Koopman-Based Stochastic Model Predictive Control with Partial Probabilistic Information for Nonlinear Systems

This paper proposes a Koopman-based stochastic model predictive control (SMPC) approach for unknown nonlinear systems by exploiting partial probabilistic information. Unlike existing Koopman-based SMPC methods that primarily rely on the first- and second-order moments of stochastic Koopman modeling error, the proposed approach further incorporates available support information into the controller design. By jointly utilizing the mean, covariance, and support information of the resulting uncertainty, the chance-constrained optimization problem is reformulated into a tractable deterministic optimization problem with reduced conservatism. Moreover, the proposed approach is theoretically shown to be no more conservative than the corresponding RMPC in terms of constraint tightening under identical constraint requirements. Furthermore, recursive feasibility and closed-loop quadratic stability of the proposed control scheme are established theoretically. Simulation studies on spacecraft attitude control demonstrate that the proposed method reduces the performance index by 6.7% and 17.0% compared with a Koopman-based SMPC using mean and covariance information and RMPC, respectively, while maintaining a comparable average computation time of approximately 0.010 s.