This monograph represents the outcome of research effort of the authors on scalable synchronization of large-scale multi-agent systems (MAS). Cooperative control of multi-agent systems has been growing in popularity and is highly interdisciplinary in recent years. The application of synchronization of MAS includes automobile systems, aerospace systems, multiple-satellite GPS, high-resolution satellite imagery, aircraft formations, highway traffic platooning, industrial process control with multiple processes, and more. Most of the proposed protocols in the literature for synchronization of MAS require some knowledge of the communication network such as bounds on the spectrum of the associated Laplacian matrix and the number of agents. These protocols suffer from scale fragility wherein stability properties are lost for large-scale networks or when the communication graph changes.
In the past few years, the authors of this monograph have worked on developing scale-free protocol design for various cases of MAS problems. The key contribution of the monograph is to offer a scale-free design framework and provide scale-free protocols to achieve synchronization, delayed synchronization, and almost synchronization in the presence of input and communication delays, input saturation and external disturbances. The scale-free design framework solely is based on the knowledge of agent models and does not depend on information about the communication network such as the spectrum of the associated Laplacian matrix or size of the network.
Drawing upon their extensive work in this area, the authors provide a thorough treatment of agents with higher-order dynamics, different classes of models for agents, and the underlying networks representing actions of the agents. The high technical level of their presentation and their rigorous mathematical approach make this monograph a timely and valuable resource that will fill a gap in the existing literature.
Author(s): Zhenwei Liu, Donya Nojavanzadeh, Ali Saberi
Series: Studies in Systems, Decision and Control, 248
Publisher: Springer
Year: 2022
Language: English
Pages: 393
City: Cham
Acknowledgements
Contents
1 Introduction
1.1 Cooperative Control of Multi-agent Systems
1.2 Outline
2 Notations and Preliminaries
2.1 Linear Algebra
2.2 Signal and System Norms
2.3 Graphs
2.4 Multi-agent Systems and Graphs
2.5 Passivity
2.5.1 Continuous-Time System
2.5.2 Discrete-Time System
3 Synchronization of Continuous-Time MAS
3.1 Problem Formulation
3.2 Scalable Output Synchronization
3.2.1 Architecture of the Protocol
3.2.2 Protocol Design
3.2.3 Special Case: Homogeneous MAS
3.3 Scalable Regulated Output Synchronization
3.3.1 Architecture of the Protocol
3.3.2 Protocol Design
3.4 Numerical Examples
4 Synchronization of Discrete-Time MAS
4.1 Homogeneous MAS with Non-introspective Agents
4.1.1 Problem Formulation
4.1.2 Scalable State Synchronization
4.2 Heterogeneous MAS with Introspective Agents
4.2.1 Scalable Output Synchronization
4.2.2 Scalable Regulated Output Synchronization
4.3 Numerical Examples
5 Regulated State Synchronization of Homogeneous MAS in the Presence of Input Delays
5.1 Problem Formulation
5.2 Scalable Regulated State Synchronization
5.2.1 Solvability Conditions
5.2.2 Protocol Design
5.2.3 Special Case: MAS with Full-State Coupling
5.3 Numerical Examples
5.3.1 Example 1: Continuous-Time MAS
5.3.2 Example 2: Discrete-Time MAS
6 State Synchronization of Homogeneous Continuous-Time MAS in the Presence of Nonuniform Communication Delays
6.1 Problem Formulation
6.2 Scalable State Synchronization
6.2.1 Solvability Condition and Protocol Design for Arbitrary Constant Reference Trajectory y Subscript r Baseline element of double struck upper R Superscript pyrinmathbbRp
6.2.2 Necessary and Sufficient Solvability Conditions and Protocol Design
