ulugbek Kamilov,
Available for download on Saturday, August 19, 2023
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