Supervisory Control and Scheduling of Resource Allocation Systems: Reachability Graph Perspective

Preface xi Acknowledgments xvii Glossary xix Acronyms xxiii About the Authors xxv Part I Resource Allocation Systems and Petri Nets 1 1 Introduction 3 1.1 Resource Allocation Systems 3 1.2 Supervisory Control and Scheduling with Petri Nets 7 1.3 Summary 9 1.4 Bibliographical Notes 9 2 Preliminaries 11 2.1 Introduction 11 2.2 Petri Nets 12 2.2.1 Basic Concepts 12 2.2.2 Modeling Power of Petri Nets 16 2.2.2.1 Sequential Execution 16 2.2.2.2 Concurrency (Parallelism) 17 2.2.2.3 Synchronization 17 2.2.2.4 Conflict (choice) 17 2.2.2.5 Merging 17 2.2.2.6 Mutual Exclusion 18 2.2.3 Behavioral Properties of Petri Nets 18 2.2.3.1 Boundedness and Safeness 18 2.2.3.2 Liveness and Deadlock 19 2.2.3.3 Reversibility 19 2.2.3.4 Conservativeness 19 2.2.4 Subclasses of Petri Nets 20 2.2.4.1 Ordinary Nets and Generalized Nets 20 2.2.4.2 Pure Petri Nets 20 2.2.4.3 State Machines 21 2.2.4.4 Marked Graphs 22 2.2.4.5 Free-choice Nets 22 2.2.4.6 Extended Free-choice Nets 22 2.2.4.7 Asymmetric Choice Nets 22 2.2.5 Petri Nets for Resource Allocation Systems 22 2.2.5.1 PC²R 23 2.2.5.2 S*PR 24 2.2.5.3 S¯5PR 25 2.2.5.4 S¯4PR, S¯4R, S³ PGR² and WS³ PSR 25 2.2.5.5 S³PR 26 2.2.5.6 ES³PR and S³PMR 26 2.2.5.7 LS³PR 27 2.2.5.8 ELS³PR 27 2.2.5.9 GLS³PR 28 2.2.6 Structural Analysis 28 2.2.7 Reachability Graph Analysis 30 2.2.7.1 Supervisory Control 30 2.2.7.2 System Scheduling 31 2.2.8 Petri Net Analysis Tools 32 2.3 Informed Heuristic Search 35 2.3.1 Basic Concepts of Heuristic A* Search 35 2.3.2 Properties of the A* Search 36 2.3.2.1 Completeness 36 2.3.2.2 Admissible Heuristics 36 2.3.2.3 Monotone (Consistent) Heuristics 36 2.3.2.4 More Informed Heuristics 36 2.4 Bibliographical Notes 37 Part II Supervisory Control 39 3 Behaviorally Maximal and Structurally Minimal Supervisor 41 3.1 Introduction 41 3.2 Petri Nets for Supervisory Synthesis 43 3.3 Optimal and Minimal Supervisory Synthesis 45 3.3.1 Reachability Graph Analysis 45 3.3.2 Supervisor Computation with Place Invariants 47 3.3.3 Optimal Supervisor Synthesis and Vector Covering Method 47 3.3.4 Optimal Supervisor with Fewest Monitors 49 3.3.5 Deadlock Prevention Policy 50 3.4 An Illustrative Example 52 3.5 Concluding Remarks 54 3.6 Bibliographical Notes 55 4 Supervisor Design with Fewer Places 57 4.1 Introduction 57 4.2 Critical and Free Activity Places 59 4.3 Properties of DP-Nets 62 4.4 Supervisor Design with Critical Activity Places 66 4.5 An Illustrative Example 70 4.6 Concluding Remarks 72 4.7 Bibliographical Notes 73 5 Redundant Constraint Elimination 75 5.1 Introduction 75 5.2 Minimal-Number-of-Monitors Problem 77 5.3 Elimination of Redundant Constraints 78 5.3.1 Redundant Reachability Constraints 78 5.3.2 Linear Program Method 79 5.3.3 Non-Linear Program Method 82 5.3.4 Supervisor Synthesis with Redundancy Elimination 84 5.4 Illustrative Examples 85 5.5 Concluding Remarks 91 5.6 Bibliographical Notes 91 6 Fast Iterative Supervisor Design 93 6.1 Introduction 93 6.2 Optimal Supervisor