Nonlinear Pinning Control of Complex Dynamical Networks: Analysis and Applications (Automation and Control Engineering)

✍ Scribed by Edgar N. Sanchez, Carlos J. Vega, Oscar J. Suarez, Guanrong Chen

• Publisher: CRC Press
• Year: 2021
• Tongue: English
• Leaves: 229
• Edition: 1
• Category: Library

✦ Synopsis

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

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Preface
Acknowledgments
Authors
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
Bibliography
2. Preliminaries
2.1. Nonlinear Systems Stability
2.2. Chaotic Systems
2.2.1. Lorenz system
2.2.2. Chen system
2.2.3. Lu system
2.2.4. Chua's circuit
2.2.5. Rossler system
2.2.6. Arneodo system
2.3. Complex Dynamical Networks
2.3.1. Pinning control strategy
2.3.2. Dynamical networks with non-identical nodes
2.4. Sliding-Mode Control
2.5. Optimal Control
2.5.1. Continuous-time case
2.5.2. Discrete-time case
2.6. Recurrent High-Order Neural Networks
2.6.1. Continuous-time model
2.6.2. Discrete-time model
2.6.3. EKF training algorithm
Bibliography
II. Sliding-Mode Control
3. Model-Based Sliding-Mode Control
3.1. Sliding-Mode Pinning Control
3.1.1. Case 1
3.1.2. Case 2
3.2. Simulation Results
3.2.1. Case 1
3.2.2. Case 2
3.3. Conclusions
Bibliography
4. Neural Sliding-Mode Control
4.1. Formulation
4.2. Neural Identifier
4.3. Output Synchronization
4.4. Simulation Results
4.5. Conclusions
Bibliography
III. Optimal Control
5. Model-Based Optimal Control
5.1. Trajectory Tracking of Complex Networks
5.2. Non-Identical Nodes
5.3. Conclusions
Bibliography
6. Neural Inverse Optimal Control
6.1. Trajectory Tracking of Complex Networks
6.1.1. Neural identifier
6.1.2. Control law for trajectory tracking
6.1.3. Simulation results
6.2. Non-Identical Nodes
6.3. Discrete-Time Case
6.3.1. Discrete-time on-line neural identifier
6.3.2. Discrete-time inverse optimal controller
6.3.3. Simulation results
6.4. Conclusions
Bibliography
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
7.3.1. Problem formulation
7.3.2. p14ARF Pinned node
7.4. Behaviors of the p53-Mdm2 Network Regulated by p14ARF without Control Action
7.4.1. p53-Mdm2 nuclear oscillatory pattern
7.4.2. Mdm2 nuclear overexpression and p53 downregulation
7.4.3. Increased expression of p53 levels
7.4.4. Sensitivity analysis for p14ARF production
7.5. Behaviors of the p53-Mdm2 Network Regulated by p14ARF with Control Action
7.5.1. Case 1: Restoration of an oscillatory pattern under gamma-radiation
7.5.2. Case 2: Achievement of a p53 level increased expression
7.6. Conclusions
Bibliography
8. Secondary Control of Microgrids
8.1. Microgrid Control Structure
8.2. Distributed Cooperative Secondary Control
8.2.1. Secondary frequency control
8.2.2. Secondary voltage control
8.3. Simulation Results
8.4. Conclusions
Bibliography
Index