Fuzzy L 1 adaptive controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

Abstract

This research work proposes a fuzzy fractional-order ${\mathcal{L}}_1$ adaptive controller to deal with projective chaos synchronization problems for a general class of uncertain fractional-order chaotic systems subject to unknown input nonlinearities (dead-zone and sector nonlinearities). The suggested control architecture includes a fractional-order sliding surface, a fuzzy system, and an ${\mathcal{L}}_1$ adaptive controller. The latter consists of a predictor, a control law, and its adaptive mechanism. The fuzzy system takes the role of an online estimator for system nonlinear uncertain functions which helps in the handling of the input nonlinearities. A designed low-pass filter is placed within the input channel of the ${\mathcal{L}}_1$ adaptive controller to ensure that the control loop is decoupled from the estimation loop, which preserves response robustness along with improving transient performances. Finally, the closed-loop stability is rigorously proved, and the acquired results are demonstrated by two simulation examples as well as a comparative study.