Fuzzy event-triggered control of fractional-order non-affine systems subject to unknown control directions, communication limitation, output constraints and input nonlinearities

Abstract

In this work, a fuzzy event-triggered control strategy has been developed for uncertain nonlinear non-affine non-strict non-commensurate fractional-order (FO) systems (FOSs) subject to unknown control directions, input nonlinearities, communication limitation, event-triggered input, and output constraints. Five kinds of input nonlinearities are considered and general sort of output constraints is addressed. Based on the FO and integer-order (IO) Lyapunov direct theorems, FO Nussbaum function (NF) technique and backstepping method, a novel fuzzy control approach has been proposed, which can overcome the shortcomings of the existing methods. To satisfy the communication limitation, an event-triggering mechanism has been applied. The actuator is protected against the event-triggered input by embedding a filter between the communication channel and actuator. By adding one additional step to the backstepping method, the closed-loop stability has been established in the presence of the filter. Also, to show the avoidance of the Zeno phenomenon, a modified procedure has been proposed. Unlike previous works, the stability is established with no restrictive assumption for the system dynamics. Fuzzy logic systems (FLSs) have been utilized to overcome the non-strict structure, prevent the complexity in the proposed scheme, and estimate virtual controllers derivatives, system unknown dynamics and unknown input nonlinearities. By decreasing the number of adaptive laws for FLSs weight vectors, the computational load has been reduced. It is shown that the system output closely follows the desired signal inside the predefined limits and all closed-loop signals remain bounded. Through three examples, the effectiveness of the proposed control algorithm is illustrated.