Robust recurrent wavelet-based CMAC control for uncertain nonlinear systems with H∞ tracking performance

In this paper, a robust intelligent tracking control (RITC) system employs a recurrent wavelet-based cerebellar model articulation controller (RWCMAC) is developed for uncertain nonlinear system to achieve H^∞ tracking performance. The dynamic structure of RWCMAC has superior capability to the conventional static cerebellar model articulation controller (CMAC) in efficient learning mechanism and dynamic response. Temporal relations are embedded in RWCMAC by adding feedback connections in the mother wavelet association memory space so that the RWCMAC captures the system dynamic, where the feedback units act as memory elements. In the RITC design, the Taylor linearization technique is employed to increase the learning ability of RWCMAC and the on-line adaptive laws are derived based on the Lyapunov stability analysis, the sliding mode control methodology and the H^∞ control technique so that the stability of the closed-loop system and H^∞ tracking performance can be guaranteed. Finally, the proposed control system is applied to control an inverted pendulum system and a Genesio chaotic system. Simulation results demonstrate that the proposed control scheme can achieve favorable tracking performances for the uncertain nonlinear systems with unknown dynamic functions and under the occurrence of external disturbance.