Fuzzy L1 adaptive controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

Abstract

This research work proposes a fuzzy fractional-order [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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.

Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis

“…Accordingly, the fractional-order differential model is concise in form and the parameter meaning is obvious, so it becomes one of the effective approaches for modeling complex mechanical and physical behaviors. Boulham et al [1] proposed an adaptive monitor for projective chaotic synchronization of general class fractional-order systems with chaotic uncertainty affected by unknown input nonlinear factors, and the closed-loop stability was strictly verified by two simulation examples and related comparative studies. Wu et al [2] used a new nonlinear fractional-order damaged pattern with viscosity, elasticity and plasticity for rock and soil materials to characterize three-stage creep behaviors, and their pattern fully calculated and predicted the deformation with hysteresis derived from the rapid creep in tunnel engineering.…”

Observer-based control of polynomial fuzzy fractional-order systems

“…In addition, the investigation by Duan and Li (2018) has examined the observer-based control of this class of systems. Recently, the authors of Boulham et al (2023) propose a fuzzy L 1 adaptive controller for FO chaotic models.…”