Sliding-Mode Control for Sojourn-Probability-Based Switching Systems With Cyber-Attacks

This study investigates an asynchronous sliding-mode control (SMC) strategy tailored for interval type-2 (IT2) fuzzy switching systems, specifically addressing challenges posed by cyber-attacks. Distinct from existing stochastic switching strategies, a novel duration-time-based switching rule is proposed that integrates both sojourn probability and mode duration, significantly reducing computational complexity and aligning more closely with practical requirements. To mitigate mode-switching-induced chattering and enhance robustness against uncertainties and disturbances, an innovative fuzzy SMC law with a learning mechanism is developed. Notably, a recursive sliding-mode learning controller is introduced, replacing abrupt switching actions with iterative learning adjustments to progressively guide system states onto the sliding surface, thereby significantly improving control smoothness and reducing chattering. To effectively handle cyber-attacks disrupting mode transmission, a comprehensive mismatched model that dynamically synchronizes the modes of the system and the controller is introduced, offering improved resilience compared to traditional fixed mismatch approaches. Utilizing the proposed learning-based SMC and Lyapunov stability theory, sufficient conditions ensuring mean-square stability of the system are derived. Finally, the practical effectiveness and distinct superiority of the proposed methods are demonstrated through simulations using mass-spring–damper and tunnel diode circuit models.