Robust Stabilization and Trajectory Tracking of General Uncertain Nonlinear Systems

Due to the existence of dynamical uncertainties, it is important to pay attention to the robustness of nonlinear control systems, especially when designing adaptive critic control strategies. In this chapter, based on the neural network learning component, the robust stabilization scheme of nonlinear systems with general uncertainties is developed. Remarkably, the involved uncertain term is more general than the matched case. Through system transformation and employing adaptive critic technique, the approximate optimal controller of the nominal plant can be applied to accomplish robust stabilization for the original uncertain dynamics. The neural network weight vector is very convenient to initialize by virtue of the improved critic learning formulation. Under the action of the approximate optimal control law, the stability issues for the closed-loop form of nominal and uncertain plants are analyzed, respectively. As a generalization result, the robust trajectory tracking method of uncertain nonlinear systems is investigated, where the augmented system construction is performed by combining the tracking error with the reference trajectory. Finally, simulation illustrations via two typical nonlinear systems and a practical power system are included to verify the control performance.