Constrained Model Predictive Control of High Dimensional Jump Markov Linear Systems

This paper proposes a model predictive control (MPC) approach for discrete-time jump Markov linear systems (JMLS) considering constraints on the inputs as well as on the expectancy of the states. Prediction equations for the first moment of the states are formulated, in which the dependencies on the inputs, on the expected values of disturbances, and on the current states are directly considered. For the computation of the matrices needed for predicting the first moment of the states, a recursive algorithm is presented. Finally, the prediction equations are used to formulate the MPC problem as a quadratic program (QP). Due to the recursive structure of the prediction equations and the formulation as a QP, the computational effort is low compared to existing approaches. Simulation results demonstrate the properties of the presented MPC approach and its capabilities of controlling large-scale JMLS online.