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Control Seminar

When can hybrid systems operate safely?

Matthew D. KvalheimPostdoctoral FellowUniversity of Pennsylvania

ABSTRACT: Safe behavior is not always achievable for nonlinear control systems. For classical systems, this follows from significant extensions [1] of results [2] 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 [3]. 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?

[1] M. D. Kvalheim and D. E. Koditschek. “Necessary conditions for feedback stabilization and safety.” Journal of Geometric Mechanics, Under Review (2021). arXiv:2106.00215
[2] R. W. Brockett. “Asymptotic stability and feedback stabilization.” Differential geometric control theory, 27.1 (1983), pp. 181–191.
[3] 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.

***Event will take place via Zoom. Zoom link and password will be distributed to the Controls Group e-mail list-serv. To join this list-serv, please send an (empty) email message to control_seminar-join@eecs.umich.edu with the word “subscribe” in the subject line. Zoom information is also available upon request to Katherine Godwin (ktgdwn@umich.edu).

Sponsored by

UM ECEBoschFordToyota

Faculty Host

Shai RevzenAssociate Professor of ECEUniversity of Michigan