  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.
