Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control
Abstract: In this talk, we revisit the Linear Quadratic Gaussian (LQG) control, one of the most fundamental problems in optimal control, and present recent progress towards its landscape analysis from a modern optimization perspective. We view the LQG cost as a function of the controller parameters and study its analytical and geometrical properties. The LQG landscape is very rich yet complicated due to the inherent symmetry induced by similarity transformations. We show that 1) the set of stabilizing controllers has at most two path-connected components, and they are diffeomorphic under a mapping defined by a similarity transformation; 2) there might exist many strictly suboptimal stationary points of the LQG cost function and these stationary points are always non-minimal; and 3) despite the nonconvexity, all minimal stationary points (controllable and observable controllers) are globally optimal, and they are identical up to a similarity transformation. These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem.
The talk is based on our recent paper: https://arxiv.org/pdf/2102.04393.pdf.
Bio: Yang Zheng is an assistant professor in the ECE department at UC San Diego. Yang Zheng received the DPhil (Ph.D.) degree in Engineering Science from the University of Oxford in 2019. He received the B.E. and M.S. degrees from Tsinghua University in 2013 and 2015, respectively. From February 2019 to August 2020, he was a postdoctoral researcher at Harvard University. He was a research associate at Imperial College London in 2021.
Dr. Zheng’s research interests include learning, optimization, and control of network systems, and their applications to cyber-physical systems, autonomous vehicles, and traffic systems. His work has been acknowledged by several awards, including the 2019 European Ph.D. Award on Control for Complex and Heterogeneous Systems, the Best Student Paper Award Finalist at the 2019 European Control Conference, the Best Student Paper Award at the 17th IEEE International Conference on Intelligent Transportation Systems, and the Best Paper Award at the 14th Intelligent Transportation Systems Asia-Pacific Forum. He received the National Scholarship, Outstanding Graduate at Tsinghua University, the Clarendon Scholarship at the University of Oxford, and the Chinese Government Award for Outstanding Self-financed Students Abroad.