Brief paperNonblocking supervisory control of timed discrete event systems under communication delays: The existence conditions☆
Introduction
Since Brandin and Wonham (1994) proposed the fundamental framework for supervisory control of timed discrete event systems (TDESs), many other supervisory control schemes including Takai and Ushio (2006) and Park, Cho, and Lim (2004) have been developed so far based on this framework to account for various situations. In the framework of Brandin and Wonham (1994), tick was introduced as an event representing the passage of time and forcible events were introduced as a new class of events that can preempt the occurrence of tick by forcing action of a supervisor. However, the control commands issued by a supervisor were assumed being applied to a system without any communication delay. In other words, if a certain event occurs in the system then no further event can occur until the information on the occurrence of the previous event is fully processed by the supervisor and a control action is delivered to the system, which is actually not the case in many practical situations. Rather, there are usually nonnegligible delays in practice for sensing, communicating, and actuating, which can lead to the occurrence of unexpected events before a proper control action is applied to the system.
Supervisory control of discrete event systems (DESs) under such communication delays has been investigated within several contexts. For instance, Balemi (1994) considered the problem of supervisor synthesis for input/output untimed DESs with communication delays when a partial specification is given by a language over an output event set. On the other hand, Debouk, Lafortune, and Teneketzis (2003) considered the problem of decentralized failure diagnosis under a communication delay. Moreover, Tripakis (2004) investigated the problem of decentralized supervisory control of untimed DESs for a given specification of responsiveness by taking account of the communication delays caused by the buffer queuing of messages transmitted among the local supervisors. Recently, Park and Cho (2006) considered the problem of supervisory control of untimed DESs to achieve a given language specification under communication delays and presented the existence conditions of such a supervisor. Based on the result, Park and Cho considered the problems of partial observation (Park & Cho, 2007a) and decentralized supervisory control (Park & Cho, 2007b) under communication delays. It has, however, not been considered in the previous studies what the necessary and sufficient conditions are for the existence of a nonblocking supervisor that can correctly achieve a given language specification for TDESs under communication delays.
This paper addresses the problem of supervisory control of TDESs under communication delays based on the framework of Brandin and Wonham (1994) since the behavior of a TDES can be completely described by formal languages and controlled by well-defined operations on automata within this framework. In the situation under consideration, a supervisory control action can be applied to the system after some time-delay within a maximal bound represented by the maximal occurrence of tick events and a finite number of uncontrollable events can occur within this time-delay. We further assume that every controllable event can occur only if it is enabled by a supervisor. The aim is to find out the existence conditions of a nonblocking supervisor that can correctly achieve a given language specification in such a situation. To this end, we present a notion of delay-nonconflictingness for a given language specification and show that this is a key condition for the existence of a supervisor that can achieve the specification.
Section snippets
Backgrounds and a problem formulation
In this paper, we adopt the supervisory control framework of TDESs proposed by Brandin and Wonham (1994). From a logical (or untimed) model and timed events, a TDES is represented by the following finite state automaton: where Q is the finite set of states, is the set of events, is the initial state, is the state transition (partial) function, and is the set of marked states. The event set includes the event t representing the tick of a global clock. The
Main results
For a given language specification , we define the following notions to develop the main idea of this paper. Definition 1 A string is enabling-required if for some and such that and for any .
Intuitively, an enabling-required string means the string after which some legal controllable events follow. In case such an enabling-required string is observed, a supervisor issues a control command that enables some controllable events.
Example
In distributed embedded systems, the task synchronization to avoid deadlock or priority inversion is known to be a very complicated problem usually due to communication delays. In this section, we show that the proposed scheme can effectively be applied to such a problem. Let us consider a simple distributed system in Fig. 3 composed of three field processors, three shared resources, one sensor, and one control processor (supervisor) that are interconnected through a communication channel such
Conclusions
In this paper, we have presented the existence conditions of a nonblocking supervisor that can achieve a given language specification for a TDES with communication delays. In case a series of uncontrollable events may occur before supervisory control actions are applied to a system due to communication delays, we have shown that the presented delay-nonconflictingness of a language specification can guarantee nonconflicting control decisions for both enabling and forcing in the supervised system.
Acknowledgments
This work was supported from the Korea Ministry of Science and Technology through the Korean Systems Biology Research Grant (M10503010001-07N030100112), the Nuclear Research Grant (M20708000001-07B0800-00110), and the 21C Frontier Microbial Genomics and Application Center Program (Grant MG05-0204-3-0), and in part from the Korea Ministry of Commerce, Industry & Energy through the Korea Bio-Hub Program (2005-B0000002).
Seong-Jin Park received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, in 1994, 1997, and 2001, respectively. From September 2001 to February 2004, he was a Senior Engineer in the Telecommunication Division, Samsung Electronics, Suwon, Korea. In March 2004, he joined the Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea, where he is currently an Assistant Professor.
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Seong-Jin Park received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, in 1994, 1997, and 2001, respectively. From September 2001 to February 2004, he was a Senior Engineer in the Telecommunication Division, Samsung Electronics, Suwon, Korea. In March 2004, he joined the Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea, where he is currently an Assistant Professor. His research interests include supervisory control theory of discrete event systems and real-time distributed & embedded systems.
Kwang-Hyun Cho received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST) in 1993, 1995, and 1998, respectively. From March 1999 to August 2004, he was a Lecturer and an Assistant Professor in the School of Electrical Engineering at the University of Ulsan, Korea. From June 2002 to August 2003, he worked at the Control Systems Centre in Department of Electrical Engineering & Electronics at the University of Manchester Institute of Science and Technology (UMIST), UK as a Visiting Professor. From January to March in 2004 he also worked at the Automatic Control Group in Department of Signals, Sensors and Systems at the Royal Institute of Technology, Sweden as a Visiting Research Fellow. He was invited to the Hamilton Institute in Ireland as a Senior Research Fellow for the systems biology research between June and August in 2004. From September 2004 to August 2007, he was an Associate Professor at the College of Medicine, Seoul National University, Korea and worked at the Bio-MAX Institute, Seoul National University, Korea as a Director of Systems Biology Laboratory. He is currently a tenured Associate Professor in the Department of Bio and Brain Engineering at the Korea Advanced Institute of Science and Technology (KAIST), also holds a joint position at the KAIST Institute for the BioCentury, and is a director of Laboratory for Systems Biology and Bio-Inspired Engineering. He has been guest editors of Simulation: Transactions of the Society for Modeling and Simulation International for the special issue of systems biology (vol. 79, no. 12, 2003) and IEEE Control Systems Magazine for the special issue of systems biology (vol. 24, no. 4, 2004). He co-founded Systems Biology as an Editor-in-Chief which is the world-first international journal in systems biology launched by IEE (changed to IET in 2007) in London from 2004. He is also an Editorial Board Member of Systems and Synthetic Biology (Springer, Netherlands, from 2006), BMC Systems Biology (BMC, London, UK, from 2007), and Gene Regulation and Systems Biology (Libertas Academica, New Zealand, from 2007). He is a Senior Member of the IEEE Engineering in Medicine and Biology Society (EMBS). His research interests cover the areas of systems science with bio-medical applications including systems biology, nonlinear dynamics, and discrete event systems. The focus has been on applications in biotechnology and bio-medical sciences, in particular, a system-level analysis of cellular signal transduction pathways, reverse engineering of biomolecular regulatory networks from time-series data, unraveling hidden cellular dynamics, and development of new kinds of control systems inspired from molecular biology. He published 75 international journal papers and contributed to five books/book chapters in these areas.
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This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Bart De Schutter under the direction of Editor Ian Petersen.