Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation.

This paper studies the issue of adaptive hybrid fuzzy output feedback control for a class of commensurate fractional-order (FO) nonlinear systems with time-varying delays and input saturation. First, a hybrid fuzzy state observer is designed to estimate the unmeasured system states, where the neuro-fuzzy network systems (NFNSs) are introduced to handle the unknown nonlinear functions. Furthermore, based on DSC technique, a modified FO filter is designed to avoid the issue of the “explosion of complexity” generated by the traditional backstepping control design approach. Moreover, based on the recursive technique and an indirect Lyapunov method, an adaptive controller is constructed to ensure that all the signals of FO closed-loop systems are bounded. Finally, the simulation results are presented to demonstrate the effectiveness of the presented control scheme.