Cooperative Control of Complex Network Systems with Dynamic Topologies

Description

Far from being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with closely linked interactions with neighbouring entities such as the Internet and power grids. Roughly speaking, a CNS refers to a networking system consisting of lots of interactional individuals, exhibiting fascinating collective behaviour that cannot always be anticipated from the inherent properties of the individuals themselves. As one of the most fundamental examples of cooperative behaviour, consensus within CNSs (or the synchronization of complex networks) has gained considerable attention from various fields of research, including systems science, control theory and electrical engineering. This book mainly studies consensus of CNSs with dynamics topologies - unlike most existing books that have focused on consensus control and analysis for CNSs under a fixed topology. As most practical networks have limited communication ability, switching graphs can be used to characterize real-world communication topologies, leading to a wider range of practical applications. This book provides some novel multiple Lyapunov functions (MLFs), good candidates for analysing the consensus of CNSs with directed switching topologies, while each chapter provides detailed theoretical analyses according to the stability theory of switched systems. Moreover, numerical simulations are provided to validate the theoretical results. Both professional researchers and laypeople will benefit from this book. Cover Half Title Title Page Copyright Page Contents Preface Chapter 1: Introduction 1.1. COMPLEX NETWORK SYSTEMS 1.2. DEFINITIONS OF SYNCHRONIZATION AND CONSENSUS 1.3. SYNCHRONIZATION OF COMPLEX NETWORKS WITH SWITCHING TOPOLOGIES 1.4. CONSENSUS OF MASS WITH SWITCHING TOPOLOGIES 1.5. EXTENSIONS AND APPLICATIONS OF CNSS WITH SWITCHING TOPOLOGIES Chapter 2: Preliminaries 2.1. NOTATIONS 2.2. MATRIX THEORY AND ORDINARY DIFFERENTIAL EQUATION 2.3. ALGEBRAIC GRAPH THEORY 2.4. SWITCHED SYSTEM THEORY 2.4.1. Solutions of differential systems 2.4.2. Multiple Lyapunov functions 2.4.3. Stability under slow switching Chapter 3: Consensus of linear CNSs with directed switching topologies 3.1. CONSENSUS OF LINEAR CNSS WITH DIRECTED SWITCHING TOPOLOGIES 3.1.1. Introduction 3.1.2. Problem formulation 3.1.3. Main results 3.1.4. Numerical simulations 3.2. DISTRIBUTED CONSENSUS TRACKING FOR GENERAL LINEAR CNSS WITH DIRECTED SWITCHING TOPOLOGIES 3.2.1. Introduction 3.2.2. Model formulation 3.2.3. Main results for an autonomous leader case 3.2.4. Main results for a nonautonomous leader case 3.2.5. Numerical simulations 3.3. CONCLUSIONS Chapter 4: Consensus disturbance rejection of MIMO linear CNSs with directed switching topologies 4.1. INTRODUCTION 4.2. MODEL FORMULATION AND UNKNOWN INPUT OBSERVER 4.3. CNSS WITH STATIC COUPLING AND SWITCHING TOPOLOGIES 4.4. CNSS WITH DYNAMIC COUPLING AND FIXED TOPOLOGY 4.5. NUMERICAL SIMULATIONS 4.6. CONCLUSIONS Chapter 5: Consensus tracking of CNSs with first-order nonlinear dynamics and directed switching topologies 5.1. INTRODUCTION 5.2. CONSENSUS TRACKING OF CNS WITH LIPSCHITZ TYPE DYNAMICS 5.2.1. Model formulation 5.2.2. Main results 5.3. CONSENSUS TRACKING OF CNSS WITH LORENZ TYPE DYNAMICS 5.3.1. Model formulation 5.3.2. Main results for directed fixed communication