Network Optimization Methods in Passivity-Based Cooperative Control (Springer Theses)

✍ Scribed by Miel Sharf

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 244
• Category: Library

✦ Synopsis

This book establishes an important mathematical connection between cooperative control problems and network optimization problems. It shows that many cooperative control problems can in fact be understood, under certain passivity assumptions, using a pair of static network optimization problems. Merging notions from passivity theory and network optimization, it describes a novel network optimization approach that can be applied to the synthesis of controllers for diffusively-coupled networks of passive (or passivity-short) dynamical systems. It also introduces a data-based, model-free approach for the synthesis of network controllers for multi-agent systems with passivity-short agents. Further, the book describes a method for monitoring link faults in multi-agent systems using passivity theory and graph connectivity. It reports on some practical case studies describing the effectivity of the developed approaches in vehicle networks. All in all, this book offers an extensive source of information and novel methods in the emerging field of multi-agent cooperative control, paving the way to future developments of autonomous systems for various application domains

✦ Table of Contents

Supervisor’s Foreword
Parts of this thesis have been published in the following documents:
Journals
Peer-Reviewed Conference Proceedings
Acknowledgements
Contents
Abbreviations
Symbols
1 Introduction
1.1 Introduction and Focus
1.1.1 Notation
1.2 Background
1.2.1 Network Optimization
1.2.2 Diffusively Coupled Networks
1.2.3 The Role of Passivity in Cooperative Control
1.3 Contributions and Thesis Outline
1.3.1 Chapter 2摥映數爠eflinkchp.MIMO22—A Network Optimization Framework for MIMO Systems
1.3.2 Chapter 3摥映數爠eflinkchp.PassiveShort33—A Network Optimization Framework for Passive-Short Agents
1.3.3 Chapter 4摥映數爠eflinkchp.Synthesis44—A Network Optimization Framework for Controller Synthesis
1.3.4 Chapter 5摥映數爠eflinkchp.DataDriven55—Applications of the Network Optimization Framework in Data-Driven Control
1.3.5 Chapter 6摥映數爠eflinkchp.NetworkIden66—Applications of the Network Optimization Framework in Network Identification
1.3.6 Chapter 7摥映數爠eflinkchp.NetwokFDI77—Applications of the Network Optimization Framework in Fault Detection and Isolation
1.3.7 Chapter 8摥映數爠eflinkchp.Conclusions88—Conclusions and Outlook
References
2 A Network Optimization Framework for MIMO Systems
2.1 Introduction
2.2 Cyclically Monotone Relations and Cooperative Control
2.2.1 Steady-States and Network Consistency
2.2.2 Connecting Steady-States to Network Optimization
2.2.3 Convergence to the Steady-State
2.3 Examples of MEICMP Systems
2.3.1 Convex-Gradient Systems with Oscillatory Terms
2.3.2 Oscillatory Systems with Damping
2.3.3 Example: A Network of Planar Oscillators
2.4 Conclusions
References
3 A Network Optimization Framework for Passive-Short Agents
3.1 Introduction
3.2 Shortage of Passivity and Failures of the Network Optimization Framework
3.2.1 Shortage of Passivity
3.2.2 Failure of the Network Optimization Framework
3.3 A Network Optimization Framework for Output Passive-Short Agents
3.3.1 Agent-Only Regularization
3.3.2 Network-Only Regularization
3.3.3 Hybrid Regularization
3.4 A Network Optimization Framework for General Passive-Short Agents
3.4.1 Monotonization of I/O Relations by Linear Transformations: A Geometric Approach
3.4.2 From Monotonization to Passivation and Implementation
3.4.3 Maximality of Input-Output Relations and the Network Optimization Framework
3.5 Case Studies
3.5.1 Unstable First Order Systems
3.5.2 Gradient Systems
3.5.3 Traffic Model
3.6 Conclusions
References
4 A Network Optimization Framework for Controller Synthesis
4.1 Introduction
4.2 Final-Value Synthesis for Multi-agent Systems
4.2.1 Characterizing Forcible Steady-States
4.2.2 Forcing Global Asymptotic Convergence
4.2.3 Changing the Objective and ``Formation Reconfiguration''
4.2.4 Plant Augmentation and Leading Agents for Non-achievable Steady States
4.2.5 Final-Value Synthesis for Other Signals
4.2.6 Case Studies
4.3 Clustering in Symmetric Multi-agent Systems
4.3.1 The Static Automorphism Group of a Multi-agent System
4.3.2 Steady-State Clustering in Multi-agent Systems
4.3.3 Homogeneous Networks and Cluster Synthesis
4.4 Conclusions
References
5 Applications of the Network Optimization Framework in Data-Driven Control
5.1 Introduction
5.2 Problem Formulation and Verification of Passivity
5.3 Uniform Gain Amplification Methods
5.3.1 Theory
5.3.2 Data-Driven Determination of Gains
5.4 Non-uniform Gain Amplification Methods
5.5 Case Studies
5.5.1 Velocity Coordination in Vehicles with Drag and Exogenous Forces
5.5.2 Clustering in Neural Networks
5.6 Conclusions
References
6 Applications of the Network Optimization Framework in Network Identification
6.1 Introduction
6.2 Network Differentiation Using Constant Exogenous Inputs
6.2.1 Motivation and Problem Definition
6.2.2 Constructing Indication Vectors Using Randomization
6.2.3 Constructing Indication Vectors Using Algebraic Methods
6.3 Network Identification with Minimal Time Complexity
6.3.1 An Algorithm for LTI Agents and Controllers
6.3.2 An Algorithm for General MEIP Agentspg and Controllers Using Linearization
6.4 Robustness and Practical Considerations
6.4.1 Robustness to Noise and Disturbances
6.4.2 Probing Inputs Supported on Subsets of Nodes
6.4.3 Time Complexity Bounds for the Network Reconstruction Problem
6.5 Case Studies
6.5.1 Linear Agents and Controllers
6.5.2 A Neural Network
6.6 Conclusions
References
7 Applications to Network Fault Detection and Isolation
7.1 Introduction
7.2 Problem Formulation and Assumptions
7.3 Asymptotic Differentiation Between Networks
7.4 Network Fault Detection and Isolation
7.4.1 Fault Detection Over Networks
7.4.2 Multi-agent Synthesis in the Presence of an Adversary
7.4.3 Network Fault Isolation in Multi-agent Systems
7.5 Online Assertion of Network Convergence
7.5.1 Asserting Convergence Using High-Rate Sampling
7.5.2 Asserting Convergence Using Convergence Profiles
7.6 Case Studies
7.6.1 Network FDI for LTI First Order Systems
7.6.2 Network FDI for Velocity-Coordinating Vehicles
7.7 Conclusions
References
8 Summary
8.1 Conclusions
8.2 Outlook
References
Appendix A Convex Analysis and Optimization Theory
A.1 Convex Sets and Convex Functions
A.2 Subdifferentials
A.3 Rockafellar's Theorem and Cyclically Monotone Relations
Appendix B Graph Theory and Algebraic Graph Theory
Appendix C Dynamical Systems, Passivity and Stability
C.1 Stability and Lyapunov Theory
C.2 Passivity
Appendix D Complexity Theory for Matrix Multiplication and Inversion
Appendix E Tools From Algebraic Number Theory
Appendix F Author Biography