Published: Sept. 10, 2019

Jorge Poveda

Department of Electrical, Computer, and Energy Engineering; University of Colorado Boulder

Real-Time Optimization with Robustness and Acceleration via Hybrid Dynamical Systems and Averaging Theory

In this talk we will discuss robust and accelerated zero-order algorithms for the solution of black-box optimization problems in dynamical systems. In particular, we will introduce a family of novel derivative-free dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems with resetting mechanisms. From this family of dynamics, we synthesize four algorithms designed for convex, strongly convex, constrained, and unconstrained zero-order optimization problems. For each case, we establish semi-global practical asymptotic or exponential stability results, and we show how to construct well-posed discretized algorithms that retain the main properties of the algorithms. Given that existing averaging theorems for singularly perturbed hybrid systems are not directly applicable to our setting, we derive a new averaging theorem that relaxes some of the existing assumptions required to apply averaging theory in hybrid systems. This allows us to make a clear link between the $\mathcal{K}\mathcal{L}$ bounds that characterize the rates of convergence of the average system and the original algorithms. We also show that our results are applicable to non-hybrid zero-order dynamics modeled as ODEs, thus providing a unifying framework for hybrid and non-hybrid zero-order dynamics. The performance of the algorithms will be illustrated via numerical examples. Potential extensions to game-theoretic and multi-agent settings will also be discussed.

Speaker Bio: Prof. Jorge I. Poveda received in 2016 and 2018 the M.Sc. and Ph.D. degrees in Electrical and Computer Engineering from the University of California at Santa Barbara. He is an Assistant Professor in the Department of Electrical, Computer, and Energy Engineering at the University of Colorado, Boulder. Before joining CU, he was a Postdoctoral Fellow at Harvard University in 2018, and a Research Intern at the Mitsubishi Electric Research Laboratory during the summers of 2017 and 2016. He was a Best Student Paper Award finalist at the 2017 IEEE Conference on Decision and Control. His research interests lie a the intersection of adaptive control, game theory, and hybrid dynamical systems theory, with applications in optimization and control of cyber-physical systems.