Formal Methods for Multi-Agent Feedback Control Systems

Table Of Contents

Preface ix
I Foundations 1
1 Introduction 3
1.1 Multi-Agent Control Systems…………………. 3
1.2 Formal Methods for Multi-Agent Control Systems………. 5
1.3 Outlook……………………………. 6
1.4 Notes and References……………………… 7
1.5 Notation……………………………. 8
2 Multi-Agent Systems and Control Theory 11
2.1 Dynamical Systems………………………. 12
2.2 Selected Topics from Nonlinear Control Theory………… 27
2.3 Multi-Agent Control Systems…………………. 39
2.4 Notes and References……………………… 42
3 Formal Methods and Spatiotemporal Logics 45
3.1 Formal Methods……………………….. 46
3.2 Spatiotemporal Logics…………………….. 54
3.3 Timed Automata Theory…………………… 64
3.4 Notes and References……………………… 72
II Multi-Agent Control Barrier Functions for Spatiotemporal
Constraints 75
4 Centralized Time-Varying Control Barrier Functions 77
4.1 Time-Varying Control Barrier Functions……………. 78
4.2 Encoding Signal Temporal Logic……………….. 80
4.3 Control Laws based on Time-Varying Control Barrier Functions… 86
4.4 Constructing Valid Time-Varying Control Barrier Functions….. 93
4.5 Unicycle Models and Unknown Dynamics…………… 102
4.6 Notes and References……………………… 105
4.7 Additional Proofs……………………….. 106
5 Decentralized Time-Varying Control Barrier Functions 109
5.1 Decentralized Collaborative Control……………… 110
5.2 Decentralized Control under Conflicting Local Specifications….. 120
5.3 Notes and References……………………… 129
5.4 Additional Proofs……………………….. 131
III Multi-Agent Funnel Control for Spatiotemporal Constraints
137
6 Centralized Funnel Control 139
6.1 Encoding Signal Temporal Logic……………….. 141
6.2 Control Laws based on a Single Funnel…………….. 145
6.3 Control Laws based on Multiple Funnels……………. 151
6.4 Notes and References……………………… 160
6.5 Additional Proofs……………………….. 162
7 Decentralized Funnel Control 165
7.1 Decentralized Collaborative Funnel Control………….. 166
7.2 Decentralized Funnel Control under Conflicting Local Specifications 170
7.3 Experiments and Practical Considerations…………… 178
7.4 Notes and References……………………… 183
IV Planning under Spatiotemporal Logic Specifications 185
8 Timed Automata-based Planning 187
8.1 Encoding Signal Interval Temporal Logic…………… 188
8.2 Timed Abstraction of Dynamical Control Systems………. 194
8.3 Dynamically Feasible Plan Synthesis……………… 197
8.4 Notes and References……………………… 200
V Moving Forward 203
9 Outlook and Open Problems 205
Bibliography 212
Index 240