Efficient Tube Model Predictive Control for Nonlinear Stochastic Systems

Model predictive control (MPC) has attracted considerable interest for its ability to generate optimal control strategies, yet its application to nonlinear systems is often constrained by high computational complexity and processing time. In this article, we propose an efficient tube MPC strategy for a class of nonlinear Itô stochastic systems with time delay. First, a feedback auxiliary controller is designed for nonlinear stochastic systems to handle the stochastic disturbances and time delay, and a robust invariant expectation of a tube around the nominal trajectory is derived via contraction theory. Second, to reduce computational complexity and enable real-time operation, we incorporate diffusion model-enhanced imitation learning with tube MPC. In this approach, the diffusion model generates a training dataset aligned with the tube’s distribution, facilitating the development of a robust control strategy while significantly lowering computational demands. Finally, we rigorously prove that under the proposed efficient tube MPC strategy, the trajectories of the considered system exponentially converge within the obtained tube. Numerical experiments are provided to validate the effectiveness of the proposed approach.