Adaptive output optimal control algorithm for unknown system dynamics based on policy iteration

In this paper, first we propose an algorithm of adaptive control scheme for systems whose dynamics are unknown and it is shown that the control converges to the approximate optimal state feedback control solution. In the algorithm, we introduce integrators in front of unknown systems, in order to transform the systems into an augmented ones whose input dynamics is known, then, we use policy iteration to find an approximate optimal control input. Second, we propose an extended algorithms, which is an adaptive output optimal control algorithm for systems which are unknown and only output is measurable. Validity are confirmed by numerical simulation.