Nonlinear Control of Dynamic Networks: 1st Edition (Paperback) book cover

Nonlinear Control of Dynamic Networks

1st Edition

By Tengfei Liu, Zhong-Ping Jiang, David J. Hill

CRC Press

345 pages | 65 B/W Illus.

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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.

Table of Contents


Control Problems with Dynamic Networks

Lyapunov Stability

Input-to-State Stability

Input-to-Output Stability

Input-to-State Stabilization and an Overview of the Book

Interconnected Nonlinear Systems

Trajectory-Based Small-Gain Theorem

Lyapunov-Based Small-Gain Theorem

Small-Gain Control Design

Large-Scale Dynamic Networks

Continuous-Time Dynamic Networks

Discrete-Time Dynamic Networks

Hybrid Dynamic Networks

Control Under Sensor Noise

Static State Measurement Feedback Control

Dynamic State Measurement Feedback Control

Decentralized Output Measurement Feedback Control

Event-Triggered and Self-Triggered Control

Synchronization Under Sensor Noise

Application: Robust Adaptive Control

Quantized Nonlinear Control

Static Quantization: A Sector Bound Approach

Dynamic Quantization

Quantized Output-Feedback Control

Distributed Nonlinear Control

A Cyclic-Small-Gain Result in Digraphs

Distributed Output-Feedback Control

Formation Control of Nonholonomic Mobile Robots

Distributed Control With Flexible Topologies

Conclusions and Future Challenges

Appendix A Related Notions in Graph Theory

Appendix B Systems With Discontinuous Dynamics

Appendix C Technical Lemmas Related to Comparison Functions

Appendix D Proofs of the Small-Gain Theorems 2.1, 3.2 and 3.6

Appendix E Proofs of Technical Lemmas in Chapter 4

Appendix F Proofs of Technical Lemmas in Chapter 5



About the Authors

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).

About the Series

Automation and Control Engineering

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Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Electronics / Circuits / General
TECHNOLOGY & ENGINEERING / Power Resources / Electrical