An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problem

In this paper, an off-policy reinforcement learning algorithm is designed to solve the continuous-time linear quadratic regulator (LQR) problem using only input-state data measured from the system. Different from other algorithms in the literature, we propose the use of a specific persistently ex-citing input as the exploration signal during the data collection step. We then show that, using this persistently excited data, the solution of the matrix equation in our algorithm is guaranteed to exist and to be unique at every iteration. Convergence of the algorithm to the optimal control input is also proven. Moreover, we formulate the policy evaluation step as the solution of a Sylvester-transpose equation, which increases the efficiency of its solution. A method to determine an initial stabilizing policy using only measured data is proposed. Finally, the advantages of the proposed method are tested via simulation.