460 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001 Multiagent Supervisory Control for Antifault Propagation in Serial Production Systems Kwang-Hyun Cho, Associate Member, IEEE, and Jong-Tae Lim, Member, IEEE Abstract—In this paper, a multiagent supervisory control methodology is proposed for antifault propagation in serial production systems by incorporating the idea of multiagent control within the fault-tolerant supervisory control scheme. Especially, the concept of antifault propagation between cascaded processes is established and the synthesis of agent supervisors is investigated based on this concept. A case study of a polypropylene polymerization process in the petrochemical industry is provided to illustrate the proposed control policy. Index Terms—Antifault propagation, discrete-event dynamic systems, multiagent control, polypropylene polymerization process, supervisory control. aug-event recognizer for NOMENCLATURE [ ] [ ] Plant model (or generator) of an automaton where is the set of states , is the set of events , is the transition function, is the initial state, and is the set of marker states. Closed behavior of or language of the and is deplant fined . Marker behavior of and . Behavior of the supervised plant . . Starting state of the event [string ] leading to (domain of [ ] leading to ). Ending state of the event [string ] from (range of [ ] from )— [ ] is [ ] to be used instead of is the initial state of the auwhere tomaton. for each with where is the state set and is the prefix closure of — is to be . used instead of Manuscript received January 18, 2000; revised October 30, 2000. Abstract published on the Internet December 18, 2000. This work was supported by the Korea Research Foundation uder Grant KRF-99-003-E00420. K.-H. Cho is with the Division of Electronic Engineering, School of Electrical Engineering and Automation, University of Ulsan, Ulsan 680-749, Korea (e-mail: ckh@uou.ulsan.ac.kr). J.-T. Lim is with the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea. Publisher Item Identifier S 0278-0046(01)02645-4. controllable language controllable sublanguage of Range of the language ( for each where is a kind of string , especially an element of the language )—in this case, always . Event augmented with its originating state with ]. [ Set of events which constitute the string . Number of events comprising the string (length of the string ). Generator such that . or Recognizer automaton for . such that where is the set of uncontrollable events of . and is controllable . I. INTRODUCTION D ISCRETE-EVENT dynamic systems (DEDSs) have attracted much attention in the area of systems modeling and control-law synthesis [1]–[3]. Within this framework, the diagnostic issues over various fields have been studied up to the present: the fault detection and isolation problems are dealt with in [4]–[6] and the failure analysis with the corresponding system controller design is addressed in [7], [8]. In particular, in [8], the abnormal status in the behavior of the DEDS was quantitatively analyzed upon a discrete-event model (DEM) [9] and the synthesis of fault-tolerant supervisor was introduced based on the failure analysis. However, the approach in [8] becomes intractable for large complex systems such as serial production systems which are common in most of the production industries, due to the state explosion in the DEMs. Moreover, the synthesis of decentralized supervisor [10]–[13] (which is the most promising way to reduce the complexity) still needs many complicated steps in the design stage to guarantee the same optimal behavior as the centralized supervisor and cannot deal with the problem of fault propagation between unit processes (i.e., local plants). To resolve these problems, it is required to consider a new concept of fault-tolerant supervisory control which independently supervises each unit process and shares the least 0278–0046/01$10.00 © 2001 IEEE CHO AND LIM: MULTIAGENT SUPERVISORY CONTROL FOR ANTIFAULT PROPAGATION amount of information just needed to prevent the fault-propagation between unit processes. Therefore, in this paper, we propose a multiagent supervisory control methodology for antifault propagation in serial production systems by incorporating the concept of multiagent control [14]–[16] with the fault-tolerant supervisory control scheme. This is an integrated action of cooperative agent supervisors endowed with high autonomy and the least common information for the fault-propagation control. The present state-of-the-art of related works involves: 1) artificial intelligence techniques; 2) a model-based approach; and 3) DEDS methods based on state machines, Petri nets, etc. The fault diagnosis using artificial intelligence techniques [18]–[20] is computationally expensive and impractical for large systems. The model-based approach to fault diagnosis [21]–[23] is extremely slow due to the expensive use of functional simulation thus is not appropriate for fault diagnosis in large-scale systems. The recent DEDS method for fault diagnosis and the system design based on state machines in [6] and [7] cannot still be applied for large-scale systems because of the use of simulation and the computational complexity of constructing the diagnosers. The Petri-net-based method [24]–[26] shows substantial reduction of complexity in the model description; however, the simulation-based analysis and design of it are still complex and hard to be generalized. On the other hand, the approach to be developed in this paper deals with the state explosion