Learning-based optimal control of linear time-varying systems over large time intervals

We solve the problem of two -point boundary optimal control of linear time -varying systems with unknown model dynamics using reinforcement learning. Leveraging singular perturbation theory techniques, we transform the time -varying optimal control problem into two time -invariant subproblems. This allows using 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 approximation accuracy improves as the control problem's time horizon increases. We also provide a simulation example to verify the results.