Multivariable Adaptive Fuzzy CMAC Control for a Class of Nonlinear Systems

Abstract

In this paper, a modified multivariable adaptive fuzzy cerebellar model articulation controller (CMAC) scheme is proposed to solve the tracking problem for a class of nonlinear systems. A FCMAC (fuzzy CMAC) module is used to approximate a nonlinear multivariable (multi-input multi-output (MIMO)) system involving uncertainty to create the desired ideal control inputs. Suitable control and adaptive laws with output feedback based on sliding surface concept are incorporated with FCMAC to yield a MIMO adaptive FCMAC (MIMO AFCMAC) control system without prior off-line learning phase required. To overcome the chattering problem associated with discontinuity derived from conventional switching robust compensation, a smooth compensation is proposed. By Lyapunov stability analysis, it is shown that all of the closed-loop signals are bounded, and the tracking errors converge exponentially to a residual set, whose size can be controlled. While the tracking precision may be sacrificed slightly, the quality of the control signal can be improved significantly. Simulation results are presented to demonstrate the validity and the applicability of the proposed methodology.