problem by making use of the structural properties of serial production systems, i.e., it divides the overall processes into the unit processes with the corresponding information function and then applies the fault diagnosis and the antifault-propagation supervisory control policy to the unit processes via the agent supervisors. The emphasis is to be on the antifault-propagation supervisory control between unit processes which has never been considered in the decentralized supervisory control and other literature, and on the formulation of the overall analytical framework based on multiagent system concepts. Throughout the remainder of this paper, it is assumed that each agent supervisor can record all the state transitions and events generated by each unit process modeled by a deterministic automaton. The paper is organized as follows. In Section II, we present the definition of multiagent supervisory control, the property of antifault propagation, and the framework of multiagent supervisory control for antifault propagation. In Section III, the synthesis of agent supervisors for multiagent supervisory control for antifault propagation is described. In Section IV, the case study of a polypropylene polymerization process in the petrochemical industry is provided. Finally, the conclusions are formulated in Section V. II. MULTIAGENT SUPERVISORY CONTROL ANTIFAULT PROPAGATION FOR In [14]–[16], multiagent systems are understood as distributed computational systems in which several semi-autonomous agents interact or work together to perform some set of tasks or satisfy some set of goals. The agent is an entity with goals, actions, and domain knowledge, situated in an environment. It can maintain autonomy while still contributing to overall system effectiveness. Motivated from these ideas, we Fig. 1. 461 Multiagent supervisory control of serial production systems. introduce a concept of multiagent supervisory control in this section. Consider the serial production systems composed of unit in tandem. The supervisor of each process , is to be called an agent supervisor and the correunit process sponding integrated action of control is to be called multiagent supervisory control. In other words, multiagent supervisory control is a cooperative integration of agent supervisors with high autonomy and the least common information for the overall control objectives. The configuration of multiagent supervisory control for serial production systems is illustrated controls through in Fig. 1, where an agent supervisor and transfers the coded information the feedback map of an actually occurred sequence after supervision , and then gets the feedback information from to . Based on , determines whether it keeps controlling or stops the current process and starts diagnosis. where represents the normal Note that the fault mode, implying some possible abnormal mode and can be designed based on the legal status in the operation. such that [1] as usual if language is achievable, i.e., controllable and observable. Since is becomes achievable if we choose assumed to be observable, [2]. However, in the closed-loop operation, where shows the abnormal operation due to some failures. In [8], the abnormal status in the behavior of the DEDS was quantitatively analyzed upon a DEM such as a “fault” representing a rather tolerable malfunction and a “failure” denoting a complete breakdown of the overall system operation. Furthermore, when some abnormal events occur during operation, if we can still find another event sequence which can reach the marker state or if we can eliminate the path to the abnormal events, then the work procedure was called “fault tolerable” and the synthesis of fault-tolerant supervisor was introduced based on the tolerable fault event sequences. The previous concepts were basically formulated for a unit process. However, these can be extended to supervision of multiprocesses such as multiagent supervisory control. In this case, the failures for one process can be further classified into failures that propagate to the subsequent process and can be compensated by the corresponding supervisor, and failures that propagate but cannot be compensated by any measure or do not propagate and leads to breakdown of the current process. In view of multiagent supervisory control, the former ones can also be treated as “faults” on the extended 462 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001 concepts of tolerable fault event sequences. If we call the fault-tolerance concept within the unit process internal fault tolerance, we can consider the fault-tolerance concept between the subsequent unit processes as antifault propagation. Definition 1: The multiagent supervisory control system and is antifault propagative between and over if any fault propagation from into can be . eliminated by the subsequent agent supervisor This concept of antifault propagation means the capability of compensating any propagated faults by certain complementary measures. Furthermore, the multiagent supervisory control is called an antifault-propagative system over , . system if it is antifault propagative for all Definition 2: Multiagent supervisory control for antifault propagation is a kind of multiagent supervisory control resulting in the antifault-propagative system over the closed-loop operation. Assume that the total set of events of , can be partitioned as where is the set of controllable events of , is the set is the set of normal events of uncontrollable events of , is the set of abnormal events of , is