Deadlock Avoidance Policies for Automated Manufacturing Systems Using Finite State Automata

This chapter considers the problem of deadlock avoidance in flexibly automated manufacturing systems, one of the most prevalent supervisory control problems that challenges the effective deployment of these environments. The problem is addressed through the modeling abstraction of the (sequential) resource allocation system (RAS), and the pursued analysis uses concepts and results from the formal modeling framework of finite state automata (FSA). A notion of optimality is defined through the notion of maximal permissiveness, but the computation of the optimal DAP is shown to be NP-Hard. Hence, the last part of the chapter discusses some approaches that have been developed by the relevant research community in its effort to deal with this negative complexity result.

[1]  Ahmed Nazeem Designing parsimonious representations of the maximally permissive deadlock avoidance policy for complex resource allocation systems through classification theory , 2012 .

[2]  F. Lin,et al.  Modeling of discrete event systems using finite state machines with parameters , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[3]  Ted K. Ralphs,et al.  Integer and Combinatorial Optimization , 2013 .

[4]  Spyros Reveliotis Real-time management of resource allocation systems : a discrete event systems approach , 2004 .

[5]  Spyros Reveliotis,et al.  Deadlock Avoidance for Sequential Resource Allocation Systems: Hard and Easy Cases , 2001 .

[6]  Roberto Cordone,et al.  Maximally permissive deadlock avoidance for sequential resource allocation systems using disjunctions of linear classifiers , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  Bengt Lennartson,et al.  Symbolic Computation of Reduced Guards in Supervisory Control , 2011, IEEE Transactions on Automation Science and Engineering.

[8]  Jean-Michel Couvreur,et al.  Hierarchical Decision Diagrams to Exploit Model Structure , 2005, FORTE.

[9]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[10]  Murat Uzam,et al.  An Optimal Deadlock Prevention Policy for Flexible Manufacturing Systems Using Petri Net Models with Resources and the Theory of Regions , 2002 .

[11]  Spyros A. Reveliotis,et al.  Efficient Enumeration of Minimal Unsafe States in Complex Resource Allocation Systems , 2014, IEEE Transactions on Automation Science and Engineering.

[12]  Lei Feng,et al.  TCT: A Computation Tool for Supervisory Control Synthesis , 2006, 2006 8th International Workshop on Discrete Event Systems.

[13]  Devadas Pillai,et al.  The future of semiconductor manufacturing , 2006, IEEE Robotics & Automation Magazine.

[14]  Mark Lawley,et al.  Polynomial-complexity deadlock avoidance policies for sequential resource allocation systems , 1997, IEEE Trans. Autom. Control..

[15]  E. Pastor,et al.  Symbolic Analysis of Bounded Petri Nets , 2001, IEEE Trans. Computers.

[16]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[17]  MengChu Zhou,et al.  A Survey and Comparison of Petri Net-Based Deadlock Prevention Policies for Flexible Manufacturing Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[18]  MuDer Jeng,et al.  Process nets with resources for manufacturing modeling and their analysis , 2002, IEEE Trans. Robotics Autom..

[19]  Scott A. Mahlke,et al.  Optimal Liveness-Enforcing Control for a Class of Petri Nets Arising in Multithreaded Software , 2013, IEEE Transactions on Automatic Control.

[20]  Nils J. Nilsson,et al.  The Mathematical Foundations of Learning Machines , 1990 .

[21]  R. Malik,et al.  Supremica - An integrated environment for verification, synthesis and simulation of discrete event systems , 2006, 2006 8th International Workshop on Discrete Event Systems.

[22]  Bruce H. Krogh,et al.  Deadlock avoidance in flexible manufacturing systems with concurrently competing process flows , 1990, IEEE Trans. Robotics Autom..

[23]  Joaquín Ezpeleta,et al.  A Banker's solution for deadlock avoidance in FMS with flexible routing and multiresource states , 2002, IEEE Trans. Robotics Autom..

[24]  D. Gerwin Manufacturing flexibility: a strategic perspective , 1993 .

[25]  Shi-Chung Chang,et al.  Dispatching-driven deadlock avoidance controller synthesis for flexible manufacturing systems , 1994, IEEE Trans. Robotics Autom..

[26]  Jr. Mikell P. Groover Automation, production systems, and computer-aided manufacturing , 1980 .

[27]  S. Lafortune,et al.  DESUMA: A Tool Integrating GIDDES and UMDES , 2006, 2006 8th International Workshop on Discrete Event Systems.

[28]  Spyros A. Reveliotis,et al.  Designing Reversibility-Enforcing Supervisors of Polynomial Complexity for Bounded Petri Nets Through the Theory of Regions , 2006, ICATPN.

[29]  Spyros A. Reveliotis,et al.  Deadlock avoidance policies for automated manufacturing cells , 1996, IEEE Trans. Robotics Autom..

[30]  Fag Lin,et al.  Robust and Adaptive Supervisory Control of Discrete Event Systems , 1992, 1992 American Control Conference.

[31]  Fabrice Kordon,et al.  Hierarchical Set Decision Diagrams and Regular Models , 2009, TACAS.

[32]  Gianfranco Ciardo Reachability Set Generation for Petri Nets: Can Brute Force Be Smart? , 2004, ICATPN.

