Observer-based indirect adaptive supervisory control for unknown time delay system

This paper proposes an indirect adaptive fuzzy neural network controller with state observer and supervisory controller for a class of uncertain nonlinear dynamic time-delay systems. The approximate function of unknown time delay system is inferred by the adaptive time delay fuzzy logic system. The supervisory controller, which can be combined with fuzzy neural network controller, will work when error dynamics is great than a constant which is determined by designer. Therefore, if the system is unstable, the supervisory controller will force the state to be stable. The free parameters of the indirect adaptive fuzzy controller can be tuned on-line by observer based output feedback control law and adaptive laws by means of Lyapunov stability criterion. The resulting of 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.