An efficient model predictive control for Markovian jump systems with all unstable modes. (English) Zbl 1485.93167
Summary: 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.
MSC:
| 93B45 | Model predictive control |
| 93E15 | Stochastic stability in control theory |
| 93C55 | Discrete-time control/observation systems |
Keywords:
efficient MPC; Markovian jump systems; polytopic uncertainties; transition probability; initial feasible region; mean-square stabilitySoftware:
LMIRankReferences:
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