Frequency-Domain Analysis and Design of Distributed Control Systems

Yu-Ping Tian is a Professor of Automation at Southeast University. His research interests include analysis and control of communication networks, formation control of robots, chaos control and synchronization, and robust and adaptive control. He won the Guan Zhao Zhi Paper Award at the Chinese Control Conference in 1995 and the Best Theory Paper Award at the 3rd World Congress on Intelligent Control and Automation in 2000. He is the recipient of the Chang Jiang Professorship awarded by the Education Ministry of China and the Distinguished Young Scholar Award of the National Natural Science Foundation of China. He has held visiting positions in Central Queensland University (1998, 2001), University of California at Berkeley (2002), and City University of Hong Kong (2004). Tian received a Bachelors degree from Tsinghua University, a Ph.D. degree from Moscow Power Institute and an Sc.D. degree from Taganrog State Radio-engineering University, Taganrog, Russia, in 1996. All his degrees are in Electrical Engineering.

• Preface xiGlossary of Symbols xiii1 Introduction 11.1 Network-Based Distributed Control System 11.2 Graph Theory and Interconnection Topology 41.2.1 Basic Definitions 41.2.2 Graph Operations 71.2.3 Algebraic Graph Theory 101.3 Distributed Control Systems 161.3.1 End-to-End Congestion Control Systems 161.3.2 Consensus-Based Formation Control 221.4 Notes and References 251.4.1 Graph Theory and Distributed Control Systems 251.4.2 Delay in Control and Control by Delay 26References 262 Symmetry, Stability and Scalability 312.1 System Model 312.1.1 Graph-Based Model of Distributed Control Systems 312.1.2 Bipartite Distributed Control Systems 342.2 Symmetry in the Frequency Domain 362.2.1 Symmetric Systems 362.2.2 Symmetry of Bipartite Systems 382.3 Stability of Multivariable Systems 392.3.1 Poles and Stability 392.3.2 Zeros and Pole-Zero Cancelation 412.4 Frequency-Domain Criteria of Stability 432.4.1 Loop Transformation and Multiplier 442.4.2 Multivariable Nyquist Stability Criterion 452.4.3 Spectral Radius Theorem and Small-Gain Theorem 502.4.4 Positive Realness Theorem 532.5 Scalable Stability Criteria 532.5.1 Estimation of Spectrum of Complex Matrices 532.5.2 Scalable Stability Criteria for Asymmetric Systems 562.5.3 Scalable Stability Criteria for Symmetric Systems 602.5.4 Robust Stability in Deformity of Symmetry 612.6 Notes and References 64References 653 Scalability in the Frequency Domain 673.1 How the Scalability Condition is Related with Frequency Responses 673.2 Clockwise Property of Parameterized Curves 713.3 Scalability of First-Order Systems 763.3.1 Continuous-Time System 763.3.2 Discrete-Time System 793.4 Scalability of Second-Order Systems 853.4.1 System of Type I 853.4.2 System of Type II 953.5 Frequency-Sweeping Condition 1033.5.1 Stable Quasi-Polynomials 1033.5.2 Frequency-Sweeping Test 1053.6 Notes and References 108References 1094 Congestion Control: Model and Algorithms 1114.1 An Introduction to Congestion Control 1114.1.1 Congestion Collapse 1124.1.2 Efficiency and Fairness 1144.1.3 Optimization-Based Resource Allocation 1144.2 Distributed Congestion Control Algorithms 1164.2.1 Penalty Function Approach and Primal Algorithm 1164.2.2 Dual Approach and Dual Algorithm 1174.2.3 Primal-Dual Algorithm 1184.2.4 REM: A Second-Order Dual Algorithm 1184.3 A General Model of Congestion Control Systems 1194.3.1 Framework of End-to-End Congestion Control under Diverse Round-Trip Delays 1194.3.2 General Primal-Dual Algorithm 1224.3.3 Frequency-Domain Symmetry of Congestion Control Systems 1244.4 Notes and References 126References 1275 Congestion Control: Stability and Scalability 1295.1 Stability of the Primal Algorithm 1295.1.1 Johari–Tan Conjecture 1295.1.2 Scalable Stability Criterion for Discrete-Time Systems 1315.1.3 Scalable Stability Criterion for Continuous-Time Systems 1355.2 Stability of REM 1385.2.1 Scalable Stability Criteria 1385.2.2 Dual Algorithm: the First-Order Limit Form of REM 1455.2.3 Design of Parameters of REM 1465.3 Stability of the Primal-Dual Algorithm 1525.3.1 Scalable Stability Criteria 1525.3.2 Proof of the Stability Criteria 1615.4 Time-Delayed Feedback Control 1635.4.1 Time-Delayed State as a Reference 1635.4.2 TDFC for Stabilization of an Unknown Equilibrium 1655.4.3 Limitation of TDFC in Stabilization 1665.5 Stabilization of Congestion Control Systems by Time-DelayedFeedback Control 1705.5.1 Introduction of TDFC into Distributed Congestion Control Systems 1705.5.2 Stabilizability under TDFC 1715.5.3 Design of TDFC with Commensurate Self-Delays 1815.6 Notes and References 1885.6.1 Stability of Congestion Control with Propagation Delays 1885.6.2 Time-Delayed Feedback Control 189References 1906 Consensus in Homogeneous Multi-Agent Systems 1936.1 Introduction to Consensus Problem 1936.1.1 Integrator Agent System 1936.1.2 Existence of Consensus Solution 1946.1.3 Consensus as a Stability Problem 1946.1.4 Discrete-Time Systems 1956.1.5 Consentability 1956.2 Second-Order Agent System 1966.2.1 Consensus and Stability 1966.2.2 Consensus and Consentability Condition 1996.2.3 Periodic Consensus Solutions 2036.2.4 Simulation Study 2046.3 High-Order Agent System 2066.3.1 System Model 2066.3.2 Consensus Condition 2086.3.3 Consentability 2116.4 Notes and References 216References 2177 Consensus in Heterogeneous Multi-Agent Systems 2197.1 Integrator Agent System with Diverse Input and Communication Delays 2197.1.1 Consensus in Discrete-Time Systems 2207.1.2 Consensus under Diverse Input Delays 2217.1.3 Consensus under Diverse Communication Delays and Input Delays 2247.1.4 Continuous-Time System 2297.1.5 Simulation Study 2307.2 Double Integrator System with Diverse Input Delays and Interconnection Uncertainties 2337.2.1 Leader-Following Consensus Algorithm 2337.2.2 Consensus Condition under Symmetric Coupling Weights 2357.2.3 Robust Consensus under Asymmetric Perturbations 2387.2.4 Simulation Study 2407.3 High-Order Consensus in High-Order Systems 2437.3.1 System Model 2437.3.2 Consensus Condition 2457.3.3 Existence of High-Order Consensus Solutions 2497.3.4 Constant Consensus 2527.3.5 Consensus in Ideal Networks 2547.4 Integrator-Chain Systems with Diverse Communication Delays 2557.4.1 Matching Condition for Self-Delay 2557.4.2 Adaptive Adjustment of Self-Delay 2557.4.3 Simulation Study 2577.5 Notes and References 265References 266Index 269