Control and decision strategy for a class of Markovian jump systems in failure prone manufacturing process

This study investigates control and decision strategy for the failure prone manufacturing process, which is modelled as a two-mode Markovian jump system (MJS). Considering the historical effects on the system, the mode transition rate matrix (MTRM) is time-varying instead of homogeneous. A piecewise homogeneous MJS is thus proposed to characterise this phenomenon, in which the MTRM is homogeneous during certain time intervals but non-homogeneous for the whole time interval. By regarding each homogeneous MTRM as one event, all the MTRMs over the whole time interval will take values in an event set and be governed by a higher-level Markov chain. To ensure such system operates normally with high probability, the decisions including preventive maintenance and corrective maintenance are introduced to adjust the higher-level Markov chain. Motivated by this, a new joint performance, consisting of both cost function for decision making and controller design, is developed. Optimal decisions are obtained by an iterative algorithm whose convergence is proved, as well as an optimal controller is designed. The effectiveness of this method is demonstrated by simulations.