Fractional-order fuzzy sliding mode control of uncertain nonlinear MIMO systems using fractional-order reinforcement learning

Abstract

Abstract This paper introduces a novel approach aimed at enhancing the control performance of a specific class of unknown multiple-input and multiple-output nonlinear systems. The proposed method involves the utilization of a fractional-order fuzzy sliding mode controller, which is implemented through online fractional-order reinforcement learning (FOFSMC-FRL). First, the proposed approach leverages two Takagi–Sugeno–Kang (TSK) fuzzy neural network actors. These actors approximate both the equivalent and switch control parts of the sliding mode control. Additionally, a critic TSK fuzzy neural network is employed to approximate the value function of the reinforcement learning process. Second, the FOFSMC-FRL parameters undergo online adaptation using an innovative fractional-order Levenberg–Marquardt learning method. This adaptive mechanism allows the controller to continuously update its parameters based on the system’s behavior, optimizing its control strategy accordingly. Third, the stability and convergence of the proposed approach are rigorously examined using Lyapunov theorem. Notably, the proposed structure offers several key advantages as it does not depend on knowledge of the system dynamics, uncertainty bounds, or disturbance characteristics. Moreover, the chattering phenomenon, often associated with sliding mode control, is effectively eliminated without compromising the system’s robustness. Finally, a comparative simulation study is conducted to demonstrate the feasibility and superiority of the proposed method over other control methods. Through this comparison, the effectiveness and performance advantages of the approach are validated.

Keywords

• Fractional-order sliding mode controller
• TSK-fuzzy system
• Actor-critic algorithm
• Levenberg Marquardt method
• Nonlinear systems