Symbolic Nonblocking Computation of Timed Discrete Event Systems

In this paper, we symbolically compute a minimally restrictive nonblocking supervisor for timed discrete event systems (TDESs), in the supervisory control theory context. The method is based on Timed Extended Finite Automata, which is an augmentation of extended finite automata (EFAs) by incorporating discrete time in the model. EFAs are ordinary automaton extended with discrete variables, guard expressions and updating functions. The main feature of this approach is that it is not based on ”tick” models that have been commonly used in this area, leading to better performance in many cases. In addition, to tackle large problems all computations are based on binary decision diagrams. As a case study, we effectively computed the minimally restrictive nonblocking supervisor for a well-known production cell.

[1]  Bengt Lennartson,et al.  Relations identification and visualization for sequence planning and automation design , 2010, 2010 IEEE International Conference on Automation Science and Engineering.

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

[3]  Ali Saadatpoor,et al.  Timed State Tree Structures: Supervisory Control and Fault Diagnosis , 2010 .

[4]  Hassane Alla,et al.  A control synthesis approach for time discrete event systems , 2006, Math. Comput. Simul..

[5]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[6]  B. Lennartson,et al.  Solving two supervisory control benchmark problems using Supremica , 2008, 2008 9th International Workshop on Discrete Event Systems.

[7]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[8]  Bengt Lennartson,et al.  BDD-based supervisory control on extended finite automata , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[9]  Bengt Lennartson,et al.  Supervisor computation and representation: A case study , 2010, WODES.

[10]  Ahmed Khoumsi,et al.  A New Method for Transforming Timed Automata , 2005, SBMF.

[11]  Bengt Lennartson,et al.  Coordination of Operations by Relation Extraction for Manufacturing Cell Controllers , 2010, IEEE Transactions on Control Systems Technology.

[12]  Walter Murray Wonham,et al.  Reduced supervisors for timed discrete-event systems , 2003, IEEE Trans. Autom. Control..

[13]  Bengt Lennartson,et al.  Automatic generation of controllers for collision-free flexible manufacturing systems , 2010, 2010 IEEE International Conference on Automation Science and Engineering.

[14]  W. M. Wonham,et al.  The control of discrete event systems , 1989 .

[15]  Bengt Lennartson,et al.  Sequence Planning for Integrated Product, Process and Automation Design , 2010, IEEE Transactions on Automation Science and Engineering.

[16]  V. Garg,et al.  Supervisory control of real-time discrete-event systems using lattice theory , 1996, IEEE Trans. Autom. Control..

[17]  Claus Lewerentz,et al.  Formal Development of Reactive Systems: Case Study Production Cell , 1995 .

[18]  Bruce H. Krogh,et al.  Maximally Permissive Policies for Controlled Time Marked Graphs , 1993 .

[19]  Bengt Lennartson,et al.  Efficient Symbolic Supervisory Synthesis and Guard Generation - Evaluating Partitioning Techniques for the State-space Exploration , 2011, ICAART.

[20]  H. Wong-Toi,et al.  The control of dense real-time discrete event systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[21]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[22]  P. Ramadge,et al.  Modular Supervisory Control of Discrete Event Systems , 1988 .

[23]  Masahiro Fujita,et al.  Spectral Transforms for Large Boolean Functions with Applications to Technology Mapping , 1993, 30th ACM/IEEE Design Automation Conference.

[24]  Chen Haoxun,et al.  Maximally permissive state feedback logic for controlled time Petri nets , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[25]  Knut Åkesson,et al.  Modeling of discrete event systems using finite automata with variables , 2007, 2007 46th IEEE Conference on Decision and Control.

[26]  Joseph Sifakis,et al.  Automatic Verification Methods for Finite State Systems , 1989, Lecture Notes in Computer Science.

[27]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[28]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[29]  Lei Feng,et al.  Designing communicating transaction processes by supervisory control theory , 2007, Formal Methods Syst. Des..

[30]  Jean-Louis Boimond,et al.  Supervisory Control of (max,+) Automata: A Behavioral Approach , 2009, Discret. Event Dyn. Syst..

[31]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[32]  Amir Pnueli,et al.  Symbolic Controller Synthesis for Discrete and Timed Systems , 1994, Hybrid Systems.

[33]  Beate Bollig,et al.  Improving the Variable Ordering of OBDDs Is NP-Complete , 1996, IEEE Trans. Computers.

[34]  W. M. Wonham,et al.  State based control of timed discrete event systems using binary decision diagrams , 2007, Syst. Control. Lett..

[35]  W. M. Wonham,et al.  A framework for real-time discrete event control , 1990 .

[36]  W.M. Wonham,et al.  STSLib and its application to two benchmarks , 2008, 2008 9th International Workshop on Discrete Event Systems.

[37]  Aniello Murano.  Communicating Sequential Processes (CSP) , 2009, Encyclopedia of Parallel Computing.

[38]  Knut Åkesson,et al.  Compositional Synthesis of Maximally Permissive Supervisors Using Supervision Equivalence , 2007, Discret. Event Dyn. Syst..

[39]  A. Saadatpoor,et al.  Supervisor State Size Reduction for Timed Discrete-Event Systems , 2007, 2007 American Control Conference.

[40]  Knut Åkesson,et al.  Supremica - A Tool for Verification and Synthesis of Discrete Event Supervisors , 2003 .

[41]  W. Wonham,et al.  Supervisory control of timed discrete-event systems , 1994, IEEE Trans. Autom. Control..

[42]  Walter Murray Wonham,et al.  Nonblocking supervisory control of state tree structures , 2005, IEEE Transactions on Automatic Control.

[43]  Kwang-Hyun Cho,et al.  Supervisory control of real-time discrete event systems under bounded time constraints , 2004 .

[44]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[45]  Y. Brave,et al.  Formulation and control of real time discrete event processes , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[46]  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.

[47]  H. Andersen.  An Introduction to Binary Decision Diagrams , 1997 .

[48]  Bengt Lennartson,et al.  Efficient supervisory synthesis of large systems , 2006 .

[49]  Bengt Lennartson,et al.  A BDD-Based Approach for Modeling Plant and Supervisor by Extended Finite Automata , 2012, IEEE Transactions on Control Systems Technology.