[33]  Emmanuelle Encrenaz-Tiphène,et al.  Data Decision Diagrams for Petri Net Analysis , 2002, ICATPN.

[34]  Javier Martínez,et al.  A Petri net based deadlock prevention policy for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

[35]  Joaquín Ezpeleta,et al.  A Petri Net Structure– Based Deadlock Prevention Solution for Sequential Resource Allocation Systems , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[36]  Spyros A. Reveliotis,et al.  On the Complexity of Maximally Permissive Deadlock Avoidance in Multi-Vehicle Traffic Systems , 2010, IEEE Transactions on Automatic Control.

[37]  MengChu Zhou,et al.  Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[38]  Roberto Cordone,et al.  Designing Optimal Deadlock Avoidance Policies for Sequential Resource Allocation Systems Through Classification Theory: Existence Results and Customized Algorithms , 2013, IEEE Transactions on Automatic Control.

[39]  Nidhal Rezg,et al.  Design of a live and maximally permissive Petri net controller using the theory of regions , 2003, IEEE Trans. Robotics Autom..

[40]  Spyros A. Reveliotis,et al.  A correct and scalable deadlock avoidance policy for flexible manufacturing systems , 1998, IEEE Trans. Robotics Autom..

[41]  Sankardeep Chakraborty,et al.  Advanced Data Structures , 2019 .

[42]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[43]  Stéphane Lafortune,et al.  Designing Compact and Maximally Permissive Deadlock Avoidance Policies for Complex Resource Allocation Systems Through Classification Theory: The Linear Case , 2011, IEEE Transactions on Automatic Control.

[44]  MengChu Zhou,et al.  Deadlock Resolution in Computer-Integrated Systems , 2004 .

[45]  Spyros A. Reveliotis,et al.  Designing maximally permissive deadlock avoidance policies for sequential resource allocation systems through classification theory , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[46]  B. Williams,et al.  Operations management. , 2001, Optometry.

[47]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[48]  B. Lennartson,et al.  Extraction and representation of a supervisor using guards in extended finite automata , 2008, 2008 9th International Workshop on Discrete Event Systems.

[49]  Spyros A. Reveliotis,et al.  An efficient algorithm for the enumeration of the minimal unsafe states in complex resource allocation systems , 2012, 2012 IEEE International Conference on Automation Science and Engineering (CASE).

[50]  Kimmo Varpaaniemi Efficient Detection of Deadlocks in Petri Nets , 1993 .

[51]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[52]  Spyros A. Reveliotis,et al.  Generalized Algebraic Deadlock Avoidance Policies for Sequential Resource Allocation Systems , 2007, IEEE Transactions on Automatic Control.

[53]  Jana Kosecka,et al.  Control of Discrete Event Systems , 1992 .

[54]  Spyros A. Reveliotis,et al.  Optimal Linear Separation of the Safe and Unsafe Subspaces of Sequential Resource Allocation Systems as a Set-Covering Problem: Algorithmic Procedures and Geometric Insights , 2013, SIAM J. Control. Optim..

[55]  Philippe Darondeau,et al.  Theory of Regions , 1996, Petri Nets.

[56]  Stéphane Lafortune,et al.  Modeling, analysis, and control of a class of resource allocation systems arising in concurrent software , 2012 .

[57]  Jonghun Park,et al.  On the “Counter-Example” in the Article “Max $^{\prime}$-Controlled Siphons for Liveness of $S^{3}PGR^{2}$” Regarding the Results in “Deadlock Avoidance in Sequential Resource Allocation Systems With Multiple Resource Acquisitions and Flexible Routings” , 2001, IEEE Transactions on Automatic Control.

[58]  Roberto Cordone,et al.  Monitor optimization in Petri net control , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[59]  Antti Valmari,et al.  Stubborn sets for reduced state space generation , 1991, Applications and Theory of Petri Nets.

[60]  Spyros A. Reveliotis,et al.  Maximally permissive deadlock avoidance for resource allocation systems with R/W-locks , 2014, Discrete Event Dynamic Systems.

[61]  John N. Tsitsiklis,et al.  On the control of discrete-event dynamical systems , 1987, 26th IEEE Conference on Decision and Control.

[62]  Gianfranco Ciardo,et al.  Efficient Reachability Set Generation and Storage Using Decision Diagrams , 1999, ICATPN.

[63]  Walter Murray Wonham,et al.  On the complexity of supervisory control design in the RW framework , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[64]  Maria Pia Fanti,et al.  Event-based feedback control for deadlock avoidance in flexible production systems , 1997, IEEE Trans. Robotics Autom..

[65]  Spyros Reveliotis,et al.  The Application and Evaluation of Banker's Algorithm for Deadlock-Free Buffer Space Allocation in Flexible Manufacturing Systems , 1998 .

[66]  Haoxun Chen,et al.  Deadlock avoidance policy for Petri-net modeling of flexible manufacturing systems with shared resources , 1996 .

[67]  Spyros A. Reveliotis,et al.  A Practical Approach for Maximally Permissive Liveness-Enforcing Supervision of Complex Resource Allocation Systems , 2011, IEEE Transactions on Automation Science and Engineering.

[68]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.