Adaptive optimal tracking control for continuous-time systems using identifier-critic based dynamic programming

This paper proposes an optimal tracking control of completely unknown affine nonlinear systems using a system augmentation scheme and a modified discounted performance function, where the feedforward and feedback control actions can be obtained simultaneously. We first present an adaptive identifier to estimate the unknown dynamics, where the estimated parameters are updated based on a new adaptive law such that these estimated parameters converge to a small neighborhood around their true values. An augmented system consisting of the tracking error and the generator of the trajectory to be tracked are then constructed, which derives an augmented tracking Hamilton-Jacobi-Bellman (HJB) equation. An online critic neural network (NN) is finally presented to approximate the optimal value function of HJB equation, and then calculate the optimal control action. This leads to an identifier-critic based adaptive dynamic programming (ADP) structure. Simulation results are presented to demonstrate the effectiveness of the proposed method.