Optimal Time-varying Sliding Mode with Constraint Satisfaction for Vehicle Control

This paper presents a constrained optimal time-varying sliding mode control strategy based on a receding horizon approach. While traditional sliding mode control provides robust performance in the presence of uncertainties, it lacks a systematic mechanism for explicitly handling constraints. To overcome these challenges, the proposed method formulates the design of the time-varying sliding surface as a constrained optimization problem. The proposed method casts the problem as a quadratic programming formulation within a model predictive control framework. Consequently, the controller can explicitly handle hard constraints. The effectiveness of the proposed algorithm is validated through MATLAB/Simulink simulations applied to a vehicle longitudinal control system. A comparative study using the linear time-varying method demonstrates that the proposed technique achieves optimal time-varying sliding while strictly satisfying all imposed constraints.