Off-policy Reinforcement Learning for a Robust Optimal Control Problem with Real Parametric Uncertainty

This paper addresses an off-policy Reinforcement learning algorithm for robust linear quadratic regulator (R-LQR) problem of continuous-time linear dynamical systems with parametric uncertainties based on policy iteration framework. A modified algebraic Riccati equation is presented for the R-LQR problem and is further transformed into standard linear quadratic regulator problem. The proposed model-free off-policy R-LQR algorithm learns the control policy using generated data samples that obviate the requirement of system dynamics. Numerical simulation examples of spring-mass system with uncertain stiffness are provided to illustrate effectiveness of the approach.