Abstract:

Optimal feedback control of densities, or distributions in general, is a topic of growing interest in the systems-control community. The mathematical development provides a unified viewpoint with two different interpretations: active control of stochastic uncertainties for a single dynamical system, and shaping the population density of an ensemble of systems. The former finds application in using feedback to allow the system meet desired statistical accuracy. The latter finds application in shaping the concentration of the dynamical agents such as in swarm control, and from this perspective, can be viewed as the continuum limit of the decentralized stochastic optimal control. Recent developments have pointed out that the unifying framework, in fact, subsumes other contemporary problems of interest in physics and machine learning, such as the Schrödinger bridge and the optimal mass transport. I will give a brief summary of the rapid developments emerging from the control literature, and then focus on the theory and algorithms for the case when the underlying trajectory-level evolution has prior nonlinear dynamics. It will be shown that several cases of interest to the control community, such as gradient, mixed conservative-dissipative, and feedback linearizable nonlinearities, lead to tractable theory and algorithms.  We will also discuss application case studies, from power systems to automated driving, to illustrate the scope of the recent progress, and also to highlight the exciting opportunities ahead.

Biography:

Abhishek Halder is an Assistant Professor in the Department of Applied Mathematics, and an affiliated faculty in the Department of Electrical and Computer Engineering at University of California, Santa Cruz. Before that he held postdoctoral positions in the Department of Mechanical and Aerospace Engineering at University of California, Irvine, and in the Department of Electrical and Computer Engineering at Texas A&M University. He obtained his Bachelors and Masters from Indian Institute of Technology Kharagpur in 2008, and Ph.D. from Texas A&M University in 2014, all in Aerospace Engineering. His research interests are in stochastic systems, control and optimization with application focus on large scale cyber-physical systems. He is a co-founder of the annual NorCal Control Workshop that brings together systems-control researchers from academia and industry in the Northern California region fostering collaboration and professional networking. He is the creator and instructor for the course “Feedback Control” in the California State Summer School for Mathematics & Science (COSMOS) which teaches feedback control theory to 8-11 graders without using calculus or linear algebra. Abhishek is a Senior Member of IEEE.