Indirect Adaptive Fuzzy Supervisory Control with State Observer for Unknown Nonlinear Time Delay System

Abstract

This paper proposes an indirect adaptive fuzzy neural network (FNN) controller with state observer and supervisory controller for a class of uncertain nonlinear dynamic time delay systems. First, the approximate function of unknown time delay system is inferred by the adaptive time delay FNN system. Next, a state observer is designed to estimate the unknown system states and the indirect adaptive fuzzy controller is constructed. Finally, the closed loop controller is obtained by incorporating the supervisory controller with the indirect adaptive fuzzy controller. Therefore, if the system tends to unstable, i.e., error dynamics is larger than a prescribed constraint which is determined by designer, the supervisory controller will activate to force the state to be stable. The free parameters of the indirect adaptive FNN controller can be tuned online by observer-based output feedback control law and adaptive laws by means of Lyapunov stability criterion. The resulting simulation example shows that the performance of nonlinear time delay chaotic system is fully tracking the reference trajectory. Meanwhile, simulation results show that the adaptive control effort of the proposed control scheme is much less due to the assist of the supervisory controller.