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Supervision Based on Place Invariants: A Survey

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Abstract

The supervision based on place invariants (SBPI) is an efficient technique for the supervisory control of Petri nets. This paper reveals the significance of the SBPI based on a literature survey, applications, and an analysis of problems and supervisory settings that can be addressed using SBPI. Special attention is given to the various settings within which the problem can be formulated. Such settings can be distinguished based on the concurrency type, the type of controllability and observability, and the centralized or decentralized type of supervision. As we show, it is possible to approach the most general settings in a purely structural way, without resorting to reachability analysis. We begin by describing the SBPI problem and the literature methods that address this problem or are related to it. Then, we proceed to show classes of problems that can be reduced to the SBPI problem. In the SBPI, the specification is described as a system of inequalities that the Petri net marking must satisfy at any time. However, as we show, problems involving more general specifications can be approached in the SBPI setting, sometimes under additional assumptions, by performing net and/or specification transformations. Four of the specifications we will consider are logic constraints, language specifications, disjunctions of linear constraints, and liveness. We conclude with a presentation of possible applications of the SBPI approach to programming with semaphores, fault tolerance, and synchronic-distance based designs.

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References

  • Achour Z, Rezg N, Xie X (2004) Supervisory control of partially observable marked graphs. IEEE Trans on Automat Contr 49(11):2007–2011

    Article  MathSciNet  Google Scholar 

  • Banaszak Z, Krogh B (1990) Deadlock avoidance in flexible manufacturing systems with concurrently competing process flows. IEEE Trans Robot Autom 6(6):724–734

    Article  Google Scholar 

  • Barkaoui K, Chaoui A, Zouari B (1997) Supervisory control of discrete event systems using structure theory of Petri nets. In: Proc. IEEE international conference on systems, man, and cybernetics, Orlando, Florida, pp 3750–3755

  • Basile F, Chiacchio P, Giua A (1998a) On the choice of suboptimal monitor places for supervisory control of Petri nets. In: Proc. IEEE international conference on systems, man, and cybernetics, San Diego, California, pp 752–757

  • Basile F, Chiacchio P, Giua, A (1998b) Supervisory control of Petri nets based on suboptimal monitors places. In: Proc. 4th international workshop on discrete event systems, Cagliari, Italy, pp 85–87

  • Basile F, Chiacchio P, Giua A (2000) Optimal control of Petri net monitors with control and observation costs. In: Proc. 39’th IEEE international conference on decision and control, Sydney, Australia, pp 424–429

  • Bemporad A, Morari M (1999) Control of systems integrating logic, dynamics, and constraints. Automatica 35(3):407–427

    Article  MATH  MathSciNet  Google Scholar 

  • Boel RK, Ben-Naoum L, Breusegem VV (1995) On forbidden state problems for a class of controlled Petri nets. IEEE Trans Automat Contr 40(1):1717–1731

    Article  MATH  Google Scholar 

  • Chen H (1998) Net structure and control logic synthesis of controlled Petri nets. IEEE Trans Automat Contr 43(10):1446–1450

    Article  MATH  Google Scholar 

  • Chen H (2000) Control synthesis of Petri nets based on S-decreases. Discret Event Dyn Syst: Theory Appl 10(3):233–250

    Article  MATH  Google Scholar 

  • Chen H, Hu B (1991) Distributed control of discrete event systems described by a class of controlled Petri nets. In: Preprints of IFAC international symposium on distributed intelligence systems

  • Chen H, Hu B (1994) Monitor-based control of a class of controlled Petri nets. In: Proc. 3rd international conference on automation, robotics and computer vision

  • Church A (1963) Logic, arithmetics, and automata. In: Proc. international congress of mathematicians, Institut Mittag-Leffler, Sweden, pp 23–35

  • Clarke E, Grumberg O, Peled D (1999) Model Checking. MIT, Cambridge, Massachusetts

    Google Scholar 

  • Darondeau P, Xie X (2003) Linear control of live marked graphs. Automatica 39(3):429–440

    Article  MATH  MathSciNet  Google Scholar 

  • Desrochers A, Al’Jaar R (1995) Applications of Petri nets in manufacturing systems: modelling, control and performance analysis. IEEE, Piscataway, New Jersey

    Google Scholar 

  • Ezpeleta J, Colom JM, Martínez J (1995) A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Trans Automat Contr 11(2):173–184

    Google Scholar 

  • Genrich HJ, Lautenbach K, Thiagarajan PS (1980) Elements of general net theory. In: Brauer W (ed) Net theory and applications. Lecture notes in computer science, vol 84. Springer, Berlin Heidelberg New York, pp 21–163

    Google Scholar 

  • Ghaffari A, Rezg N, Xie X (2003a) Design of a live and maximally permissive Petri net controller using the theory of regions. IEEE Trans Robot Autom 19(1):137–142

