Rare chance constrained model predictive control via large deviation theory

Abstract Implementing model predictive control (MPC) in uncertain systems becomes particularly challenging when strict constraint satisfaction is required under rare but high‐impact disturbances. Fully robust MPC is often infeasible in such cases due to the unbounded nature of uncertainty. This paper addresses a rare chance‐constrained MPC problem, where the constraints are required to hold with high probability close to one. To avoid the computational burden and variance of sampling‐based approaches, we propose a sample‐free approximation of the chance constraint based on large deviation theory. The resulting formulation remains tractable even in the rare‐event regime and enables efficient online implementation. To ensure recursive feasibility under this formulation, we further develop a multistep probabilistic control invariant set. Numerical case studies confirm that the proposed method maintains high constraint satisfaction while significantly reducing computational cost, demonstrating its practical effectiveness for safe MPC in uncertain environments.