Constrained model predictive control synthesis for uncertain discrete‐time Markovian jump linear systems

Abstract

This study is concerned with model predictive control (MPC) for discrete-time Markovian jump linear systems subject to polytopic uncertainties both in system matrices and in transition probabilities between modes. The multi-step mode-dependent state-feedback control law is utilised to minimise an upper bound on the expected worst-case infinite horizon cost function. MPC designs for three cases: unconstrained case, constrained case and constrained case with low online computational burden (LOCB) are developed, respectively. All of them are proved to guarantee mean-square stability. In the constrained case, the minimisation of the expected worst-case infinite horizon cost function and constraints handling are dealt with in a separate way. The corresponding algorithm is proved to guarantee both the mean-square stability and the satisfaction of the hard mode-dependent constraints on inputs and states. To reduce the computational complexity, an algorithm with LOCB is developed by making use of the affine property of the solution to linear matrix inequalities. Finally, a numerical example is given to illustrate the proposed results.