By Prashant Girdharilal Mehta (University of Illinois)
Talk Abstract: This talk is concerned with optimal control problems for control systems in continuous time, and interacting particle system methods designed to construct approximate control solutions. Particular attention is given to the linear quadratic (LQ) control problem. There is a growing interest in revisiting this classical problem, in part due to the successes of model-based reinforcement learning (RL). The main question of this body of research (and also of our work) is to approximate the optimal control law without explicitly solving the Riccati equation.
In this talk, a novel simulation-based algorithm, namely a dual ensemble Kalman filter (EnKF), is introduced. The algorithm is used to obtain formulae for optimal control, expressed entirely in terms of the EnKF particles. An extension to the nonlinear case is also presented. The theoretical results and algorithms are illustrated with numerical experiments against the state-of-the-art.
This is joint work with Anant Joshi, Amirhossein Taghvaei and Sean Meyn. The talk is closely based on the paper.
Speaker Bio: Prashant Mehta is a Professor in the Coordinated Science Laboratory and the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign (UIUC). He received his Ph.D. in Applied Mathematics from Cornell University in 2004. He was the co-founder and the Chief Science Officer of the startup Rithmio whose gesture recognition technology was acquired by Bosch Sensortec in 2017. Prior to his academic appointment at UIUC in 2005, he worked at United Technologies Research Center (UTRC) where he invented the symmetry-breaking solution to suppress combustion instabilities. This solution — which helped solve a sixty-year old open problem — has since become an industry standard and is widely deployed in jet engines and afterburners sold by Pratt & Whitney.
Prashant Mehta received the Outstanding Achievement Award at UTRC for his contributions to modeling and control of combustion instabilities in jet-engines. His students have received the Best Student Paper Awards at the IEEE Conference on Decision and Control in 2007, 2009 and most recently in 2019; and have been finalists for these awards in 2010 and 2012. He serves as an Associate Editor for the IEEE Transactions on Automatic Control (2019-), the Systems and Control Letters (2011-14), and the ASME Journal of Dynamic Systems, Measurement and Control (2012-16).