Verification and Control of Hybrid Systems (eBook)
XV, 202 Seiten
Springer US (Verlag)
978-1-4419-0224-5 (ISBN)
Hybrid systems describe the interaction of software, described by finite models such as finite-state machines, with the physical world, described by infinite models such as differential equations. This book addresses problems of verification and controller synthesis for hybrid systems. Although these problems are very difficult to solve for general hybrid systems, several authors have identified classes of hybrid systems that admit symbolic or finite models. The novelty of the book lies on the systematic presentation of these classes of hybrid systems along with the relationships between the hybrid systems and the corresponding symbolic models. To show how the existence of symbolic models can be used for verification and controller synthesis, the book also outlines several key results for the verification and controller design of finite systems. Several examples illustrate the different methods and techniques discussed in the book.
Hybrid systems describe the interaction of software, described by finite models such as finite-state machines, with the physical world, described by infinite models such as differential equations. This book addresses problems of verification and controller synthesis for hybrid systems. Although these problems are very difficult to solve for general hybrid systems, several authors have identified classes of hybrid systems that admit symbolic or finite models. The novelty of the book lies on the systematic presentation of these classes of hybrid systems along with the relationships between the hybrid systems and the corresponding symbolic models. To show how the existence of symbolic models can be used for verification and controller synthesis, the book also outlines several key results for the verification and controller design of finite systems. Several examples illustrate the different methods and techniques discussed in the book.
Foreword 6
Contents 11
Part I Basic concepts 14
1 Systems 15
1.1 System definition 15
1.2 System behavior 18
1.3 Examples 20
1.4 Composing systems 31
1.5 Notes 33
2 Verification problems 35
2.1 Sa = Sb 35
2.2 Sa < = Sb
3 Control problems 37
3.1 Sc x Sa = Sb 37
3.2 Sc x Sa < = Sb
Part II Finite systems 39
4 Exact system relationships 40
4.1 Behavioral relationships 41
4.2 Similarity relationships 44
4.3 Alternating similarity relationships 51
4.4 Notes 53
5 Verification 54
5.1 Behavioral relations 54
5.2 Similarity relations 56
5.3 Notes 61
6 Control 62
6.1 Feedback composition 63
6.2 Safety games 66
6.3 Reachability games 72
6.4 Behavioral games 75
6.5 Similarity games 75
6.6 Notes 81
Part III In nite Systems: Exact symbolic models 82
7 Exact symbolic models for veri cation 83
7.1 Dynamical and hybrid dynamical systems as systems 84
7.2 Timed automata 90
7.3 Order minimal hybrid dynamical systems 97
7.4 Sign based abstractions 104
7.5 Barrier certi cates 113
7.6 Computation of reachable sets 115
7.7 Advanced topics 119
7.8 Notes 120
8 Exact symbolic models for control 122
8.1 Control systems as systems 123
8.2 Controller re nemen 126
8.3 Discrete-time linear control systems 127
8.4 Continuous-time multi-a ne control systems 142
8.5 Notes 151
Part IV Infnite Systems: Approximate symbolic models 152
9 Approximate system relationships 153
9.1 Approximate similarity relationships 153
9.2 Approximate alternating similarity relationships 156
9.3 Notes 157
10 Approximate symbolic models for veri cation 158
10.1 Stability of linear dynamical systems 159
10.2 Dynamical systems as systems 162
10.3 Symbolic models for a ne dynamical systems 163
10.4 Advanced topics 170
10.5 Notes 173
11 Approximate symbolic models for control 174
11.1 Stability of linear control systems 175
11.2 Control and switched systems as systems 177
11.3 Approximate feedback composition and controller re nement 179
11.4 Symbolic models for a ne control systems 182
11.5 Symbolic models for switched a ne systems 190
11.7 Notes 196
Appendix 197
Index 206
| Erscheint lt. Verlag | 12.6.2009 |
|---|---|
| Zusatzinfo | XV, 202 p. 200 illus. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Informatik ► Web / Internet | |
| Mathematik / Informatik ► Mathematik | |
| Naturwissenschaften | |
| Technik | |
| Schlagworte | approximate bisimulation • approximate simulation • bisimulation • control synthesis • Simulation • symbolic models • System • verification |
| ISBN-10 | 1-4419-0224-4 / 1441902244 |
| ISBN-13 | 978-1-4419-0224-5 / 9781441902245 |
| Haben Sie eine Frage zum Produkt? |
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