Nonblocking and deterministic decentralized control for networked discrete event systems under communication delays
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Nonblocking and deterministic decentralized control for networked discrete event systems under communication delays Pan Xu1
· Shaolong Shu1 · Feng Lin1,2
Received: 17 February 2019 / Accepted: 5 October 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Nonblocking is an important issue in supervisory control of discrete event systems. In this paper, we investigate nonblocking control for networked discrete event systems. In networked discrete event systems, there are two types of supervisory controls: nondeterministic control and deterministic control. Following the deterministic control, we investigate the nonblocking control problem in a decentralized control framework where communication among the plant and the local supervisors are subject to nondeterministic but bounded delays. We introduce delay co-observability to capture the nondeterminism caused by observation delays. With delay co-observability, we derive a necessary and sufficient condition for the existence of solutions of the nonblocking control problem. When the condition is satisfied, we propose to use state-estimate-based predictive local networked supervisors to control the plant. To illustrate the applications of the results, we consider a black start problem in micro grids. Keywords Discrete event systems · Supervisory control · Networked control · Deterministic control · Nonblocking · Decentralized control · Delay co-observability · Micro grids · Black start
This paper is supported by the Fundamental Research Funds for the Central Universities, the National Science Foundation of China under Grants 61673297, 61773287 and by the National Science Foundation of USA under Grant 1507096. Pan Xu
panxu [email protected] Shaolong Shu [email protected] Feng Lin [email protected] 1
School of Electronics and Information Engineering, Tongji University, Shanghai, 201804, China
2
Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA
Discrete Event Dynamic Systems
1 Introduction Supervisory control of discrete event systems (DES) has been studied for many years (Wonham et al. 2017). After controllability (Ramadge and Wonham 1987) and observability (Lin and Wonham 1988), many difficult problems are investigated, such as decentralized (Rudie and Wonham 1992) or hierarchical control (Zhong and Wonham 1990) for large-scale DES, robust control (Lin 1993) to deal with uncertainty, relative observability (Cai et al. 2015) and maximally permissive supervisors (Yin and Lafortune 2016a) for partially observed DES. All these works consider instantaneous communications between the supervisor and the plant. Nowadays, networks are used more and more widely in practice, where communication delays are unavoidable (Lunze 2014). In such a networked control system, communication delays exist in both observation (called observation delays) and control (called control delays). These delays, if not treated properly, can have detrimental effects on the closed-loop system. In our previous
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