Practical Finite-Time Fuzzy Synchronization of Chaotic Systems with Non-Integer Orders: Two Chattering-Free Approaches

Abstract

The controlling and synchronizing chaotic systems (CSs) are crucial aspects of engineering, with broad applications across various applied sciences, such as secure communications, nonlinear circuit design, biomedical engineering, and image processing. This paper deals with the complex problem of achieving finite-time projective synchronization for uncertain CSs with incommensurate non-integer orders using adaptive fuzzy sliding-mode control (AFSMC). Specifically, we focus on practical projective synchronization, introducing two novel control approaches that effectively mitigate the chattering phenomenon, a common issue in conventional sliding mode control. To achieve this, two innovative non-singular sliding surfaces with finite-time properties are formulated. This type of sliding surface enhances projective synchronization accuracy, response speed, and robustness. The adaptive fuzzy logic systems, known for their universal approximation capability, are employed to estimate continuous functional uncertainties. We rigorously analyzed the stability of both approaches using Lyapunov’s direct method. Extensive simulations confirm the effectiveness and benefits of our proposed methods. These methods significantly reduce or eliminate chattering and achieve practical projective synchronization in a finite time. This makes them well-suited for real-world applications in complex CSs.

Keywords

Practical finite-time synchronization / incommensurate fractional-order systems / fuzzy control / chaotic master-slave systems

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Systems Engineering Society of China and Springer-Verlag GmbH Germany