Evaluation of language measure parameters for discrete event manufacturing systems with multiproduct machines

The concept of language measure provides a mathematical framework for quantitative analysis and synthesis of discrete event supervisory control systems. The language measure is assigned two parameters, namely the state transition cost matrix and the state cost vector. In a recent paper (Khatab and Nourelfath 2006 Khatab, A and Nourelfath, M. 2006. Analytical approach to evaluate language measure parameters for discreteevent supervisory control. Int. J. Control, 79: 688–706.  Google Scholar]), an analytical approach has been formulated to evaluate the language measure parameters for discrete event manufacturing systems composed of several monoproduct machines, i.e., each machine is able to perform only one kind of product. This paper generalizes these results to the multiproduct case, i.e., to the case where each machine in the manufacturing system is able to perform different kinds of products. The proposed approach is based on the theory of Markov stochastic processes and Kronecker algebra. The main advantage of the proposed approach is that the mathematical expressions of the system language measure parameters are derived from data of individual elementary machines without generating the whole, possibly huge, system state space.