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Data-driven system analysis using polynomial optimization and the Koopman operator

Jason Bramburger, Concordia University
Tuesday September 10, 12-1pm
Zoom Link:听
In Person: 550 Sherbrooke, Room 189

Abstract: Many important statements about dynamical systems can be proven by finding scalar-valued auxiliary functions whose time evolution along trajectories obeys certain pointwise inequality that imply the desired result. The most familiar of these auxiliary functions is a Lyapunov function to prove steady-state stability, but such functions can also be used to bound averages of ergodic systems, define trapping boundaries, and so much more. In this talk I will highlight a method of identifying auxiliary functions from data using polynomial optimization. The method leverages recent advances in approximating the Koopman operator from data, so-called extended dynamic mode decomposition, to provide system-level information without system identification. The result is a flexible, data-driven, model-agnostic computational method that does not require explicit model discovery. Furthermore, it can be applied to data generated through deterministic or stochastic processes with no prior adjustments to the implementation. It can be used to bound quantities of interest, develop optimal state-dependent feedback controllers, and discover invariant measures.