Nov 29 (Tue) @ 11:00am:”Design and Analysis of Hybrid and Hybrid-Inspired Control Systems in Stochastic and Non-Stochastic Settings,” Matina Baradaran, ECE PhD Defense
Abstract
This talk is divided into three parts. In the first part, a class of stochastic dynamical systems designed to solve non-convex optimization problems on smooth manifolds is presented. We develop the stochastic, hybrid optimization algorithm and show that the proposed dynamics combine continuous-time flows, characterized by a differential equation, and discrete-time jumps, characterized by a stochastic difference inclusion in order to guarantee convergence with probability one to the set of global minimizers of the cost function. By using the framework of stochastic hybrid inclusions, a detailed stability characterization of the dynamics, as well as extensions to address learning problems on manifolds, and optimization on a unit sphere with half-space constraints is given.
In the second part, we characterize the asymptotic behavior that results from switching among asymptotically stable systems with distinct equilibria when the switching frequency satisfies an average dwell-time constraint with a small average rate. The asymptotic characterization is in terms of the Omega-limit set of an associated ideal hybrid system containing an average dwell-time automaton with the rate parameter set equal to zero. This set is globally asymptotically stable for the ideal system. The actual switched system, including small disturbances, constitutes a small perturbation of this ideal system, resulting in semi-global, practical asymptotic stability. We then consider some convex optimization engineering challenges, such as those involving multi-agent systems and resource allocation, where the objective function can persistently switch during the execution of an optimization algorithm. Motivated by such applications, we analyze the effect of persistently switching objectives in continuous-time optimization algorithms. In particular, we extend our results for switched systems with distinct equilibria to systems described by differential inclusions, making the results applicable to recent optimization algorithms that employ differential inclusions for improving efficiency and/or robustness.
In the last part, the Input-to-state stability (ISS) is considered for a nonlinear “soft-reset” system with inputs. The latter is a system that approximates a hard-reset system, which is modeled as a hybrid system with inputs. In contrast, a soft-reset system is modeled as a differential inclusion with inputs. Lyapunov conditions on the hard-reset system are given that guarantee ISS for the soft-reset system. In turn, it is shown when global asymptotic stability for the origin of the zero-input reset system guarantees ISS for nonzero inputs.
Bio
Matina is a Ph.D. candidate at the Center for Control, Dynamical Systems and Computation in the Department of Electrical and Computer Engineering at the University of California, Santa Barbara. She received her M.S. degree in Electrical and Computer Engineering from USCB in 2019 and her B. Eng. from Aachen University of Applied Sciences, Germany in 2015. During her graduate studies, she interned at Bosch Research and Technology Center, Romeo Power, and Bloom Energy.
Hosted by: Prof. Andrew R. Teel
Submitted by: Matina Baradaran Hosseini <baradaranhosseini@ucsb.edu>
