Online adaptive learning of optimal control solutions using integral reinforcement learning

In this paper we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous-time optimal control solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data based approach to the solution of the Hamilton-Jacobi-Bellman equation and it does not require explicit knowledge on the system´s drift dynamics. The adaptive algorithm is based on policy iteration, and it is implemented on an actor/critic structure. Both actor and critic neural networks are adapted simultaneously a persistence of excitation condition is required to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for both critic and actor networks, with extra terms in the actor tuning law being required to guarantee closed-loop dynamical stability. The convergence to the optimal controller is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result.