Table of Contents

List of Figures.....ix

List of Tables

Foreword.....xiii

Preface.....xv

1

INTRODUCTION.....1

2

PETRI NETS.....5

2.1

Petri Net Definitions.....6

2.2

Structural Invariants.....9

2.3

Siphons and Traps.....10

2.4

Classes of Petri Nets.....13

2.5

Petri Nets and Automata.....14

2.6

Petri Nets in Control.....19

3

INVARIANT BASED CONTROL DESIGN.....23

3.1

Monitor Based Supervisors.....25

3.2

Supervisor Synthesis using Place Invariants.....27

3.3

Maximally Permissive Supervision.....31

4

UNCONTROLLABLE AND UNOBSERVABLE TRANSITIONS.....33

4.1

Uncontrollable Transitions.....34

4.2

Unobservable Transitions.....35

4.3

Constraint Transformations.....35

4.4

Vector Discrete Event Systems.....38

4.5

Petri Net Modeled Supervisors.....43

5

CONSTRAINT TRANSFORMATION AND CONTROLLER SYNTHESIS.....51

5.1

Computing Constraint Transformations.....51

5.2

Structure of Admissible Constraints and Controls.....58

5.3

Admissible Constraints and Controller Synthesis.....60

5.4

Enforcing Disjunctions of Linear Constraints.....67

5.5

Petri Net Modeled Supervisors.....43

6

RESOURCE MANAGEMENT AND DEADLOCK AVOIDANCE.....73

6.1

Modeling of Finite Resources.....73

6.2

Conditions for Liveness.....75

6.3

Deadlock Avoidance.....81

7

OTHER CONTROL SPECIFICATIONS.....89

7.1

Equality Constraints.....90

7.2

Constraints involving the Firing Vector.....91

7.3

Logical Constraints on System Behavior.....97

7.4

Constraints Involving Time.....99

7.5

Limits of the Constraint Inequality.....106

8

EXAMPLE APPLICATIONS.....113

8.1

The Cat and Mouse Problem.....113

8.2

Automated Guided Vehicle Coordination.....119

8.3

The Unreliable Machine.....122

8.4

Piston Rod Robotic Assembly Cells.....129

8.5

Asynchronous Transfer Mode Switch.....136

8.6

The Three Tanks Problem.....139

8.7

Hybrid Control System Example.....148

9

SUMMARY AND CONCLUSIONS.....153

Glossary.....157

References.....171

List of Symbols.....177

Index.....179

About the Authors.....187