Modeling and control of discrete-event dynamical systems : with Petri nets and other tool

Discrete-event dynamic systems (DEDs) permeate our world, being of great importance in modern manufacturing processes, transportation and various forms of computer and communications networking.

"Modeling and Control of Discrete-event Dynamic Systems" begins with the mathematical basics required for the study of DEDs and moves on to present various tools used in their modeling and control. Among the instruments explained are many forms of Petri net, the sequential function chart, state charts, formal languages and max-plus algebra.

Industrial examples illustrate the concepts and methods discussed. Using them, readers will be able to understand DEDs quickly and to master the control methods to analyze and improve the performance of their systems.

Final-year undergraduates and graduates embarking on further courses in control, manufacturing and process engineering, computer studies or operations research will find this text an invaluable aid in learning about the control of this important class of systems.

Author Notes

Branislav Hrúz received his Ph.D. from the Slovak Academy of Sciences, Institute of Technical Cybernetics in Bratislava, in 1968. He joined the Research Institute of Mathematical Machines in Prague in 1960 and then the Institute of Technical Cybernetics of the Slovak Academy of Sciences, Bratislava, Slovak Republic, in 1963, and then the State Forest Products Research Institute in Bratislava, Control Engineering Laboratory, in 1971, where he led the first projects of computer automation of the woodworking industry in the former Czechoslovakia. Since 1991 he has been an Associate Professor at the Slovak University of Technology, a member of Faculty of Electrical Engineering and Information Technology, vice-head of Department of Automatic Control Systems. His main interests are in modeling and control of complex systems (especially those of a discrete-event nature), threshold logic functions, finite automata, Petri nets, control methods applied in manufacturing, and instruments and tools for the computer programming of control in practical applications. Dr. Hrúz is author or co-author of 100+ publications including three books and he has presented over fifty papers at national or international conferences. He has served as a member of programming or organizing committees of many international conferences. He acted as a visiting Professor at the Vienna University in Austria and he has lectured (by invitation) in Finland, Germany, USA, and France.

MengChu Zhou received his Ph.D. from Rensselaer Polytechnic Institute. He joined New Jersey Institute of Technology (NJIT) in 1990, and is currently a Professor of Electrical and Computer Engineering and Director of the Discrete-Event Systems Laboratory. His interests are in computer-integrated systems, Petri nets, networks, and manufacturing. He has 200+ publications including six books and 80+ journal papers. He is Managing Editor of IEEE Transactions on Systems, Man and Cybernetics (SMC), AssociateEditor of IEEE Transactions on Automation Science and Engineering , and Editor-in-Chief of International Journal of Intelligent Control and Systems . He has served as General and Program Chair of many international conferences. Dr. Zhou has led or participated in twenty-eight research and education projects with total budget over $10M, funded by the National Science Foundation, (US) Department of Defense, and industry. He was the recipient of the CIM University-LEAD Award from the Society of Manufacturing Engineers, the Perlis Research Award by NJIT, the Humboldt Research Award for US Senior Scientists, and is a Distinguished Lecturer of IEEE SMC Society. He has been invited to lecture in Australia, Canada, China, France, Germany, Hong Kong, Italy, Japan, Korea, Mexico, Taiwan, and US. He was founding chair of Discrete Event Systems Technical Committee of IEEE SMC Society, and a Co-Chair (founding) of the Semiconductor Factory Automation Technical Committee of the IEEE Robotics and Automation Society. He is a life member of the Chinese Association for Science and Technology-USA and served as its President in 1999. He is Fellow of IEEE .

