Robust adaptive optimal control for unknown dynamical systems with discontinuous cost function

In this paper, we propose an algorithm to derive an approximated optimal `discontinuous´ cost function and a controller for partially unknown dynamical systems. The algorithm is based on REPI algorithm which we have already proposed, but th new algorithm can deal with a discontinuous cost function explicitly. In general, approximation of a discontinuous function using some smooth basis functions, e.g. RBF, is not valid because of their smoothness. In our method, an approximated function is represented as piecewise differentiable functions. The effectiveness of the proposed method is shown by a numerical simulation.