Nonlinear Control of Dynamic Networks

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ISBN 9781466584594
Cat# K19046



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ISBN 9781466584600
Cat# KE22932



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  • Includes refined small-gain results for nonlinear system networks and control applications subject to sensor noise, quantization error, and communication issues
  • Provides new essential theory and readily usable tools for analysis and design of nonlinear control systems undergoing diverse network behaviors and information constraints
  • Serves as a clear and concise reference for high-level undergraduate and graduate students studying nonlinear control theory, networked control, robot control, and related problems


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

Author Bio(s)