An efficient model predictive control for Markovian jump systems with all unstable modes. (May 2022) - Zhang, Bin; Song, Yan; Cai, Hongbin
Abstract: This paper is concerned with the efficient model predictive control (EMPC) problem for a class of Markovian jump systems (MJSs) with unstable modes under polytopic uncertainties and hard constraints. The transition probability matrix and a dual-mode control strategy in the framework of EMPC are co-designed. To achieve a nice tradeoff among the computation burden, the initial feasible region, and the control performance, the EMPC is proposed, whose main idea is two-fold: (1) the terminal constraint set, the corresponding feedback gain, and proper switching rules (i.e. the transition probability) are designed simultaneously by solving an off-line "min–max" problem related to subsystem modes; and (2) a fairly large initial feasible region is obtained off-line by adjusting the dimension of the control perturbation sequence, meanwhile such a perturbation sequence is designed online to steer the system state belonging to initial feasible region into the terminal constraint set within the pre-determined steps. Furthermore, sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying MJS. Finally, an illustrative example regarding the economic system is provided to verify the feasibility and effectiveness of the developed algorithm.