Notation	p. xvii
1 Basic Description of Discrete-event Dynamic Systems	p. 1
1.1 Introduction	p. 1
1.2 Discrete Variables and Relations	p. 4
1.3 Discrete Processes	p. 6
1.4 Basic Properties of DEDS and their Specification	p. 10
1.5 Basic Transition System	p. 11
1.6 Problems and Exercises	p. 20
2 Graphs in Modeling DEDS	p. 23
2.1 Simple Non-labeled Directed Mathematical Graphs	p. 23
2.2 Labeled Mathematical Graphs	p. 24
2.3 Subgraphs and Components	p. 25
2.4 Directed Paths	p. 27
2.5 Problems and Exercises	p. 29
3 Formal Languages	p. 33
3.1 Notion of the Formal Language	p. 33
3.2 Formal Grammars and Classification of Formal Languages	p. 34
3.3 Regular Expressions	p. 38
3.4 Problems and Exercises	p. 40
4 Control of DEDS	p. 41
4.1 State and Control Variables	p. 41
4.2 Control System and Control Function	p. 42
4.3 Problems and Exercises	p. 46
5 Finite Automata	p. 49
5.1 Basic Definitions	p. 49
5.2 Description of the System Behavior Using Finite Automata	p. 52
5.3 Control Specification Using Finite Automata	p. 55
5.4 Non-deterministic Finite Automata	p. 60
5.5 Problems and Exercises	p. 60
6 Reactive Flow Diagrams	p. 63
6.1 Standard Flow Diagrams	p. 63
6.2 Reactive Flow Diagrams	p. 64
6.3 Problems and Exercises	p. 67
7 Petri Net Models of DEDS	p. 69
7.1 Notion of Petri Nets	p. 69
7.2 Basic Definitions	p. 76
7.3 Vector and Matrix Representation of Petri Nets	p. 80
7.4 Petri Net Classes	p. 91
7.5 Petri Nets Interpreted for Control	p. 95
7.6 Petri Nets with Capacities	p. 99
7.7 Problems and Exercises	p. 102
8 Properties of Petri Nets	p. 107
8.1 Marking Reachability	p. 107
8.2 Reachability Graph	p. 109
8.3 Boundedness	p. 115
8.4 Coverability	p. 116
8.5 Coverability Graph	p. 118
8.6 Liveness	p. 124
8.7 Reversibility	p. 127
8.8 Persistence and Fairness	p. 128
8.9 Conservativeness	p. 129
8.10 P-invariants and T-invariants	p. 134
8.11 Concurrency and Conflict	p. 149
8.12 Analysis of Petri Net Properties	p. 152
8.13 Structural Properties	p. 155
8.14 Problems and Exercises	p. 157
9 Grafcet	p. 161
9.1 Basic Grafcet Components	p. 161
9.2 Dynamics Modeling with Grafcet	p. 164
9.3 Comparison of Petri Nets and Grafcet	p. 169
9.4 Problems and Exercises	p. 173
10 Timed and High-level Petri Nets	p. 177
10.1 From Standard to Higher-level Petri Nets	p. 177
10.2 Deterministic Timed Petri Nets	p. 178
10.3 Stochastic Timed Petri Nets	p. 180
10.4 Colored Petri Nets	p. 185
10.5 Fuzzy Petri Nets	p. 192
10.6 Adaptive Petri Nets	p. 196
10.7 Petri Net-based Design Tools	p. 204
10.8 Problems and Exercises	p. 205
11 Statecharts	p. 209
11.1 Introduction	p. 209
11.2 Basic Statechart Components	p. 209
11.3 Statechart Application	p. 213
11.4 Problems and Exercises	p. 214
12 DEDS Modeling, Control and Programming	p. 217
12.1 Modeling Methodology	p. 217
12.2 Resolution of Conflicts	p. 225
12.3 Control Programs in DEDS	p. 234
12.4 Ladder Logic Diagrams	p. 246
12.5 Problems and Exercises	p. 256
13 Supervisory Control	p. 261
13.1 Basic Notion	p. 261
13.2 System Controllability	p. 262
13.3 Supervisory Control Solution Based on Finite Automata	p. 269
13.4 Supervisory Control Solution with P-invariants	p. 282
13.5 Supervisory Control Solution with Reachability Graph	p. 295
13.6 Problems and Exercises	p. 301
14 Job Scheduling	p. 305
14.1 Problem Formulation	p. 305
14.2 Job Scheduling and Petri Nets	p. 309
14.3 Job Scheduling Based on the Max-plus Algebra	p. 313
14.4 Problems and Exercises	p. 321
References	p. 325
Index	p. 333

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