of a DP-net 94 6.3 Fast Synthesis of Optimal and Simple Supervisors 95 6.3.1 Multiobjective Supervisory Control 96 6.3.2 Design of an Optimal Control Place 97 6.3.3 Identification of Redundant Constraints 99 6.3.4 Iterative Deadlock Prevention 102 6.4 Illustrative Examples 107 6.5 Concluding Remarks 115 6.6 Bibliographical Notes 115 7 Supervisor Synthesis with Uncontrollable and Unobservable Transitions 117 7.1 Introduction 117 7.2 Supervisor Synthesis with Uncontrollability and Unobservability 119 7.2.1 DP-Nets with Uncontrollable and/or Unobservable Transitions 119 7.2.2 Admissible Markings and First-Met Inadmissible Markings 120 7.2.3 Design of an Admissible Monitor 123 7.2.4 Admissible and Structure-Minimal Supervisor Synthesis 125 7.3 Deadlock Prevention Policy 127 7.4 Illustrative Experiments 132 7.5 Concluding Remarks 136 7.6 Bibliographical Notes 136 Part III Heuristic Scheduling 137 8 Informed Heuristic Search in Reachability Graph 139 8.1 Introduction 139 8.2 System Scheduling with Place-Timed Petri Nets 140 8.2.1 Place-Timed Petri Nets 140 8.2.2 Conversion from an Untimed Petri Net 141 8.2.3 Synthesis of a Place-Timed Petri Net 143 8.2.3.1 Top-down Method 144 8.2.3.2 Bottom-up Method 145 8.3 State Evolution of Place-Timed Nets 145 8.4 A* Search on a Reachability Graph 152 8.5 A* Search with State Check 153 8.6 An Illustrative Example 155 8.7 Concluding Remarks 156 8.8 Bibliographical Notes 156 9 Controllable Heuristic Search 157 9.1 Introduction 157 9.2 Alternative Routes with Different Lengths 159 9.3 An Admissible Heuristic for SC-nets 160 9.4 A Controllable Heuristic Search 163 9.5 Randomly Generated Examples 166 9.6 Another Controllable Heuristic Search 168 9.6.1 A* Search and Depth-First Search 168 9.6.2 Controllable Hybrid Heuristic Search 171 9.7 Illustrative Results 176 9.8 Concluding Remarks 178 9.9 Bibliographical Notes 179 10 Hybrid Heuristic Search 181 10.1 Introduction 181 10.2 A*-BT Combinations 182 10.3 Illustrative Examples 187 10.4 Concluding Remarks 190 10.5 Bibliographical Notes 191 11 A* Search with More Informed Heuristics Functions 193 11.1 Introduction 193 11.2 More Informed Heuristics in A* Search 194 11.3 Combination of Admissible and Inadmissible Heuristics 195 11.4 Illustrative Examples 197 11.5 Concluding Remarks 203 11.6 Bibliographical Notes 204 12 Symbolic Heuristic Search 205 12.1 Introduction 205 12.2 Boolean Algebra and Binary Decision Diagram 206 12.3 Symbolic Evolution of Place-Timed Petri Nets 207 12.4 Symbolic Heuristic Search 213 12.5 Illustrative Examples 218 12.6 Concluding Remarks 224 12.7 Bibliographical Notes 226 13 Open Problems 227 13.1 Structural Analysis of Generalized Nets 227 13.2 Robust Supervisor Synthesis with Unreliable Resources 227 13.3 Alleviation of the State Explosion Problem 228 13.4 Optimization of Symbolic Variable Ordering 229 13.5 Multiobjective Scheduling 230 13.6 Anytime Heuristic Scheduling 230 13.7 Parallel Heuristic Search 231 13.8 Bidirectional Heuristic Search 232 13.9 Computing and Scheduling with GPUs 232 References 235 Index 253