the of , , and is the set of unset of compensable events of . Let be a fault-tolerant compensable events of where denotes the composupervisor of . sition of two DEMs [9], and implies that there exists a comIn the foregoing, such that plementary measure for some and where is the set of complementary measures in , , , , and . Hence, we can achieve the overall control objective without interrupting the via the corresponding agent supervisor current process in this case. Based on this concept, we consider action on the following domain of antifault propagation. , Definition 3: The domain of antifault propagation of is the set of states of , from which any postlanguages could be supplemented to meet the antifault propagation beand by the subsequent agent supervisor . tween Physically, the domain of antifault propagation corresponds to the endurable status at the end of the job, capable of continuing the current process in spite of the occurrence of some faults. Along with the previous definitions about , we know where . be the actually occurred sequence over Let then we can examine the existence of satisfying the antifault propagation between and in the following. such Theorem 1: There exists an achievable if and only if that . Proof: Sufficient Condition: If then it becomes trivially true. If then from and following Definition 3. Assume occurs, then choose where and , resulting in (where ) (for some ) . due to the structural Hence and property following the definitions of . Necessary Condition: Assume then and resulting in such that . Therefore, if such then that . Theorem 1 implies that whenever the range of the actually oclies within the domain of antifault curred sequence of , we can make and propagation of antifault propagative since is reconfigurable based on the . The synthesis of recognizer automaton of the achievable the corresponding agent supervisors and the implementation of the supervised system are to be developed in the following section. Note that if the existence condition of Theorem 1 is not sat, then we cannot achieve the anisfied for certain . Physically, this situation cortifault propagation by any responds to the cases when some uncompensable event occurs or the complementary measure of is not included in in due to the operational restriction of the process. In addition, the proposed approach is not applicable if we cannot identify the occurrence of abnormal events for the uncertainty embedded in the system. Remark 1: Here we considered only the case of two-tier fault propagation (i.e., a fault propagation between the subsequent two processes among those s connected in series). However, the proposed approach is also applicable to the cases of any kind of multi-tier fault propagation by considering the fault propagated from just the prior tier composed of unit processes hitherto undergone and by using the proposed approach in the same way, consecutively. and III. SYNTHESIS OF AGENT SUPERVISORS ANTIFAULT PROPAGATION FOR A. Synthesis Procedures In this section, we consider the synthesis of agent supervisors in multiagent supervisory control for antifault propagation when the condition of Theorem 1 is satisfied such that an achievable exists. Let, for each , and be defined such that CHO AND LIM: MULTIAGENT SUPERVISORY CONTROL FOR ANTIFAULT PROPAGATION for the corresponding where means such as 2s complement in the mathematical complement of case of a binary number. These could be listed in the complementary measures table (CMT) at the outset. Let be defined for each and be a function composed of a sequence of , for . Furthermore, let a certain coded information of be a function representing the orderly information of for the successive events comprising . Based such that on these, we choose a function where 1) if , for with for some , with , and , implies then where with ; . 2) otherwise, Here, we employ the coding scheme to ensure the least common information between agent supervisors for the autonomy and of encapsulation. In particular, the orderly information is utilized to transfer the information about the occurrence and is further used for constructing of abnormal events via through based on and . is also capable of providing the On the other hand, to such that it can determine feedback information or stops and starts diagnosis. whether it keeps controlling is defined as The feedback information if otherwise. is interpreted as “keep controlling” and 0 “stop and . This transfers the information regarding the diagnose” by condition of Theorem 1. is achievable, we can synthesize as Since (1) where and ognizer automaton for is the feedback map defined as if otherwise is a rec- and , and . in which then the agent Theorem 2: If for in (1) meets the antifault propagation supervisor and . between occurred after Proof: Assume such that [i.e., ] anymore due to where . Then should be from and such that . These are mapped into through and the corresponding agent supervisor 463 in (1) over (where subsequent to generate and ) for some and from Theorem 1. Therefore, any fault in this way, which propagated from can be eliminated by . results in the antifault propagation between and Based on the transferred coded information , Theorem 2 in (1) makes and anshows that exists under Thetifault propagative if the corresponding orem 1. Remark 2: As it follows from Theorems 1 and 2, in order to achieve the antifault propagation in the multiagent supervisory control of serial production systems, the minimal information we need within the proposed framework is the coded information