topology 5.3.3. Main results for directed switching communication topologies 5.4. NUMERICAL SIMULATIONS 5.5. CONCLUSIONS Chapter 6: Consensus tracking of CNSs with higher-order dynamics and directed switching topologies 6.1. INTRODUCTION 6.2. CONSENSUS TRACKING OF CNSS WITH HIGHER-ORDER NONLINEAR 6.2.1. Problem formulation 6.2.2. Main results for fixed topology containing a directed spanning tree 6.2.3. Main results for switching topologies with each topology containing a directed spanning tree 6.2.4. Main results for switching topologies frequently containing a directed spanning tree 6.3. CONSENSUS TRACKING OF CNSS WITH OCCASIONALLY MISSING CONTROL INPUTS 6.3.1. Model formulation 6.3.2. Main results 6.3.3. Discussions on the convergence rate 6.4. NUMERICAL SIMULATIONS 6.5. CONCLUSIONS Chapter 7: H-infinity consensus of CNSs with directed switching topologies 7.1. INTRODUCTION 7.2. H∞ CONSENSUS OF LINEAR CNSS WITH DISTURBANCES 7.2.1. Model formulation 7.2.2. Main results 7.2.3. Discussions on the convergence rate 7.3. H∞ CONSENSUS OF CNSS WITH LIPSCHITZ NONLINEAR DYNAMICS AND APERIODIC SAMPLED DATA COMMUNICATIONS 7.3.1. Model formulation 7.3.2. Selective pinning strategy 7.3.3. Main results 7.3.4. Extension to H∞ consensus of CNSs with directed switching topologies 7.4. NUMERICAL SIMULATIONS 7.5. CONCLUSIONS Chapter 8: Distributed tracking of nonlinear CNSs with directed switching topologies: An observer-based protocol 8.1. INTRODUCTION 8.2. PROBLEM FORMULATION 8.3. MAIN RESULTS 8.4. CONSENSUS TRACKING PROTOCOL DESIGN: INDEPENDENT TOPOLOGY CASE 8.5. NUMERICAL SIMULATIONS 8.6. CONCLUSIONS Chapter 9: Cooperative tracking of CNSs with a high-dimensional leader and directed switching topologies 9.1. INTRODUCTION 9.2. MODEL FORMULATION 9.3. CONSENSUS TRACKING AND ITS L2-GAIN PERFORMANCE OF CNSS WITH DIRECTED SWITCHING TOPOLOGIES 9.4. CONSENSUS TRACKING AND ITS L2-GAIN PERFORMANCE OF CNSS WITH UNDIRECTED FIXED TOPOLOGY 9.5. NUMERICAL SIMULATIONS 9.6. CONCLUSIONS Chapter 10: Neuro-adaptive consensus of CNSs with uncertain dynamics 10.1. INTRODUCTION 10.2. PRACTICAL CONSENSUS TRACKING OF CNSS WITH A HIGHDIMENSIONAL LEADER AND DIRECTED SWITCHING TOPOLOGIES 10.2.1. Model formulation 10.2.2. CNSs with fixed topology 10.2.3. CNSs with switching topologies 10.2.4. Numerical simulations 10.3. ASYMPTOTIC CONSENSUS TRACKING OF CNSS WITH A HIGH DIMENSIONAL LEADER AND DIRECTED FIXED TOPOLOGY 10.3.1. Model formulation 10.3.2. Theoretical analysis 10.3.3. Numerical simulations 10.4. PRACTICAL AND ASYMPTOTIC CONTAINMENT TRACKING OF CNSS WITH MULTIPLE LEADERS 10.4.1. Model formulation 10.4.2. Practical containment of uncertain CNSs 10.4.3. Asymptotical containment of uncertain CNSs 10.4.4. Numerical simulations 10.5. CONCLUSIONS Chapter 11: Resilient consensus of CNSs with input saturation and malicious attack under switching topologies 11.1. INTRODUCTION 11.2. CONSENSUS OF LINEAR CNSS WITH INPUT SATURATION UNDER SWITCHING TOPOLOGIES 11.2.1. Problem formulation 11.2.2. CNSs with relative output information 11.2.3. CNSs with absolute output information 11.2.4. Numerical simulation 11.3. RESILIENT CONSENSUS OF CNSS WITH MALICIOUS ATTACK UNDER SWITCHING TOPOLOGIES 11.3.1. Problem formulation 11.3.2. Joint (r, s)-robustness 11.3.3. Resilient consensus of switching topologies 11.3.4. Numerical simulation 11.4. CONCLUSIONS Bibliography Index