Supervisory Control and Scheduling of Resource Allocation Systems Reachability Graph Perspective IEEE Press Series on Systems Science and Engineering Series

Presents strategies with reachability graph analysis for optimizing resource allocation systems

Supervisory Control and Scheduling of Resource Allocation Systems offers an important guide to Petri net (PN) models and methods for supervisory control and system scheduling of resource allocation systems (RASs). Resource allocation systems are common in automated manufacturing systems, project management systems, cloud data centers, and software engineering systems. The authors?two experts on the topic?present a definition, techniques, models, and state-of-the art applications of supervisory control and scheduling problems.

The book introduces the basic concepts and research background on resource allocation systems and Petri nets. The authors then focus on the deadlock-free supervisor synthesis for RASs using Petri nets. The book also investigates the heuristic scheduling of RASs based on timed Petri nets. Conclusions and open problems are provided in the last section of the book. 

This important book:

• Includes multiple methods for supervisory control and scheduling with reachability graphs, and provides illustrative examples
• Reveals how to accelerate the supervisory controller design and system scheduling of RASs based on PN reachability graphs, with optimal or near-optimal results
• Highlights both solution quality and computational speed in RAS deadlock handling and system scheduling

Written for researchers, engineers, scientists, and professionals in system planning and control, engineering, operation, and management, Supervisory Control and Scheduling of Resource Allocation Systems provides an essential guide to the supervisory control and scheduling of resource allocation systems (RASs) using Petri net reachability graphs, which allow for multiple resource acquisitions and ?exible routings.

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 S⁵PR 25

2.2.5.4 S⁴PR, S⁴R, 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

BO HUANG, PHD, is a Full Professor with the School of Computer Science and Engineering at Nanjing University of Science and Technology (NUST).

MENGCHU ZHOU, PHD, is a Distinguished Professor of Electrical and Computer Engineering and the Director of Discrete-Event Systems Laboratory at the New Jersey Institute of Technology (NJIT).