    Article  MathSciNet  Google Scholar 

  • Ghaffari A, Rezg N, Xie X (2003b) Feedback control logic for forbidden-state problems of marked graphs: application to a real manufacturing system. IEEE Trans Automat Contr 48(1):2–17

    Article  MathSciNet  Google Scholar 

  • Giua A, DiCesare F (1991) Supervisory design using Petri nets. In: Proc. 30’th IEEE international conference on decision and control, Brighton, UK, pp 92–97

  • Giua A, DiCesare F (1994) Blocking and controllability of Petri nets in supervisory control. IEEE Trans Automat Contr 39(4):818–823

    Article  MATH  MathSciNet  Google Scholar 

  • Giua A, DiCesare F (1995) Decidability and closure properties of weak Petri net languages in supervisory control. IEEE Trans Automat Contr 40(5):906–910

    Article  MATH  MathSciNet  Google Scholar 

  • Giua A, DiCesare F, Silva M (1992) Generalized mutual exclusion constraints on nets with uncontrollable transitions. In: Proc. IEEE international conference on systems, man and cybernetics, Chicago, Illinois, pp 974–979

  • Giua A, Seatzu C (2001) Supervisory control of railway networks with Petri nets. In: Proc. 40’th IEEE conference on decision and control, pp 5004–5009

  • Giua A, Seatzu C (2002) Observability of place/transition nets. IEEE Trans Automat Contr 47(9):1424–1437

    Article  MathSciNet  Google Scholar 

  • Giua A, Seatzu C, Basile F (2004) Observer-based state feedback control of timed Petri nets with deadlock recovery. IEEE Trans Automat Contr 49(1):17–29

    Article  MathSciNet  Google Scholar 

  • Golaszewski CH, Ramadge PJ (1988a) Discrete event processes with arbitrary controls. In: Denham MJ, Laub AJ (eds.): Advanced computing concepts and techniques in control engineering, Springer, Berlin Heidelberg New York, pp 459–469

    Google Scholar 

  • Golaszewski CH, Ramadge PJ (1988b) Mutual exclusion problems for discrete event systems with shared events. In: Proc. 27th IEEE conference on decision and control, Austin, Texas, pp 234–239

  • Hadjicostis CN, Verghese GC (1999) Monitoring discrete event systems using Petri net embeddings. In: Application and theory of Petri nets 1999. vol 1639. Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, pp 188–207

    Google Scholar 

  • He K, Lemmon M (2000) On the transformation of maximally permissive marking-based supervisors into monitor supervisors. In: Proc. IEEE conference on decision and control, Sydney, Australia, pp 2657–2662

  • Holloway L, Guan X, Zhang L (1996) A generalization of state avoidance policies for controlled Petri nets. IEEE Trans Automat Contr 41(6):804–816

    Article  MATH  MathSciNet  Google Scholar 

  • Holloway L, Krogh B (1990) Synthesis of feedback control logic for a class of controlled Petri nets. IEEE Trans Automat Contr 35(5):514–523

    Article  MATH  MathSciNet  Google Scholar 

  • Holloway L, Krogh B (1992) On closed-loop liveness of discrete-event systems under maximally permissive control. IEEE Trans Automat Contr 37(5):692–697

    Article  MathSciNet  Google Scholar 

  • Holloway LE, Krogh BH (1994) Controlled Petri nets: A tutorial survey. In: 11th international conference on analysis and optimization of systems: discrete event systems. Lecture notes in control and information science, vol 199. Springer, Berlin Heidelberg New York, pp 158–168

    Chapter  Google Scholar 

  • Holloway LE, Krogh BH, Giua A (1997) A survey of Petri net methods for controlled discrete event systems. Discret Event Dyn Syst 7(2):151–190

    Article  MATH  Google Scholar 

  • Ichikawa A, Hiraishi K (1988) Analysis and control of discrete event systems represented by Petri nets. In: Varaiyo P, Kurzhanski AB (eds) Disrete event systems: models and applications. Lecture notes in control and information sciences, vol 103. Springer, Berlin Heidelberg New York, pp 115–134

    Google Scholar 

  • Ichikawa A, Yokoyama K, Kurogi S (1985) Reachability and control of discrete event systems represented by conflict-free Petri nets. In: Internationl symposium on circuits and systems, proceedings, Kyoto, Japan. IEEE, New York, pp 487–490

    Google Scholar 

  • Iordache M, Antsaklis P (2003a) Design of T-liveness enforcing supervisors in Petri nets. IEEE Trans Automat Contr 48(11):1962–1974

    Article  MathSciNet  Google Scholar 

  • Iordache M, Antsaklis P (2003b) Synthesis of supervisors enforcing general linear vector constraints in Petri nets. IEEE Trans Automat Contr 48(11):2036–2039

