A learning-based sliding mode control for switching systems with dead zone

This paper focuses on the problem of adaptive neural network sliding mode control for switching systems affected by dead zones. Distinct from existing rules defined by transition and sojourn probabilities, a broader switching rule is proposed based on duration-time-dependent sojourn probabilities. A neural network strategy for compensation is implemented to mitigate the effects of the dead zone. Moreover, a sliding mode control law incorporating a learning term is designed, effectively reducing chattering compared to conventional sliding mode control. Employing a stochastic Lyapunov function grounded in the joint distribution of duration time and system mode, sufficient criteria for designing the adaptive neural network-based controller are established. Finally, the effectiveness of the proposed method is demonstrated through two simulated examples.