When can hybrid systems operate safely?
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ABSTRACT: Safe behavior is not always achievable for nonlinear control systems. For classical systems, this follows from significant extensions  of results  on the fundamental limitations of continuous feedback; circumventing these limitations motivates the introduction of hybrid control. Yet hybrid control systems have their own fundamental limitations, and understanding these is an important challenge for the coming decade. In the closed-loop setting, classes of hybrid dynamical systems with strong properties have recently emerged via topological methods . Will topological points of view also pave the way to an understanding of hybrid control system limitations and, in particular, when safe operation is impossible?
 R. W. Brockett. “Asymptotic stability and feedback stabilization.” Differential geometric control theory, 27.1 (1983), pp. 181–191.
 M. D. Kvalheim, P. Gustafson, and D. E. Koditschek. “Conley’s fundamental theorem for a class of hybrid systems.” SIAM Journal on Applied Dynamical Systems, 20.2 (2021), pp. 784-825.
Preview the seminar with these slides.
BIO: Matthew D. Kvalheim is currently a postdoctoral researcher at the University of Pennsylvania. He received a Ph.D. in electrical engineering (2018), an M.S. in mathematics (2017), and an M.S. in electrical engineering (2017) from the University of Michigan; he received a B.S in electrical engineering (2013) from Ohio University. His general research interests lie in the intersection of dynamics, control, and topology. Specific research interests include invariant manifolds, bifurcations, closed one-forms in dynamics, Morse/Conley theory, hybrid systems, stochastic processes, necessary conditions in control theory, geometric mechanics, and Koopman operators.
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