Symbolic Synthesis and Verification of Hierarchical Interface-based Supervisory Control

Hierarchical interface-based supervisory control (HISC) decomposes a discrete-event system (DES) into a high-level subsystem which communicates with n ges 1 low-level subsystems, through separate interfaces which restrict the interaction of the subsystems. It provides a set of local conditions that can be used to verify global conditions such as nonblocking and controllability. The current HISC verification and synthesis algorithms are based upon explicit state and transition listings which limit the size of a given level to about 107 states when 1GB of memory is used. In this paper, we extend the HISC approach by introducing a set of predicate based fixed point operators that allow us to do a per level synthesis to construct for each level a maximally permissive supervisor that satisfies the corresponding HISC conditions. We prove that these fixpoint operators compute the required level-wise supremal languages. We then present algorithms that implement the fixpoint operators. Based on these algorithms, a symbolic implementation is briefly discussed which can be implemented using binary decision diagrams. We also discuss a method to implement our synthesized supervisors in a more compact manner. A large manufacturing system example (worst case state space on the order of 1030) extended from the ALP example is briefly discussed. The example showed that we can now handle a given level with a statespace as large as 10 15 states, using less than 160MB of memory. This represents a significant improvement in the size of systems that can be handled by the HISC approach. A software tool for synthesis and verification of HISC systems using our approach was also developed

[1]  Stephan Merz,et al.  Model Checking , 2000 .

[2]  Peter E. Caines,et al.  Dynamical consistency in hierarchical supervisory control , 2002, IEEE Trans. Autom. Control..

[3]  P. Ramadge,et al.  On the supremal controllable sublanguage of a given language , 1984, The 23rd IEEE Conference on Decision and Control.

[4]  W. Wonham,et al.  Control of vector discrete-event systems. I. The base model , 1993, IEEE Trans. Autom. Control..

[5]  Stéphane Lafortune,et al.  Decentralized supervisory control with communicating controllers , 2000, IEEE Trans. Autom. Control..

[6]  Olivier Coudert,et al.  Verification of Synchronous Sequential Machines Based on Symbolic Execution , 1989, Automatic Verification Methods for Finite State Systems.

[7]  Murat Uzam Petri-net-based supervisory control of discrete event systems and their ladder logic diagram implementations , 1998 .

[8]  Richard Rudell Dynamic variable ordering for ordered binary decision diagrams , 1993, ICCAD.

[9]  W. M. Wonham,et al.  STCT: An Efficient Algorithm for Supervisory Control Design , 2002 .

[10]  R. Leduc Hierarchical Interface-based Supervisory Control , 2003 .

[11]  José E. R. Cury,et al.  Modular Supervisory Control of Large Scale Discrete Event Systems , 2000 .

[12]  W. Murray Wonham,et al.  Control of state tree structures , 2003 .

[13]  W. M. Wonham,et al.  Existence and design of supervisors for vector discrete event systems , 1995, Proceedings 1995 Canadian Conference on Electrical and Computer Engineering.

[14]  Mark Lawford,et al.  Hierarchical interface-based supervisory control of a flexible manufacturing system , 2006, IEEE Transactions on Control Systems Technology.

[15]  Walter Murray Wonham,et al.  Hierarchical interface-based supervisory control-part II: parallel case , 2005, IEEE Transactions on Automatic Control.

[16]  W. M. Wonham,et al.  Modular supervisory control of discrete-event systems , 1988, Math. Control. Signals Syst..

[17]  Ryan J. Leduc,et al.  Synthesis Method for Hierarchical Interface-based Supervisory Control , 2007, ACC.

[18]  Jan H. Richter,et al.  HIERARCHICAL INTERFACE-BASED SUPERVISORY CONTROL OF A BOTTLING PLANT , 2005 .

[19]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[20]  Panos J. Antsaklis,et al.  Supervisory Control of Discrete Event Systems Using Petri Nets , 1998, The International Series on Discrete Event Dynamic Systems.

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

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

[23]  Dennis S. Arnon,et al.  A Bibliography of Quantifier Elimination for Real Closed Fields , 1988, J. Symb. Comput..

[24]  Haoxun Chen,et al.  Model aggregation for hierarchical control synthesis of discrete event systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

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

[26]  W. M. Wonham,et al.  Decentralized control and coordination of discrete-event systems with partial observation , 1990 .

[27]  Ryan J. Leduc,et al.  Synthesis Method for Hierarchical Interface-based Supervisory Control , 2007, 2007 American Control Conference.

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

[29]  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 .

[30]  B. A. Brandin,et al.  The supervisory control of the automated manufacturing system of the AIP , 1994, Proceedings of the Fourth International Conference on Computer Integrated Manufacturing and Automation Technology.

[31]  César R. C. Torrico,et al.  Hierarchical supervisory control of discrete event systems based on state aggregation , 2002 .

[32]  R. Bryant Graph-Based Algorithms for Boolean Function Manipulation12 , 1986 .

[33]  L. Grigorov Hierarchical control of discrete-event systems , 2005 .

[34]  A. Vahidi,et al.  Efficient Analysis of Large Discrete-Event Systems with Binary Decision Diagrams , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[35]  Mark Lawford,et al.  Hierarchical interface-based supervisory control: Bi-level systems , 2001 .

[36]  W. Wonham,et al.  Control of vector discrete-event systems. II. Controller synthesis , 1994, IEEE Trans. Autom. Control..

[37]  P. Ramadge,et al.  Modular feedback logic for discrete event systems , 1987 .

[38]  A. Tarski A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[39]  Valentin Goranko,et al.  Logic in Computer Science: Modelling and Reasoning About Systems , 2007, J. Log. Lang. Inf..

[40]  Ryan J. Leduc PLC implementation of a DES supervisor for a manufacturing testbed: An implementation perspective , 1996 .

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

[42]  Stéphane Lafortune,et al.  A General Architecture for Decentralized Supervisory Control of Discrete-Event Systems , 2002, Discret. Event Dyn. Syst..

[43]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[44]  K. C. Wong,et al.  Decentralized supervisory control of discrete-event systems with communication , 1996 .

[45]  Walter Murray Wonham,et al.  Hierarchical interface-based supervisory Control-part I: serial case , 2005, IEEE Transactions on Automatic Control.

[46]  Ken Q. Pu Modeling and control of discrete-event systems with hierarchical abstraction , 2000 .