1st Edition

Nonlinear Pinning Control of Complex Dynamical Networks Analysis and Applications

    228 Pages 46 B/W Illustrations
    by CRC Press

    228 Pages 46 B/W Illustrations
    by CRC Press

    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.

    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


    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.