# American Institute of Mathematical Sciences

January  2008, 4(1): 107-123. doi: 10.3934/jimo.2008.4.107

## A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback

 1 School of Management, Fudan University, Shanghai 200433, China 2 School of Science, Shenzhen University, Guang Dong 518060, China 3 Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501

Received  October 2006 Revised  July 2007 Published  January 2008

This paper presents a new basic model based on automatons for the state feedback control of discrete event systems (DES), including (repeated) concurrent DES. So, this new model unifies the Ramadge-Wonham framework and the controlled Petri nets, with or without concurrency or repeated concurrency. The repeated concurrent model under Ramadge-Wonham framework is first presented here. We study relationships between the concurrent models and the basic model. Based on this, we show that the uniqueness of the maximal permissive state feedback (PSF) of a predicate $P$ is equivalent to the weak interaction of $P$, which is also equivalent to that the set of PSF is closed under a disjunction. These results are also true for the concurrent systems, but the weak interaction may be difficult to be verified. Hence, we try to simplify the weak interaction by introducing concepts of cover, transitivity and local concurrently well-posedness (CWP). We show that the local CWP can ensure that the set of PSF for the concurrent systems equals that for the basic system.
Citation: Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback. Journal of Industrial & Management Optimization, 2008, 4 (1) : 107-123. doi: 10.3934/jimo.2008.4.107
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