Policy Optimization Methods for Linear Quadratic Regulator

My research focuses on innovative policy optimization methods for the continuous-time Linear Quadratic Regulator (LQR) problem with an infinite time horizon. One part of this work involves the development of dynamic state-feedback controllers, known as policy gradient flows, that efficiently solve the LQR problem. These dynamic controllers can stabilize polytopic linear parameter-varying systems even in the presence of abrupt parameter changes. This approach enables online solutions to the time-varying LQR problem, thereby improving the transient performance of the closed-loop system.

In addition, I develop data-driven policy optimization methods that learn optimal feedback directly from measured input and state data without explicit system identification. In this context, I investigate both behavioral system parameterizations and integral reinforcement learning approaches, from which I develop novel data-driven gradient flows, policy iterations, convex optimization methods, and a data-driven continuous-time algebraic Riccati equation. My work bridges classical control methods, reinforcement learning techniques, and data-driven approaches.