Minimal Constraint Violation Probability in Model Predictive Control for Linear Systems

Handling uncertainty in model predictive control (MPC) comes with various challenges, especially when considering state constraints under uncertainty. Most methods focus on either the conservative approach of robustly accounting for uncertainty or allowing a small probability of constraint violation. In this work, we propose a linear MPC approach that minimizes the probability that linear state constraints are violated in the presence of additive uncertainty. This is achieved by first determining a set of inputs that minimize the probability of constraint violation. Then, this resulting set is used to define admissible inputs for the optimal control problem. Recursive feasibility is guaranteed and input-to-state stability is proved under assumptions. Numerical results illustrate the benefits of the proposed MPC approach.