Analytical approach to evaluate language measure parameters for discrete-event supervisory control

Abstract

The discrete-event dynamic behaviour of physical plants is usually represented by regular languages that can be realized as deterministic finite state automata (DFSA). The concept and construction of signed real measure of regular languages have been recently developed in literature. The language measure is assigned two parameters, namely a state transition cost matrix and a state cost vector. This article formulates an analytical approach to determine the language measure parameters. The proposed approach is based on the theory of Markov stochastic processes. The DFSA of the discrete-event dynamic behaviour is first transformed into a Markov chain. Therefore, an event cost is calculated by the occurrence probability of this event in a given state of a discrete-time Markov chain. The determination of the state cost vector is based on the underlying continuous-time Markov chain to evaluate the steady state-state probabilities. Kronecker algebra is used to facilitate the description of large systems, while minimizing memory requirements. It is shown, through a manufacturing example, how the formulated method may provide a systematic way for quantitative evaluation and comparison of the discrete-event dynamic behaviour of the supervised plants.