Significant progress has been made on nonlinear control systems in the past two decades. However, many of the existing nonlinear control methods cannot be readily used to cope with communication and networking issues without nontrivial modifications. For example, small quantization errors may cause the performance of a "well-designed" nonlinear control system to deteriorate. Motivated by the need for new tools to solve complex problems resulting from smart power grids, biological processes, distributed computing networks, transportation networks, robotic systems, and other cutting-edge control applications, Nonlinear Control of Dynamic Networks tackles newly arising theoretical and real-world challenges for stability analysis and control design, including nonlinearity, dimensionality, uncertainty, and information constraints as well as behaviors stemming from quantization, data-sampling, and impulses.Delivering a systematic review of the nonlinear small-gain theorems, the text: * Supplies novel cyclic-small-gain theorems for large-scale nonlinear dynamic networks * Offers a cyclic-small-gain framework for nonlinear control with static or dynamic quantization * Contains a combination of cyclic-small-gain and set-valued map designs for robust control of nonlinear uncertain systems subject to sensor noise * Presents a cyclic-small-gain result in directed graphs and distributed control of nonlinear multi-agent systems with fixed or dynamically changing topology Based on the authors' recent research, Nonlinear Control of Dynamic Networks provides a unified framework for robust, quantized, and distributed control under information constraints. Suggesting avenues for further exploration, the book encourages readers to take into consideration more communication and networking issues in control designs to better handle the arising challenges.
Chapter 1 Introduction 1 (18)
1.1 Control Problems with Dynamic Networks 1 (3)
1.2 Lyapunov Stability 4 (4)
1.3 Input-to-State Stability 8 (7)
1.4 Input-to-Output Stability 15 (1)
1.5 Input-to-State Stabilization and an 16 (3)
Overview of the Book
Chapter 2 Interconnected Nonlinear Systems 19 (20)
2.1 Trajectory-Based Small-Gain Theorem 21 (5)
2.2 Lyapunov-Based Small-Gain Theorem 26 (4)
2.3 Small-Gain Control Design 30 (6)
2.4 Notes 36 (3)
Chapter 3 Large-Scale Dynamic Networks 39 (40)
3.1 Continuous-Time Dynamic Networks 42 (12)
3.2 Discrete-Time Dynamic Networks 54 (9)
3.3 Hybrid Dynamic Networks 63 (12)
3.4 Notes 75 (4)
Chapter 4 Control under Sensor Noise 79 (64)
4.1 Static State Measurement Feedback 80 (13)
Control
4.2 Dynamic State Measurement Feedback 93 (8)
Control
4.3 Decentralized Output Measurement 101(15)
Feedback Control
4.4 Event-Triggered and Self-Triggered 116(15)
Control
4.5 Synchronization under Censor Noise 131(6)
4.6 Application: Robust Adaptive Control 137(2)
4.7 Notes 139(4)
Chapter 5 Quantized Nonlinear Control 143(50)
5.1 Static Quantization: A Sector Bound 144(13)
Approach
5.2 Dynamic Quantization 157(23)
5.3 Quantized Output-Feedback Control 180(10)
5.4 Notes 190(3)
Chapter 6 Distributed Nonlinear Control 193(62)
6.1 A Cyclic-Small-Gain Result in Digraphs 196(2)
6.2 Distributed Output-Feedback Control 198(9)
6.3 Formation Control of Nonholonomic 207(17)
Mobile Robots
6.4 Distributed Control with Flexible 224(26)
Topologies
6.5 Notes 250(5)
Chapter 7 Conclusions and Future Challenges 255(6)
Appendix A Related Notions in Graph Theory 261(2)
Appendix B Systems with Discontinuous Dynamics 263(6)
B.1 Basic Definitions 263(1)
B.2 Extended Filippov Solution 264(1)
B.3 Input-to-State Stability 265(1)
B.4 Large-Scale Dynamic Networks of 266(3)
Discontinuous Subsystems
Appendix C Technical Lemmas Related to 269(4)
Comparison Functions
Appendix D Proofs of the Small-Gain Theorems 273(12)
2.1, 3.2 and 3.6
D.1 A Useful Technical Lemma 273(1)
D.2 Proof of Theorem 2.1: The Asymptotic 273(2)
Gain Approach
D.3 Sketch of Proof of Theorem 3.2 275(4)
D.4 Proof of Theorem 3.6 279(6)
Appendix E Proofs of Technical Lemmas in 285(8)
Chapter 4
E.1 Proof of Lemma 4.2 285(1)
E.2 Proof of Lemma 4.3 286(1)
E.3 Proof of Lemma 4.5 287(2)
E.4 Proof of Lemma 4.6 289(4)
Appendix F Proofs of Technical Lemmas in 293(12)
Chapter 5
F.1 Proof of Lemma 5.1 293(2)
F.2 Proof of Lemma 5.3 295(2)
F.3 Proof of Lemma 5.4 297(1)
F.4 Proof of Lemma 5.5 298(5)
F.5 Proof of Lemma 5.8 303(2)
References 305(16)
Index 321
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