Nonlinear Pinning Control of Complex Dynamical Networks : Analysis and Applications book cover
1st Edition

Nonlinear Pinning Control of Complex Dynamical Networks
Analysis and Applications

ISBN 9781032020877
Published August 20, 2021 by CRC Press
228 Pages 46 B/W Illustrations

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Book Description

This book presents two nonlinear control strategies for complex dynamical networks. First, sliding-mode control is used, and then the inverse optimal control approach is employed. For both cases, model-based is considered in Chapter 3 and Chapter 5; then, Chapter 4 and Chapter 6 are based on determining a model for the unknow system using a recurrent neural network, using on-line extended Kalman filtering for learning.

The book is organized in four sections. The first one covers mathematical preliminaries, with a brief review for complex networks, and the pinning methodology. Additionally, sliding-mode control and inverse optimal control are introduced. Neural network structures are also discussed along with a description of the high-order ones. The second section presents the analysis and simulation results for sliding-mode control for identical as well as non-identical nodes. The third section describes analysis and simulation results for inverse optimal control considering identical or non-identical nodes. Finally, the last section presents applications of these schemes, using gene regulatory networks and microgrids as examples.

Table of Contents

I Analyses and Preliminaries
1 Introduction
1.1 Complex Dynamical Networks
1.2 Pinning Control
1.3 Sliding-Mode Control
1.4 Optimal Nonlinear Control
1.5 Artificial Neural Networks
1.6 Gene Regulatory Networks
1.7 Microgrids
1.8 Motivation
1.9 Book Structure
1.10 Notation
1.11 Acronyms

2 Preliminaries
2.1 Nonlinear Systems Stability
2.2 Chaotic Systems
2.3 Complex Dynamical Networks
2.4 Sliding-Mode Control
2.5 Optimal Control
2.6 Recurrent  High-Order Neural Networks

II Sliding-Mode Control
3 Model-Based Control
3.1 Sliding-Mode Pinning Control
3.2 Simulation Results
3.3 Conclusions

4 Neural Model
4.1 Formulation
4.2 Neural Identifier
4.3 Output Synchronization
4.4 Simulation Results
4.5 Conclusions

III Optimal Control
5 Model-Based Control
5.1 Trajectory Tracking  of Complex Networks
5.2 Non-Identical Nodes
5.3 Conclusions

6 Neural Model
6.1 Trajectory Tracking  of Complex Networks
6.2 Non-Identical Nodes
6.3 Discrete-Time Case
6.4 Conclusions

IV Applications
7 Pinning Control for the p53-Mdm2 Network
7.1 p53-Mdm2 Model Regulated  by p14ARF
7.2 Mathematical  Description
7.3 Pinning Control Methodology
7.4 Behaviors of the p53-Mdm2 Network  Regulated  by  p14ARF without Control Action
7.5 Behaviors of the p53-Mdm2 Network Regulated by p14ARF with Control Action
7.6 Conclusions

8 Secondary Control of Microgrids
8.1 Microgrid Control Structure
8.2 Distributed  Cooperative Secondary Control
8.3 Simulation Results
8.4 Conclusions

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Edgar N. Sanchez works at CINVESTAV-IPN, Guadalajara Campus, Mexico, as a professor of electrical engineering graduate programs. Carlos J. Vega received D.Sc. in Electrical Engineering degree from the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Guadalajara, Mexico in 2020. His research interests include complex networks, nonlinear control, inverse optimal control, neural networks, and power systems. Oscar J. Suarez is a Professor of engineering programs for undergraduate and graduate programs both in Colombia and Mexico. Currently, he is a Junior Research fellow of the Ministerio de Ciencia Tecnología e Innovación (Minciencias) in Colombia. Guanrong Chen has been a Chair Professor and the Founding Director of the Centre for Chaos and Complex Networks, City University of Hong Kong, Hong Kong, since 2000.