Model predictive control synthesis for constrained Markovian jump linear systems with bounded disturbance

Abstract

For controller design, exogenous disturbance, which commonly exists in real applications, is an important factor to be considered. However, the existing results on constrained model predictive control (MPC) design for Markovian jump linear systems (MJLS) mainly focused on the disturbance-free case. This motivated to study constrained MPC synthesis for MJLS with bounded additive disturbance. By projecting the desired closed loop trajectories onto a set of predetermined trajectories, the adopted predictive control law is a sum of these corresponding stabilising control laws. Constraints are guaranteed by restricting the augmented state into a maximal output admissible set. Then the MPC algorithm is given by optimising the infinite horizon sum of deviation of the quadratic cost from its steady-state value. Under the MPC algorithm, the long run average cost is proved to be less than or equal to its steady-state value, which equals to the optimal one when one of the constituent control laws is chosen to be the optimal control law. The optimisation and analysis of determination of projection coefficients have also been discussed. Finally, a numerical example is given to illustrate the proposed results.