    Article  MathSciNet  Google Scholar 

  • Iordache MV (2003) Methods for the supervisory control of concurrent systems based on Petri net abstractions. PhD thesis, University of Notre Dame, Indiana

  • Iordache MV, Antsaklis PJ (2002). Software tools for the supervisory control of Petri nets based on place invariants. Technical report isis-2002-003, University of Notre Dame, Indiana

  • Iordache MV, Antsaklis PJ (2003c) Admissible decentralized control of Petri nets. In: Proc. 2003 American control conf., Denver, Colorado, pp 332–337

  • Iordache MV, Antsaklis PJ (2003d) Decentralized control of Petri nets with constraint transformations. In: Proc. 2003 American control conference, Denver, Colorado, pp 314–319

  • Iordache MV, Antsaklis PJ (2004) Resilience to failures and reconfigurations in the supervision based on place invariants. In: Proc. 2004 American control conference, Boston, Massachusetts, pp 4477–4482

  • Iordache MV, Antsaklis PJ (2005) A structural approach to the enforcement of language and disjunctive constraints. In: Proc. 2005 American control conference, Portland, Oregon, pp 3920–3925

  • Iordache MV, Moody JO, Antsaklis PJ (2002) Synthesis of deadlock prevention supervisors using Petri nets. IEEE Trans Robot Autom 18(1):59–68

    Article  Google Scholar 

  • Kosaraju SR (1973) Limitations of Dijkstra’s semaphore primitives and Petri nets. Oper Syst Rev 7(4):122–126

    Article  Google Scholar 

  • Krogh B (1987) Controlled Petri nets andmaximally permissive feedback logic. In: Proc. 25th Annual Allerton conference, University of Illinois, Urbana, Illinois, pp 317–326

  • Krogh B, Holloway L (1991) Synthesis of feedback control logic for manufacturing systems. Automatica 27(4):641–651

    Article  Google Scholar 

  • Kumar R, Holloway L (1996) Supervisory control of Petri nets with regular specification languages. IEEE Trans Automat Contr 41(2):245–249

    Article  MATH  MathSciNet  Google Scholar 

  • Lautenbach K, Thiagarajan PS (1979) Analysis of a resource allocation problem using Petri nets. In: Proc. 1st European conference on parallel and distributed processing, Cepadues Editions, Toulouse, France, pp 260–266

  • Lemmon M, He K (2000) Supervisory plug-ins for distributed software. In: Pezze M, Shatz M (eds) Proc. workshop on software engineering and Petri nets, University of Aarhus, Department of Computer Science, Aarhus, Denmark, pp 155–172

  • Lemmon M, He K, Shatz S (2000) Dynamic reconfiguration of software objects using Petri nets and network unfolding. In: Proc. IEEE international conference on systems, man, and cybernetics, Nashville, Tennessee, pp 3069–3074

  • Li Y, Wonham W (1993) Control of vector discrete-event systems I-The base model. IEEE Trans Automat Contr 38(8):1214–1227

    Article  MATH  MathSciNet  Google Scholar 

  • Li Y, Wonham W (1994) Control of vector discrete-event systems II-Controller synthesis. IEEE Trans Automat Contr 39(3):512–530

    Article  MATH  MathSciNet  Google Scholar 

  • Li Y, Wonham W (1995) Concurrent vector discrete-event systems. IEEE Trans Automat Contr 40(4):628–638

    Article  MATH  MathSciNet  Google Scholar 

  • Moody JO, Antsaklis PJ (1998) Supervisory control of discrete event systems using Petri nets, Kluwer, Boston, Massachusetts

    MATH  Google Scholar 

  • Moody JO, Antsaklis PJ (2000) Petri net supervisors for DES with uncontrollable and unobservable transitions. IEEE Trans Automat Contr 45(3):462–476

    Article  MATH  MathSciNet  Google Scholar 

  • Park J, Reveliotis S (2001) Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and flexible routings. IEEE Trans Automat Contr 46(10):1572–1583

    Article  MATH  MathSciNet  Google Scholar 

  • Park J, Reveliotis S (2002) Liveness-enforcing supervision for resource allocation systems with uncontrollable behavior and forbidden states. IEEE Trans Robot Autom 18(2):234–240

    Article  Google Scholar 

  • Peterson JL (1981) Petri net theory and the modeling of systems. Prentice Hall, Englewood Cliffs, New Jersey

    MATH  Google Scholar 

  • Pnueli A, Rosner R (1989) On the synthesis of a reactive module. In: Proc. ACM symposium on principles of programming languages, Austin, Texas, pp 179–190

  • Ramadge P (1989) Some tractable supervisory control problems for discrete-event systems modeled by Büchi Automata. IEEE Trans Automat Contr 34(1):10–19

