Efficient Model Predictive Control for Markov Jump Nonlinear Systems via Controllable Sets and Sum-of-Square Programming

This study is concerned with computationally efficient one-step model predictive control (MPC) for a class of Markov jump nonlinear systems (MJNSs) subject to polynomial vector field and hard constraints. To ensure the recursive feasibility, Sum-of-Square (SOS) conditions are developed to characterize mode-dependent one-step controllable sets for MJNSs. On this basis, the constraints of one-step ahead state can be offline designed, formulating a low computational demanding MPC with flexible performance optimization. Considering the effect of mode switching, the one-step MPC is extended with a stochastic performance index, and the terminal sets are designed with stochastic performance optimization and invariance guarantee. The proposed efficient one-step MPC approach ensures the feasibility and mean-square stability for MJNSs, while achieving lower conservatism in feasible region and performance optimization compared with existing approaches. An illustrative example is provided to show the potential and merits of the proposed MPC approach.