Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

Abstract

Although robust regulation problem has been well studied, solving robust tracking control via online learning has not been fully solved, in particular for nonlinear systems. This paper develops an online adaptive learning technique to complete the robust tracking control design for nonlinear uncertain systems, which uses the ideas of adaptive dynamic programming (ADP) proposed for optimal control. An augmented system is first constructed using the tracking error and reference trajectory, so as to reformulate the tracking control into a modified robust regulation problem. Then, an equivalence between the robust control and the optimal control is established by using a constructive discounted cost function, which allows to design the robust control by tackling the optimal control of its nominal system. Then, the derived Hamilton–Jacobi-Bellman (HJB) equation is solved by training a critic neural network (NN). Finally, an adaptive learning algorithm is adopted to online directly update the unknown NN weights, where the convergence can be guaranteed. The closed-loop system stability is rigorously proved and extensive simulation results are given to show the effectiveness of the developed learning algorithm.