    Article  MATH  MathSciNet  Google Scholar 

  • Ramadge P, Wonham W (1987) Modular feedback logic for discrete-event systems. SIAM J Control Optim 25(5):1202–1218

    Article  MATH  MathSciNet  Google Scholar 

  • Ramadge P, Wonham W ( 1989) The control of discrete event systems. Proc. IEEE 77(1):81–98

    Article  Google Scholar 

  • Reveliotis S (2005) Real-time management of resource allocation systems: A discrete event systems approach. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Sifakis J (1979) Realization of fault-tolerant systems by coding Petri nets. J Des Autom Fault-Toler Comput 3:93–107

    MathSciNet  Google Scholar 

  • Sreenivas RS (2000) On a minimally restrictive supervisory policy that enforces liveness in partially controlled free choice Petri nets. In: Proc. 39th IEEE conference on decision and control, Sydney, Australia, pp 2651–2656

  • Stremersch G (2001) Supervision of Petri nets. Kluwer, Boston, Massachusetts

    MATH  Google Scholar 

  • Stremersch G, Boel RK (1999) Enforcing k-safeness in controlled state machines. In: Proc. 38th IEEE conference on decision and control, Phoenix, Arizona, pp 1737–1742

  • Stremersch G, Boel RK (2000) Reduction of the supervisory control problem for Petri nets. IEEE Trans Automat Contr 45(12):2358–2363

    Article  MATH  MathSciNet  Google Scholar 

  • Stremersch G, Boel RK (2001) Decomposition of the supervisory control problem for Petri nets under preservation of maximal permissiveness. IEEE Trans Automat Contr 46(9):1490–1496

    Article  MATH  MathSciNet  Google Scholar 

  • Stremersch G, Boel RK (2002) Structuring acyclic Petri nets for reachability analysis and control. Discret Event Dyn Syst 12(1):7–41

    Article  MATH  MathSciNet  Google Scholar 

  • Suarez MS (1985) Error detection and correction on Petri net models of discrete events control systems. In: International symposium on circuits and systems. IEEE, Kyoto, Japan, pp 921–924

    Google Scholar 

  • Suarez MS (1987) Towards a synchrony theory for P/T nets. In: Voss K, Genrich HJ, Rozenberg G (eds) Concurrency and nets–advances in Petri nets, Springer, Berlin, Heidelberg, New York, pp 435–460

    Google Scholar 

  • Suraj Z (1980) Resource allocation problem. In: Proc. of the 3rd symp. on math. foundations of comput. science, ICS PAS reports, Zaborow, Poland, pp 83–86

  • Tittus M, Egardt B (1999) Hierarchical supervisory control for batch processes. IEEE Trans Control Syst Technol 7(5):542–554

    Article  Google Scholar 

  • Tricas F, Garcia-Valles F, Colom JM, Ezpeleta J (2000) New methods for deadlock prevention and avoidance in concurrent systems. Actas de las Jornadas de Concurrencia, Cuenca, Spain, pp 97–110

  • Valk R, Jantzen M (1985) The residue of vector sets with applications to decidability problems in Petri nets. Acta Inform 21:643–674

    Article  MATH  MathSciNet  Google Scholar 

  • Williams HP (1987) Linear and integer programming applied to the propositional calculus. Int J Syst Sci 2:81–100

    Google Scholar 

  • Williams HP (1993) Model building in mathematical programming (3rd edn). Wiley, Chichester, New York

    MATH  Google Scholar 

  • Xing K, Hu B, Chen H (1996) Deadlock avoidance policy for Petri net modeling of flexible manufacturing systems with shared resources. IEEE Trans Automat Contr 41(2):289–295

    Article  MATH  MathSciNet  Google Scholar 

  • Yamalidou E, Kantor J (1991) Modeling and optimal control of discrete-event chemical processes using Petri nets. Comput Chem Eng 15(7):503–519

    Article  Google Scholar 

  • Yamalidou E, Moody JO, Antsaklis PJ, Lemmon MD (1996) Feedback control of Petri nets based on place invariants. Automatica 32(1):15–28

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang L, Holloway LE (1995) Forbidden state avoidance in controlled Petri nets under partial observation. In: Proc. 33rd annual allerton conference on communications, control, and computing, Monticello, Illinois, pp 146–155

  • Zuberek WM (1999) Petri net models of process synchronization mechanisms. In: Proc. IEEE international conference on systems, man, and cybernetics, Tokyo, Japan, pp 841–847

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  1. School of Engineering & Engineering Technology, LeTourneau University, Longview, TX, 75607, USA

    M. V. Iordache

  2. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    P. J. Antsaklis

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  1. M. V. Iordache
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Iordache, M.V., Antsaklis, P.J. Supervision Based on Place Invariants: A Survey. Discrete Event Dyn Syst 16, 451–492 (2006). https://doi.org/10.1007/s10626-006-0021-9

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