An efficient robust model predictive control for nonlinear Markov jump systems with persistent disturbances using matrix partition

For a class of nonlinear Markov jump systems (MJSs), an efficient robust model predictive control (MPC) is designed with bounded persistent perturbations and hard constraints. Nonlinearity is considered as a description of polyhedral form. First, affine control inputs are introduced for the polytopic MJSs to provide the expected performance. Quadratic boundedness is then used to deal with bounded persistent perturbations to improve the robustness of the closed loop system. Then the large amount of online MPC computation problem is solved efficiently by matrix partitioning. The efficient MPC strategy not only ensures that the closed-loop system is stochastically stable but also reduces the amount of on-line computation and improves the efficiency of on-line computation. Finally, a numerical example and a nonlinear mechanical mass-spring-damper system are applied to elucidate the proposed algorithm.