Similarity-Based Supervisory Control of Discrete-Event Systems

Y. Cao, M. Ying
2006 IEEE Transactions on Automatic Control  
Due to the appearance of uncontrollable events in discrete event systems, one may wish to replace the behavior leading to the uncontrollability of pre-specified language by some quite similar one. To capture this similarity, we introduce metric to traditional supervisory control of discrete event systems. In this setting, we first generalize the concept of original controllability to λ-controllability, where the index λ is used to represent the similarity degree of two languages. Informally, a
more » ... anguage K is said to be λ-controllable if there exists a language K, called a realization of K, which is both controllable and similar to K with index λ. A necessary and sufficient condition for a language to be λ-controllable is provided. We then examine some basic algebraic properties of λ-controllable languages and investigate the supremal λ-controllable sublanguage of a given language. Finally, noting that a realization of a λ-controllable language may not be optimal in some sense, we turn our attention to finding a Pareto optimal one which involves a trade-off between the common behavior and the different behavior of the realization and the λ-controllable language itself.
doi:10.1109/tac.2005.863515 fatcat:h3ni2z46zbf3hj6ehij6lfcvai