of the compensable events and the corresponding complementary measures in the CMT. B. Comments on Implementation For the implementation of the foregoing supervisory control policy, we can make use of either the command response model introduced in [27] or the extended process model proposed in [28]. According to the semantics of [27], we can implement the supervised control system via the three-layered structure: the supervisor/controller, the implementation interface composed of command/response interpreter and equipment drivers, and the plant. The supervisor/controller module schedules and generates commands in the form of allowed languages for the plant based on the reported responses. Then, the command/response interpreter converts commands from the supervisor in lower level commands for the equipment drivers such as discrete actions, continuous actions, or changes in software execution according to the attributes of the plant. On the other side, it supplies the supervisor with logical responses that reflect the information provided by the sensor measurements such as discrete-state changes or continuous-state changes, and the software execution messages. The plant is operated by the actuators activated by the equipment drivers and also produces the responses via sensor measurements or program execution messages. In the framework of [28], the process coupled with the controller is regarded as the extended process which generates events spontaneously. Then the inputs of the supervisor are the outputs of the extended process and the supervisor confines the behavior of the extended process by prohibiting some of the generated events. IV. A CASE STUDY OF A POLYPROPYLENE POLYMERIZATION PROCESS In this section, we consider the utilization of multiagent supervisory control for antifault propagation through a case study of a polypropylene polymerization process based on a pilot plant in the petrochemical industry. The polypropylene polymerization process is a kind of petrochemical process producing the polypropylene [17] from the propylene by polymerization and composed of several unit processes such as a prepolymerization process, a polymerization process, and posterior processes 464 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001 Fig. 2. Overall schematic diagram of a polypropylene polymerization process. TABLE I NOMINAL REACTION CONDITIONS AT LR1 AND LR2 connected in serial as illustrated in Fig. 2. The propylene and MUD/TEAL/Donor mixture are fed into the prepolymerization reactor and then transferred to the polymerization reactors together with the hydrogen, propylene, ethylene, and Butene-1. Polymers are formed in the polymerization process under specific reaction conditions and the polypropylene is finally produced after several posterior processes. In the following, we consider the polymerization process which comprises two loop reactors (LRs) connected in tandem to elevate the productivity over unit volume and to reduce the residence time in the reactors. The specific nominal reaction conditions at each LR are described in Table I, in the case of terpolymer polymerization. The material feed rates are controlled by flow controllers (FCs). Suppose that the FC of LR1 is subject to abnormal events which be the aucause deviation from the nominal set values. Let 1 or 2) in view of flow tomaton of the process in LRi ( and . control. Fig. 3 illustrates the component DEMs of (“set to nominal value”), (“reset to initial In Fig. 3, (“adjust to higher value”), (“reset to nominal value”), (“adjust to lower value”), (“reset to nominal value”), value”) are the normal controllable events of , where represents one of (“Hydrogen”), (“Propylene”), (“Ethylene”), Fig. 3. Component DEMs of (ethylene); (Butene-1)]. b and G and G [m: h (hydrogen); p (propylene); e (“Butene-1”). is also subject to abnormal events of (“stuck to higher value”) and (“stuck to lower value”). are composed of (Initial Value of The states of in ), (Nominal Value of in ), (Higher in ), (Stuck to Higher Value of in Value of ), (Lower Value of in ), and (Stuck to has similarly the normal controlLower Value of in ). and its states comprise lable events of . Therefore, we know that CHO AND LIM: MULTIAGENT SUPERVISORY CONTROL FOR ANTIFAULT PROPAGATION TABLE II CMT FOR 6 AND 6 465 TABLE III STATES DEFINITION FOR PARTS OF DEMS OF G AND G and For the action enforcement in the implementation, the interface is needed to interpret the commands corresponding to the events and to act on the physical system as mentioned in Section III-B. The commands given to the interface carry implicitly continuous attributes in this case and initiate a continuous control action of the FC. For example, the command corresponding causes the FC of LR1 to control the propylene feed rate to to LR1 at the higher value than the nominal feed rate until the next control action. Hence, in this case, the equipment driver is responsible for the real-time dynamic control of the continuous subsystem, e.g., FC. Note that the deviation from the nominal values in LR1 can be compensated by adjusting the corresponding material feed rate in LR2 accordingly for propylene, ethylene, and Butene-1 in view of overall polymerization process conditions. However, if hydrogen is stuck to a higher value, then the transfer line becomes plugged before the reaction mixture transfers to LR2 since hydrogen controls the intrinsic viscosity of polymers in the mixture, which cannot be adjusted in LR2. Hence, we know From these and Definition 3, the domain of fault tolerance of