Efficient Symbolic Supervisor Synthesis for Extended Finite Automata

The state-space explosion problem, resulting from the reachability computations in controller synthesis, is one of the main obstacles preventing supervisory control theory from having an industrial breakthrough. To alleviate this problem, a strategy is to symbolically perform the synthesis procedure using binary decision diagrams. Based on this principle, the work presented in this brief develops an efficient symbolic reachability approach for discrete event systems that are modeled as finite automata with variables, referred to as extended finite automata. Using a disjunctive event partitioning technique, the proposed approach first partitions the transition relation of the considered system into a set of partial transition relations. These partial transition relations are then selected systematically to perform the reachability analysis, which is the most fundamental challenge for synthesizing supervisors. It has been shown through solving a set of benchmark supervisory control problems for EFA that the proposed approach significantly improves scalability in comparison with the previously published results.

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

[2]  Hervé Marchand,et al.  Supervisory control problems of hierarchical finite state machines , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  Bruce H. Krogh,et al.  Synthesis of feedback control logic for a class of controlled Petri nets , 1990 .

[4]  Goran Cengic,et al.  A Control Software Development Method Using IEC 61499 Function Blocks, Simulation and Formal Verification , 2008 .

[5]  Robert K. Brayton,et al.  BDD Variable Ordering for Interacting Finite State Machines , 1994, 31st Design Automation Conference.

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

[7]  Edmund M. Clarke,et al.  Symbolic model checking for sequential circuit verification , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

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

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

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

[11]  Bengt Lennartson,et al.  Symbolic State-Space Exploration and Guard Generation in Supervisory Control Theory , 2011, ICAART.

[12]  Jos C. M. Baeten,et al.  A process-theoretic approach to supervisory control theory , 2011, Proceedings of the 2011 American Control Conference.

[13]  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.

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

[15]  Howard Wong-Toi,et al.  Symbolic Synthesis of Supervisory Controllers , 1992, 1992 American Control Conference.

[16]  Knut Åkesson,et al.  Modeling sequential resource allocation systems using Extended Finite Automata , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[17]  Alessandro Giua,et al.  A Survey of Petri Net Methods for Controlled Discrete Event Systems , 1997, Discret. Event Dyn. Syst..

[18]  Ryan J. Leduc,et al.  Hierarchical Interface-based Supervisory Control , 2003 .

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

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

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

[22]  David Harel,et al.  Statecharts: A Visual Formalism for Complex Systems , 1987, Sci. Comput. Program..

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