Approximate optimal tracking control for continuous-time unknown nonlinear systems

This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control for continuous-time nonlinear systems with unknown system dynamics, which is achieved in terms of a novel identifier-critic based approximate dynamic programming (ADP) structure. To obviate the requirement of complete knowledge of system dynamics, an adaptive neural network (NN) identifier is designed with a novel adaptive law. A steady-state control in conjunction with an adaptive optimal control is proposed to stabilize the tracking error dynamics in an optimal manner. A critic NN is utilized to approximate the optimal value function and to obtain the optimal control action. Novel adaptive laws based on parameter estimation error are developed to guarantee that both the identifier NN weights and critic NN weights converge to small neighborhoods of their ideal values. The closed-loop system stability and the convergence to the optimal solution are all proved based on Lyapunov theory. Simulation results exemplify the efficacy of the proposed methods.