Stochastic Model Predictive Control with Minimal Constraint Violation Probability for Time-Variant Chance Constraints

Despite the effectiveness of Robust and Stochastic Model Predictive Control, not all scenarios require robust trajectories or permit constraint violations. Achieving a balance between safety and performance is crucial. A Model Predictive Control approach is proposed that provides an optimal control law by minimizing the probability of constraint violations for time-variant constraints while aiming at achieving a performance criterion. Either the constraints are satisfied robustly or with minimal probability of constraint violation. Further, the proposed method switches between minimizing the performance criterion and minimizing the constraint violation probability whenever either does not meet the requirements anymore. () and stability of the method are proved. The approach is evaluated for overtaking of an autonomous vehicle in a simulation study.