<p>This paper investigates the synchronization of two uncertain, dissimilar chaotic systems with incommensurate fractional orders by proposing novel fixed-time fuzzy sliding-mode control (FTFSMC) schemes. Unlike many classical synchronization strategies that typically assume identical system structures and known dynamics, the proposed methods achieve synchronization between distinct chaotic systems in the presence of system uncertainties, external disturbances and incommensurate fractional-orders. Two robust controllers are developed by integrating fuzzy logic systems with sliding-mode control to approximate unknown nonlinearities. Fixed-time convergence is rigorously ensured, guaranteeing that the synchronization error reaches zero within a predetermined time, regardless of the initial conditions. A Lyapunov stability-based approach is employed to demonstrate fast fixed-time convergence of the closed-loop system. Simulation results on illustrative examples demonstrate the efficiency, robustness, and superior performance of the proposed synchronization schemes. It is worth noting that one of the two controllers operates smoothly, effectively reducing chattering phenomena. Overall, the developed control strategies significantly enhance the practical applicability of chaos synchronization in uncertain and mismatched environments.</p>

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Novel fixed-time fuzzy sliding-mode synchronization schemes of two uncertain dissimilar chaotic systems

  • A. Boulkroune,
  • A. Boubellouta,
  • A. Bouzeriba,
  • F. Zouari

摘要

This paper investigates the synchronization of two uncertain, dissimilar chaotic systems with incommensurate fractional orders by proposing novel fixed-time fuzzy sliding-mode control (FTFSMC) schemes. Unlike many classical synchronization strategies that typically assume identical system structures and known dynamics, the proposed methods achieve synchronization between distinct chaotic systems in the presence of system uncertainties, external disturbances and incommensurate fractional-orders. Two robust controllers are developed by integrating fuzzy logic systems with sliding-mode control to approximate unknown nonlinearities. Fixed-time convergence is rigorously ensured, guaranteeing that the synchronization error reaches zero within a predetermined time, regardless of the initial conditions. A Lyapunov stability-based approach is employed to demonstrate fast fixed-time convergence of the closed-loop system. Simulation results on illustrative examples demonstrate the efficiency, robustness, and superior performance of the proposed synchronization schemes. It is worth noting that one of the two controllers operates smoothly, effectively reducing chattering phenomena. Overall, the developed control strategies significantly enhance the practical applicability of chaos synchronization in uncertain and mismatched environments.