1st Edition

Nonlinear Control of Dynamic Networks

    346 Pages 65 B/W Illustrations
    by CRC Press

    346 Pages 65 B/W Illustrations
    by CRC Press

    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.

    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


    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).