Nonlinear Pinning Control of Complex Dynamical Networks Analysis and Applications

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.

IAnalyses and Preliminaries1Introduction1.1Complex Dynamical Networks1.2Pinning Control1.3Sliding-Mode Control1.4Optimal Nonlinear Control1.5Artificial Neural Networks1.6Gene Regulatory Networks1.7Microgrids1.8Motivation1.9Book Structure1.10Notation1.11AcronymsBibliography 2Preliminaries2.1Nonlinear Systems Stability2.2Chaotic Systems2.3Complex Dynamical Networks2.4Sliding-Mode Control2.5Optimal Control2.6Recurrent High-Order Neural NetworksBibliography IISliding-Mode Control3 Model-Based Control3.1Sliding-Mode Pinning Control3.2Simulation Results3.3ConclusionsBibliography 4Neural Model4.1Formulation4.2Neural Identifier4.3Output Synchronization4.4Simulation Results4.5ConclusionsBibliography IIIOptimal Control5Model-Based Control5.1Trajectory Tracking of Complex Networks5.2Non-Identical Nodes5.3ConclusionsBibliography 6Neural Model6.1Trajectory Tracking of Complex Networks6.2Non-Identical Nodes6.3Discrete-Time Case6.4ConclusionsBibliography IVApplications7Pinning Control for the p53-Mdm2 Network7.1p53-Mdm2 Model Regulated by p14ARF7.2Mathematical Description7.3Pinning Control Methodology7.4Behaviors of the p53-Mdm2 Network Regulated by p14ARF without Control Action7.5Behaviors of the p53-Mdm2 Network Regulated by p14ARF with Control Action7.6ConclusionsBibliography 8Secondary Control of Microgrids8.1Microgrid Control Structure8.2Distributed Cooperative Secondary Control8.3Simulation Results8.4ConclusionsBibliographyIndex

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.