Asymptotically stable adaptive critic design for uncertain nonlinear systems

Recently, Adaptive critic design (ACD) has been applied to controller design extensively. It is a powerful approach to cope with the model nonlinearity and uncertainties. Existing ACD-based controllers have been proven as uniformly ultimately bounded (UUB). However, UUB only makes the tracking error converge to a certain bounded region. Although we can minimize the bounded region by increasing the number of the hidden nodes of the neural networks in the ACD, the computation cost of the ACD-based controller increases. In many engineering applications, we prefer the asymptotical stability which can ensure the tracking error converges to zero. In this paper, we propose a novel asymptotically stable ACD-based controller for a class of uncertain nonlinear systems. This controller firstly uses the feedback linearization to improve the system dynamic characteristics, and then combines ACD and variable structure control to achieve the asymptotical stability under large model uncertainties. An empirical study is conducted on a 2-link manipulator to validate the new controller design approach. Results show that the nonlinear system using the proposed controller can achieve asymptotical stability and good dynamic response characteristics when large model uncertainties exist.