Constrained Model Predictive Control for Nonlinear Markov Jump System With Persistent Disturbance via Quadratic Boundedness

In this article, a robust quadratic-boundedness-based model predictive control (MPC) scheme, for a discrete-time nonlinear Markov jump system (MJS), is extended to the case with persistent bounded disturbance and nonhomogeneous transition probability. By applying the S-procedure, the constraint conditions, the persistent bounded disturbance and the sufficient stability conditions are all derived in term of a few linear matrix inequalities (LMIs), thus the original min-max optimization problem is transformed into a convex optimization problem in LMI paradigm. At each sampling time, the control moves satisfying the control constraint are obtained online and implemented in the nonlinear MJS. Quadratically boundedness and min-max MPC are combined to achieve the closed-loop stochastic stability of the controller with respect to the persistent bounded disturbance. A numerical example is presented to demonstrate the effectiveness of the proposed results.