becomes for all where represents the state of the component DEM of with . Let the complebe defined for and mentary measure function as appeared in the CMT of Table II where the binary . Under normal number is used such that , is chosen to be to operating conditions of satisfy the nominal reaction conditions. However, suppose and occur such that due to . In this case, and are faults and on which can be reconfigured to there exists and since meet the antifault propagation between from Theorem 1. Therefore, the returns 1 to expefeedback information dite the current process without interruption. In view of , it can be synthesized as follows. Let reconfiguration of be defined as for and with the binary number where , and such that in case of no duplication between the occurwith rence of events. Moreover, let where for , and be defined as in carries the orderly the binary representation. In this case, via the ascending binary value relationinformation of , let, e.g., , ship. From , , , , , , , , , , , , , , where and are described in Table III. Then, and we know with and with . The occurrence of abnormal events is identified by the transferred coded in this way. Furthermore, we can formulate information such that as since and from the CMT. Therefore, it becomes which assures the antifault propagation between and in accordance with Theorem 2. occurs such that On the other hand, if due to then becomes a failure since as presumed returns 0 which by Theorem 1. Therefore, to stop the current process and do failure diagrequires physically causes the nosis. This is because the failure event transfer line plugged, which cannot be complemented by any . measure of 466 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001 V. CONCLUSIONS We have studied the multiagent supervisory control methodology for antifault propagation in serial production systems. The major characteristic of the proposed scheme lies in the fact that it allows as much autonomy as possible for each agent supervisor and the least shared information between agent supervisors cooperating for overall goals in view of antifault propagation. The main contribution of this paper can be summarized as follows. 1) The idea of multiagent control is introduced for supervisory control of serial production systems in view of fault-propagation prevention. 2) The concept of antifault propagation between cascaded processes is established. 3) The synthesis of each agent supervisor satisfying the antifault propagation, the coded information for the actually occurred sequence of the closed-loop operation in the prior process, and the feedback information from the posterior process are proposed and developed in a concrete form. 4) The analytical framework of multiagent supervisory control systems for antifault propagation is established. 5) The case study of a polypropylene polymerization process in the petrochemical industry is provided to illustrate the proposed control policy. REFERENCES [1] P. J. Ramadge and W. M. Wonham, “Supervisory control of a class of discrete event processes,” SIAM J. Control Optim., vol. 25, pp. 206–230, 1987. 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Figueiredo, “A fault tolerant colored Petri net resource allocation manager for manufacturing systems,” in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, 1997, pp. 1210–1215. [26] W. H. R. Yeung and P. R. Moore, “Toward a fault tolerant cell controller for flexible assembly systems: An approach using color Petrinets,” Mechatron., vol. 8, pp. 747–764, 1998. [27] S. Balemi, G. J. Hoffmann, P. Gyugyi, H. Wong-Toi, and G. F. Franklin, “Supervisory control of a rapid thermal multiprocessor,” IEEE Trans. Automat. Contr., vol. 38, pp. 1040–1059, July 1993. [28] F. Charbonnier, H. Alla, and R. David, “Discrete-event dynamic systems,” IEEE Trans. Contr. Syst. Technol., vol. 7, pp. 175–187, Mar. 1999. Kwang-Hyun Cho (S’94–A’00) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea, in 1993, 1995, and 1998, respectively. From September 1998 to February 1999, he was a Research Associate in the Department of Electrical Engineering, KAIST. In 1999, he joined the School of Electrical Engineering and Automation, University of Ulsan, Ulsan, Korea, where he is currently an Assistant Professor. His research interests include analysis and supervisory control of discrete-event dynamic systems, nonlinear systems, hybrid systems, and application of system and control theory to communication networks and bioelectronics. Prof. Cho is a member of the Institute of Electronics Engineers of Korea and Institute of Control, Automation and Systems Engineers. Jong-Tae Lim (M’88) received the B.S.E.E. degree from Yonsei University, Seoul, Korea, the M.S.E.E. degree from Illinois Institute of Technology, Chicago, and the Ph.D. degree in computer, information, and control engineering from the University of Michigan, Ann Arbor, in 1975, 1983, and 1986, respectively. From 1975 to 1981, he was an Engineer with Korea Electric Company. From 1987 to 1988, he was a Research Fellow in the Department of Electrical Engineering and Computer Science, University of Michigan. In 1988, he joined the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea, as an Assistant Professor. He is currently a Professor. His research interests are in the areas of system and control theory, communications networks, and manufacturing systems. Prof. Lim is a member of the Institute of Control, Automation and Systems Engineers, Korean Institute of Electrical Engineers, and Institute of Electronics Engineers of Korea.