Joint Decision and Control Strategy for a Class of Nonhomogeneous Markovian Jump Systems with Input Constraints

Abstract

This paper is concerned with the joint decision and control strategy for a class of nonhomogeneous Markovian jump systems subject to input constraints. By assuming the mode transition rate matrix (MTRM) of Markovian jump systems is piecewise homogeneous instead of homogeneous, a higher-level Markov chain represented by the higher-level mode transition rate matrix (HMTRM) is introduced to describe the variation of MTRM. Based on this, taking into account the minimization of system cost, a novel joint decision and control strategy is proposed in the presence of input constraints. This strategy consists of two sections: decisions are applied to the HMTRM such that the occurrence probability of subsystems is adjusted ultimately; next on the basis of altered HMTRM, controller is designed in view of input constraints. In comparison with conventional control method, this strategy not only guarantees the stability of the considered system well, but also decreases the system cost effectively. Numeral examples along with comparisons are put forward to illustrate the effectiveness of the proposed strategy.