Composite iterative learning adaptive fuzzy control of fractional-order chaotic systems using robust differentiators

In conventional adaptive fuzzy control, to improve the approximation ability of fuzzy logic systems (FLSs), more fuzzy rules should be employed, which will greatly increase the computational burden. This paper investigates the adaptive fuzzy backstepping control of a specific category of incommensurate fractional -order chaotic systems afflicted by functional uncertainties and actuator faults. To address the challenging "explosion of complexity"issue, a novel modified fractional-order robust differentiator is proposed, capable of effectively suppressing noise. Importantly, an iterative learning adaptation law including parameter errors between adjacent periods and prediction errors derived from a series-parallel model is developed to improve the approximation accuracy of FLSs without using abundant fuzzy rules. Utilizing the frequency distribution model and the Lyapunov stability criterion, this approach guarantees the semi-global uniform boundedness of the closed-loop system and facilitates the convergence of tracking errors to a small region. Finally, the effectiveness of theoretical results is demonstrated through numerical simulation examples.