奇异多智能体系统容许一致性分析与设计

本书研究了高阶奇异多智能体系统容许一致性分析和设计问题，深入探索了信息延迟、外部扰动、切换拓扑、协议状态、拓扑结构和性能约束等影响因素对容许一致性的影响机理。状态空间分解方法是处理容许一致性问题的核心方法，可将奇异多智能体系统整体运动分解为两个部分：相对运动和整体运动，相对运动独立于整体运动，进而综合应用Lyapunov分析方法、线性矩阵不等式工具和广义Riccati方程方法确定了不同影响因素条件下容许一致性分析和设计的判据条件。

Contents1 Introduction 11.1 Background of Consensus for Multi-agent Systems 11.1.1 Collective Behavior of Animal Groups in Nature 21.1.2 Cooperative Operation of Multi-agent Systems in Society 81.1.3 Consensus with Interaction Topology on Graphs 131.2 Basic Knowledges of Singular Multi-agent Systems 191.2.1 Models of Singular Multi-agent Systems 201.2.2 Examples of Singular Multi-agent Systems 221.3 Development Direction of Consensus: Literature Reviews 321.3.1 Consensus of Multi-agent Systems with Dynamics of Different Orders 321.3.2 Consensus of Multi-agent Systems with Different Interaction Topologies 411.3.3 Consensus of Multi-agent Systems with Cost Indexes 451.4 Notes 48References 492 Fundamental Theory 572.1 Algebraic Graph Theory 572.1.1 Definitions 572.1.2 Example 592.2 Linear Algebra 612.2.1 Consensus Decomposition of Linear Space 612.2.2 Kronecker Product 622.2.3 Orthogonal Matrix 622.2.4 Linear Matrix Inequality 622.2.5 Eigenvalues and Eigenvectors 632.3 Linear System Theory 632.4 Singular System Theory 652.4.1 Regularity 662.4.2 Constrained System Equivalence and System Decomposition 662.4.3 Temporal Response 682.4.4 Admissibility 702.4.5 Controllability 732.4.6 Duality 762.4.7 Observability 762.5 Consensus for High-Order LTI Multi-agent Systems 782.5.1 Consensus and Consensualization 792.5.2 Consensus Functions 832.6 Notes 85References 853 Admissible Consensus and Consensualization on Interaction Topology 873.1 Structure and Variance of Interaction Topology 883.1.1 Structure of Interaction Topology 883.1.2 Variance of Interaction Topology 903.2 Admissible Consensus and Consensualization with Fixed Topology 913.2.1 Admissible Consensus Protocol with Fixed Topology 923.2.2 Conditions for Admissible Consensus Analysis 933.2.3 Admissible Consensus Design Criteria 983.2.4 Consensus Functions on Fixed Topology 1003.2.5 Numerical Simulation 1023.3 Admissible Consensus and Consensualization with Switching Topologies 1043.3.1 Admissible Consensus Protocol with Switching Topologies 1053.3.2 Necessary and Sufficient Conditions for Admissible Consensus Analysis with Switching Topologies 1063.3.3 Admissible Consensus Design Criteria: Switching Topology Case 1083.3.4 Consensus Functions on Switching Topologies 1093.3.5 Numerical Simulation 1113.4 Notes 113References 1144 Admissible Consensus and Consensualization with Time Delays 1174.1 Introduction of Time Delays 1174.1.1 Classification of Time Delays 1184.1.2 The Influence of Time Delays on Consensus Control 1184.2 Delay-Dependent Admissible Consensus and Consensualization 1194.2.1 Dynamic Output Feedback Consensus Protocol with Time Delays 1204.2.2 Necessary and Sufficient Conditions for Delay-Dependent Admissible Consensus Analysis 1214.2.3 Delay-Dependent Admissible Consensus Design Criteria 1244.2.4 Consensus Functions 1294.2.5 Numerical Simulation 1324.3 Admissible Output Consensualization with Time Delays 1334.3.1 Output Consensus Protocol with Local Delayed Output Information 1344.3.2 Conditions of Admissible Output Consensus Design with Time Delays 1354.3.3 Output Consensus Functions 1414.3.4 Numerical Simulation 1444.4 Notes 146References 1465 Admissible L？ Consensus and Consensualization with External Disturbances 1495.1 Properties of External Disturbances 1505.1.1 Disturbance Types 1505.1.2 Disturbance Suppression Methods 1515.2 Problem Description of Admissible L？ Consensus Control 1535.3 Admissible L？ Consensus with External Disturbance 1555.3.1 Necessary and Sufficient Conditions for Admissible Consensus Without Disturbance 1555.3.2 Admissible L？ Consensus Function 1575.3.3 Admissible L？ Consensus Analysis and Design Criteria 1595.4 Numerical Simulation 1665.5 Notes 168References 1686 Admissible Consensus and Consensualization with Protocol State Constraints 1736.1 Dynamic Output Feedback Protocol 1746.1.1 Static Output Feedback Consensus Protocol 1746.1.2 Dynamic Output Feedback Consensus Protocol 1756.1.3 Stable Consensus Protocol 1766.2 Stable-Protocol Admissible Consensus with Time Delays 1786.2.1 Singular Dynamic Output Feedback Consensus Protocol 1786.2.2 Stable-Protocol Admissible Consensus Analysis Conditions 1806.2.3 Consensus Functions 1846.2.4 Numerical Simulation 1896.3 Stable-Protocol Admissible Consensualization with Switching Topologies 1906.3.1 Problem Description and Transformation 1926.3.2 Admissible Consensus Criteria for Connected Switching Topology Cases 2006.3.3 Admissible Consensus Criteria for Jointly Connected Switching Topology Cases 2026.3.4 Numerical Simulation 2056.4 Notes 210References 2117 Admissible Consensus and Consensualization with Energy Constraints 2137.1 Problems of Optimal and Suboptimal Consensus 2147.1.1 Decentralized Optimization Cooperative Control 2147.1.2 Global Optimization Cooperative Control 2157.2 Problem Description of Guaranteed-Cost Admissible Consensus 2187.3 Conditions of Guaranteed-Cost Admissible Consensus Analysis and Design 2207.3.1 Guaranteed-Cost Admissible Consensus Analysis Criteria 2217.3.2 Conditions of Guaranteed-Cost Admissible Consensus Design 2267.3.3 Consensus Functions 2287.4 Numerical Simulation 2307.5 Notes 236References 2368 Admissible Formation Tracking with Energy Constraints 2398.1 Problems of Formation Control 2408.1.1 Time-Invariant Formation 2408.1.2 Time-Varying Formation 2418.1.3 Formation Tracking Problems 2428.1.4 Leaderless Formation Control Problems 2438.1.5 Formation Control Examples of Multiple UAVs 2448.2 Formation Tracking Control Protocol with Energy Constraint 2468.3 Energy-Constraint Admissible Formation Tracking Criteria 2498.3.1 Case of Switching Topologies Containing a Spanning Tree 2498.3.2 Case of Switching Topologies Containing a Joint Spanning Tree 2568.4 Numerical Simulation 2618.5 Notes 267References 270