Feedback Predictive Control Based on Periodic Invariant Set for Markov Jump Systems

Abstract

In this paper, a feedback predictive controller design method based on a periodic invariant set is proposed for input/state-constrained Markov jump systems (MJSs). The design procedure is divided into two parts: an offline part and an online part. Firstly, the mode-dependent invariant sets are obtained offline combined with the known transition probability matrix, guaranteeing stochastic stability of the MJS. Then, the periodic invariant set is constructed online by the convex combination of precomputed mode-dependent invariant sets. In this way, we could not only obtain the feedback control sequence based on the periodic invariant set, but also guarantee stochastic stability. This proposed control strategy, which does not directly depend on the jumping modes, could offer more degrees of design freedom and provide a larger stabilizable set. The online variables that need to be solved are numerical parameters, and the online computational burden is reduced.