Tabuada Verification and Control of Hybrid Systems

A Symbolic Approach
1. Auflage 2009
ISBN: 978-1-4419-0224-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 202 Seiten

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.

Autoren/Hrsg.

Tabuada, Paulo

Inhaltsverzeichnis

1;Foreword;6
2;Contents;11
3;Part I Basic concepts;14
3.1;1 Systems;15
3.1.1;1.1 System definition;15
3.1.2;1.2 System behavior;18
3.1.3;1.3 Examples;20
3.1.4;1.4 Composing systems;31
3.1.5;1.5 Notes;33
3.2;2 Verification problems;35
3.2.1;2.1 Sa = Sb;35
3.2.2;2.2 Sa <= Sb;36
3.3;3 Control problems;37
3.3.1;3.1 Sc x Sa = Sb;37
3.3.2;3.2 Sc x Sa <= Sb;38
4;Part II Finite systems;39
4.1;4 Exact system relationships;40
4.1.1;4.1 Behavioral relationships;41
4.1.2;4.2 Similarity relationships;44
4.1.3;4.3 Alternating similarity relationships;51
4.1.4;4.4 Notes;53
4.2;5 Verification;54
4.2.1;5.1 Behavioral relations;54
4.2.2;5.2 Similarity relations;56
4.2.3;5.3 Notes;61
4.3;6 Control;62
4.3.1;6.1 Feedback composition;63
4.3.2;6.2 Safety games;66
4.3.3;6.3 Reachability games;72
4.3.4;6.4 Behavioral games;75
4.3.5;6.5 Similarity games;75
4.3.6;6.6 Notes;81
5;Part III In nite Systems: Exact symbolic models;82
5.1;7 Exact symbolic models for veri cation;83
5.1.1;7.1 Dynamical and hybrid dynamical systems as systems;84
5.1.2;7.2 Timed automata;90
5.1.3;7.3 Order minimal hybrid dynamical systems;97
5.1.4;7.4 Sign based abstractions;104
5.1.5;7.5 Barrier certi cates;113
5.1.6;7.6 Computation of reachable sets;115
5.1.7;7.7 Advanced topics;119
5.1.8;7.8 Notes;120
5.2;8 Exact symbolic models for control;122
5.2.1;8.1 Control systems as systems;123
5.2.2;8.2 Controller re nemen;126
5.2.3;8.3 Discrete-time linear control systems;127
5.2.4;8.4 Continuous-time multi-a ne control systems;142
5.2.5;8.5 Notes;151
6;Part IV Infnite Systems: Approximate symbolic models;152
6.1;9 Approximate system relationships;153
6.1.1;9.1 Approximate similarity relationships;153
6.1.2;9.2 Approximate alternating similarity relationships;156
6.1.3;9.3 Notes;157
6.2;10 Approximate symbolic models for veri cation;158
6.2.1;10.1 Stability of linear dynamical systems;159
6.2.2;10.2 Dynamical systems as systems;162
6.2.3;10.3 Symbolic models for a ne dynamical systems;163
6.2.4;10.4 Advanced topics;170
6.2.5;10.5 Notes;173
6.3;11 Approximate symbolic models for control;174
6.3.1;11.1 Stability of linear control systems;175
6.3.2;11.2 Control and switched systems as systems;177
6.3.3;11.3 Approximate feedback composition and controller re nement;179
6.3.4;11.4 Symbolic models for a ne control systems;182
6.3.5;11.5 Symbolic models for switched a ne systems;190
6.3.6;11.7 Notes;196
7;Appendix;197
8;Index;206