| Preface | 6 |
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| Contents | 9 |
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| Symbols | 13 |
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| 1 Introduction | 16 |
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| 1.1 Contribution and Background | 16 |
| 1.2 Outline of the Book | 19 |
| 2 An Introduction to Petri Nets | 22 |
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| 2.1 Automata | 22 |
| 2.2 Petri Nets | 24 |
| 2.3 Petri Nets versus Automata | 36 |
| 2.4 Bibliographical Notes | 43 |
| 3 The Supervision of Petri Nets | 44 |
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| 3.1 Introduction | 44 |
| 3.2 Supervision Based on Place Invariants | 45 |
| 3.3 Supervision Settings | 48 |
| 3.4 Admissible and Feasible Sets of Constraints | 52 |
| 3.5 Transformations to Admissible Constraints | 54 |
| 3.6 Overview of Supervisory Methods | 57 |
| 3.7 Concluding Remarks | 65 |
| 4 Enforcing General Specifications | 66 |
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| 4.1 Introduction | 66 |
| 4.2 Enforcing Generalized Linear Constraints | 67 |
| 4.3 Language Constraints | 99 |
| 4.4 Disjunctions of Constraints | 101 |
| 5 Decentralized Supervision of Petri Nets | 107 |
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| 5.1 Introduction | 107 |
| 5.2 Related Work | 110 |
| 5.3 Preliminaries | 114 |
| 5.4 The Model | 115 |
| 5.5 Decentralized Admissibility | 117 |
| 5.6 Distributing a Centralized Supervisory Policy | 126 |
| 5.7 Design with Constraint Transformations | 130 |
| 5.8 Example | 134 |
| 6 Deadlock and Liveness Properties of Petri Nets | 138 |
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| 6.1 Introduction | 138 |
| 6.2 Preliminaries | 140 |
| 6.3 Results | 142 |
| 6.4 Implications and Discussion | 155 |
| 6.5 Algorithms | 159 |
| 7 Liveness Enforcement in Petri Nets: A Structural Approach. Part I | 165 |
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| 7.1 Introduction | 165 |
| 7.2 Related Work | 167 |
| 7.3 Problem Statement | 170 |
| 7.4 Motivation | 171 |
| 7.5 Procedure Definition | 175 |
| 7.6 Examples | 184 |
| 7.7 Properties | 188 |
| 7.8 Extending the Permissiveness of the Procedure | 195 |
| 8 Liveness Enforcement in Petri Nets: A Structural Approach. Part II | 198 |
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| 8.1 Introduction | 198 |
| 8.2 Problem Statement | 198 |
| 8.3 Motivation | 200 |
| 8.4 Procedure Definition | 204 |
| 8.5 Examples | 212 |
| 8.6 Properties | 216 |
| 8.7 Extending Permissiveness | 221 |
| 8.8 Convergence Issues | 224 |
| 8.9 Applications | 228 |
| 9 DES Control of Concurrent Hybrid Systems | 235 |
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| 9.1 Introduction | 235 |
| 9.2 Related Work | 238 |
| 9.3 Modeling | 239 |
| 9.4 DES-Level Supervision | 246 |
| 10 Hybrid System Level Control | 254 |
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| 10.1 Introduction | 254 |
| 10.2 Related Work | 255 |
| 10.3 The Hybrid Automaton Model | 257 |
| 10.4 Extracting the DES Abstraction | 259 |
| 10.5 Computation of the Controllable Invariant Sets | 265 |
| 10.6 Computation of the Predecessor | 270 |
| References | 273 |
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| Index | 287 |