Wavelet-based adaptive robust control for a class of MIMO uncertain nonlinear systems

In this study, a wavelet neural network (WNN)-based adaptive robust control (WARC) strategy is investigated to resolve the tracking control problem of a class of multi-input multi-output (MIMO) uncertain nonlinear systems. The proposed control system comprises of an adaptive wavelet controller and a robust controller. The adaptive wavelet controller acts as the main tracking controller, which is designed via a WNN to mimic the merits of a feedback linearization control (FLC) law. The proportional-integral (PI) adaptation laws of the MIMO control system are derived from the Lyapunov stability theorem, which are utilized to update the adjustable parameters of WNN on-line for further assuring system stability and obtaining a fast convergence. Moreover, based on H _∞ control technique, the robust controller is developed to attenuate the effect of the approximation error caused by WNN approximator, so that the desired tracking performance can be achieved. Finally, two MIMO uncertain nonlinear systems, the ecological system and the unified chaotic system, are performed to verify the effectiveness and robustness of the proposed WARC strategy. Furthermore, the salient merits are also indicated in comparison with the FLC system.