Model Predictive Control with High-Probability Safety Guarantee for Nonlinear Stochastic Systems

We present a model predictive control (MPC) framework for nonlinear stochastic systems that ensures safety guarantee with high probability. Unlike most existing stochastic MPC schemes, our method adopts a set-erosion that converts the probabilistic safety constraint into a tractable deterministic safety constraint on a smaller safe set over deterministic dynamics. As a result, our method is compatible with any off-the-shelf deterministic MPC algorithm. The key to the effectiveness of our method is a tight bound on the stochastic fluctuation of a stochastic trajectory around its nominal version. Our method is scalable and can guarantee safety with high probability level (e.g., 99.99%), making it particularly suitable for safety-critical applications involving complex nonlinear dynamics. Rigorous analysis is conducted to establish a theoretical safety guarantee, and numerical experiments are provided to validate the effectiveness of the proposed MPC method.