Robust Adaptive Fuzzy Fractional Control for Nonlinear Chaotic Systems with Uncertainties

Abstract

The control of nonlinear chaotic systems with uncertainties is a challenging problem that has attracted the attention of researchers in recent years. In this paper, we propose a robust adaptive fuzzy fractional control strategy for stabilizing nonlinear chaotic systems with uncertainties. The proposed strategy combined a fuzzy logic controller with fractional-order calculus to accurately model the system’s behavior and adapt to uncertainties in real-time. The proposed controller was based on a supervised sliding mode controller and an optimal robust adaptive fractional PID controller subjected to fuzzy rules. The stability of the closed-loop system was guaranteed using Lyapunov theory. To evaluate the performance of the proposed controller, we applied it to the Duffing–Holmes oscillator. Simulation results demonstrated that the proposed control method outperformed a recently introduced controller in the literature. The response of the system was significantly improved, highlighting the effectiveness and robustness of the proposed approach. The presented results provide strong evidence of the potential of the proposed strategy in a range of applications involving nonlinear chaotic systems with uncertainties.

Hyperbolic-Secant-Function-Based Fast Sliding Mode Control for Pantograph Robots

“…In this section, the desired θ 1 and θ 2 are derived as per (30) for the given end-effector position along the X-Y axis, i.e., X E and Y E .…”

“…In this section, firstly, the proposed control structure is explained, and then the proposed algorithm is derived, followed by the stability analysis. At first, the desired position of the end-effector of the PR along the X-Y axis is given and, with the help of inverse kinematics as per (30), the desired θ d 1 and θ d 2 are calculated, which are required for the design of the proposed HSF-based SMC. As per Section 3.2, the proposed SMCs are designed, which can control the actual positions of both motors, i.e., θ 1 and θ 2 , by generating two control inputs u 1 and u 2 , respectively.…”

“…A robust control which requires less computational power, is simple in design, and feasible for real-time systems is much-needed. For nonlinear chaotic systems, an another adaptive fuzzy fractional control based on a supervised SMC is proposed to deal with uncertainties, but it is prone to slower convergence and overall lack in robustness for trajectory tracking [30].…”