Singular Perturbation-based Reinforcement Learning of Two-Point Boundary Optimal Control Systems

This work presents a technique for learning systems, where the learning process is guided by knowledge of the physics of the system. In particular, we solve the problem of the two-point boundary optimal control problem of linear time-varying systems with unknown model dynamics using reinforcement learning. Borrowing techniques from singular perturbation theory, we transform the time-varying optimal control problem into a couple of time-invariant subproblems. This allows the utilization of an off-policy iteration method to learn the controller gains. We show that the performance of the learning-based controller approximates that of the model-based optimal controller and the accuracy of the approximation improves as the time horizon of the control problem increases. Finally, we provide a simulation example to verify the results of the paper.