ADP-Based Robust Tracking Control for a Class of Nonlinear Systems with Unmatched Uncertainties

In this paper, an approximately optimal control strategy is developed for the tracking control of a class of continuous-time nonlinear systems with unmatched uncertainties. By transforming the unmatched uncertain term, the auxiliary system associated with the uncertain nonlinear system is established. The auxiliary system is divided into steady and transient parts, and the related controllers are separately solved, meanwhile the transient tracking error system is also obtained by introducing the reference system. A neural network-based adaptive dynamic programming method is used to get the approximately optimal tracking control law of uncertain nonlinear systems with a predefined cost function. Furthermore, the ultimately uniform boundedness of neural network weights and the stability of tracking error systems are both proved through Lyapunov theory. Two cases of nonlinear systems with unmatched uncertainties are investigated to illustrate the effectiveness of the proposed robust tracking control strategy.