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.
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1 | (18) |
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1.1 Control Problems with Dynamic Networks |
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1 | (3) |
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4 | (4) |
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1.3 Input-to-State Stability |
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8 | (7) |
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1.4 Input-to-Output Stability |
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15 | (1) |
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1.5 Input-to-State Stabilization and an Overview of the Book |
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16 | (3) |
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Chapter 2 Interconnected Nonlinear Systems |
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19 | (20) |
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2.1 Trajectory-Based Small-Gain Theorem |
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21 | (5) |
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2.2 Lyapunov-Based Small-Gain Theorem |
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26 | (4) |
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2.3 Small-Gain Control Design |
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30 | (6) |
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36 | (3) |
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Chapter 3 Large-Scale Dynamic Networks |
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39 | (40) |
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3.1 Continuous-Time Dynamic Networks |
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42 | (12) |
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3.2 Discrete-Time Dynamic Networks |
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54 | (9) |
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3.3 Hybrid Dynamic Networks |
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63 | (12) |
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75 | (4) |
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Chapter 4 Control under Sensor Noise |
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79 | (64) |
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4.1 Static State Measurement Feedback Control |
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80 | (13) |
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4.2 Dynamic State Measurement Feedback Control |
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93 | (8) |
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4.3 Decentralized Output Measurement Feedback Control |
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101 | (15) |
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4.4 Event-Triggered and Self-Triggered Control |
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116 | (15) |
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4.5 Synchronization under Censor Noise |
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131 | (6) |
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4.6 Application: Robust Adaptive Control |
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137 | (2) |
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139 | (4) |
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Chapter 5 Quantized Nonlinear Control |
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143 | (50) |
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5.1 Static Quantization: A Sector Bound Approach |
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144 | (13) |
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157 | (23) |
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5.3 Quantized Output-Feedback Control |
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180 | (10) |
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190 | (3) |
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Chapter 6 Distributed Nonlinear Control |
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193 | (62) |
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6.1 A Cyclic-Small-Gain Result in Digraphs |
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196 | (2) |
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6.2 Distributed Output-Feedback Control |
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198 | (9) |
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6.3 Formation Control of Nonholonomic Mobile Robots |
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207 | (17) |
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6.4 Distributed Control with Flexible Topologies |
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224 | (26) |
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250 | (5) |
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Chapter 7 Conclusions and Future Challenges |
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255 | (6) |
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Appendix A Related Notions in Graph Theory |
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261 | (2) |
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Appendix B Systems with Discontinuous Dynamics |
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263 | (6) |
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263 | (1) |
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B.2 Extended Filippov Solution |
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264 | (1) |
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B.3 Input-to-State Stability |
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265 | (1) |
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B.4 Large-Scale Dynamic Networks of Discontinuous Subsystems |
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266 | (3) |
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Appendix C Technical Lemmas Related to Comparison Functions |
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269 | (4) |
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Appendix D Proofs of the Small-Gain Theorems 2.1, 3.2 and 3.6 |
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273 | (12) |
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D.1 A Useful Technical Lemma |
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273 | (1) |
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D.2 Proof of Theorem 2.1: The Asymptotic Gain Approach |
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273 | (2) |
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D.3 Sketch of Proof of Theorem 3.2 |
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275 | (4) |
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279 | (6) |
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Appendix E Proofs of Technical Lemmas in
Chapter 4 |
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285 | (8) |
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285 | (1) |
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286 | (1) |
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287 | (2) |
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289 | (4) |
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Appendix F Proofs of Technical Lemmas in
Chapter 5 |
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293 | (12) |
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293 | (2) |
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295 | (2) |
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297 | (1) |
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298 | (5) |
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303 | (2) |
| References |
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305 | (16) |
| Index |
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321 | |
Dr. Tengfei Liu holds a BE in automation and ME in control theory and engineering from the South China University of Technology, Guangzhou, as well as a Ph.D in engineering from the Australian National University, Acton, Canberra. He is a visiting assistant professor at the Polytechnic Institute of New York University, Brooklyn, USA. His current research interests include stability theory and robust nonlinear, quantized, and distributed control and their applications in mechanical, power, and transportation systems. Dr. Liu, with Prof. Zhong-Ping Jiang and Prof. David J. Hill, received the Guan Zhao-Zhi Best Paper Award at the 2011 Chinese Control Conference.
Prof. Zhong-Ping Jiang holds a BS in mathematics from the University of Wuhan, China; MS in statistics from the University of Paris XI, France; and Ph.D in automatic control and mathematics from the Ecole des Mines de Paris, France. Currently, he is full professor of electrical and computer engineering at New York University, Brooklyn, USA. His research interests include stability theory, robust and adaptive nonlinear control, and adaptive dynamic programming and their applications to underactuated mechanical systems, communication networks, multi-agent systems, smart grids, and neuroscience. An IEEE and IFAC fellow, he has coauthored two books and edited several publications.
Prof. David J. Hill holds a BE and BS from the University of Queensland, Australia, as well as a Ph.D from the University of Newcastle, Australia. Currently, he holds the chair of electrical engineering at the University of Hong Kong. He is also part-time professor at the University of Sydney, Australia. An IEEE, SIAM, and Australian Academies fellow and IVA (Sweden) foreign member, he has held various positions at Sydney University and the universities of Melbourne (Australia), California (Berkeley), Newcastle, Lund (Sweden), Munich (Germany), and Hong Kong (City and Polytechnic).
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