Improved control of uncertain chaotic systems using hybrid fuzzy sliding mode techniques: Chattering elimination and robust performance

This paper proposes hybrid fuzzy sliding mode control (SMC) schemes for the robust stabilization of uncertain chaotic systems subject to bounded disturbances and unknown dynamics. A fuzzy second-order SMC framework combined with a variable-universe Takagi-Sugeno fuzzy adaptation mechanism is developed to suppress chattering and improve tracking performance. Finite-time convergence of the sliding variable is rigorously established via Lyapunov analysis, guaranteeing that system trajectories reach the sliding manifold within a bounded time, while the reduced-order dynamics ensure stable closed-loop behavior. A fuzzified sliding surface together with a fuzzy boundary layer dynamically smooths the control input without sacrificing robustness. Numerical simulations on benchmark chaotic systems–including the Hysteresis system, Duffing oscillator, Logistic map, and T-system–demonstrate improved chattering attenuation, faster convergence, and improved tracking accuracy compared with conventional and existing fuzzy SMC methods.