6.3 Numerical Examples
7 State Synchronization of Homogeneous Discrete-Time MAS in the Presence of Nonuniform Communication Delays
7.1 Problem Formulation
7.2 Scalable State Synchronization
7.3 Numerical Examples
8 Regulated Output Synchronization of Heterogeneous MAS in the Presence of Nonuniform Communication Delays
8.1 Problem Formulation
8.2 Scalable Regulated Output Synchronization
8.2.1 Architecture of the Protocol
8.2.2 Protocol Design
8.3 Numerical Examples
8.3.1 Continuous-Time MAS
8.3.2 Discrete-Time MAS
9 Delayed Regulated Synchronization of Continuous-Time MAS in the Presence of Unknown, Non-uniform, and Arbitrarily Large Communication Delays
9.1 Homogeneous MAS with Non-introspective Agents
9.1.1 Problem Formulation
9.1.2 Scalable Delayed Regulated State Synchronization
9.2 Heterogeneous MAS with Introspective Agents
9.2.1 Problem Formulation
9.2.2 Scalable Delayed Regulated Output Synchronization
9.3 Numerical Examples
9.3.1 Example 1. Homogeneous MAS
9.3.2 Example 2. Heterogeneous MAS
10 Delayed Regulated Synchronization of Discrete-Time MAS in the Presence of Unknown, Non-uniform, and Arbitrarily Large Communication Delays
10.1 Homogeneous MAS with Non-introspective Agents
10.1.1 Problem Formulation
10.1.2 Scalable Delayed Regulated State Synchronization
10.2 Heterogeneous MAS with Introspective Agents
10.2.1 Problem Formulation
10.2.2 Scalable Delayed Regulated Output Synchronization
10.3 Numerical Examples
10.3.1 Example 1. Homogeneous MAS
10.3.2 Example 2. Heterogeneous MAS
11 Global Regulated State Synchronization of Homogeneous Continuous-Time MAS with Non-introspective Agents in the Presence of Input Saturation
11.1 Problem Formulation
11.2 Scalable Global Regulated State Synchronization …
11.2.1 Protocol Design for Partial-State Coupling Case
11.2.2 Protocol Design for Full-State Coupling Case
11.3 Scalable Global Regulated State Synchronization via Linear …
11.3.1 Protocol Design for Partial-State Coupling Case
11.3.2 Protocol Design for Full-State Coupling Case
11.4 Numerical Examples
11.4.1 Example 1: Nonlinear Protocol Design
11.4.2 Example 2: Linear Observer-Based Protocol Design
12 Global Regulated State Synchronization of Homogeneous Discrete-Time MAS with Non-introspective Agents in the Presence of Input Saturation
12.1 Problem Formulation
12.2 Scalable Global Regulated State Synchronization …
12.2.1 Protocol Design for Full-State Coupling Case
12.2.2 Protocol Design for Partial-State Coupling Case
12.3 Scalable Global Regulated State Synchronization via Linear …
12.3.1 MAS Consisting of Neutrally Stable Agents
12.3.2 MAS Consisting of Double-Integrator Agents
12.4 Numerical Examples
12.4.1 Nonlinear Protocol
12.4.2 Linear Protocol for MAS with Neutrally Stable Agents
12.4.3 Linear Protocol for MAS with Double-Integrator Agents
13 State and Regulated State Synchronization of Continuous-Time MAS with Arbitrarily Fast Convergence
13.1 Definition of Asymptotic Convergence Rate
13.2 Problem Formulation
13.3 Scalable State Synchronization with Arbitrarily Fast Convergence
13.3.1 Protocol Design for Full-State Coupling Case
13.3.2 Protocol Design for Partial-State Coupling Case
13.4 Scalable Regulated State Synchronization …
13.4.1 Protocol Design for Full-State Coupling Case
13.4.2 Protocol Design for Partial-State Coupling Case
13.5 Numerical Examples
14 upper H Subscript normal infinityHinfty and upper H 2H2 Almost State Synchronization of Homogeneous MAS with Non-introspective Agents
14.1 Problem Formulation
14.2 Scalable upper H Subscript normal infinityHinfty Almost State Synchronization
14.2.1 Full-State Coupling—Solvability Conditions and Protocol Design
14.2.2 Partial-state Coupling—Solvability Conditions and Protocol Design
14.3 Scalable upper H 2H2 Almost State Synchronization
14.3.1 Full-State Coupling–Solvability Conditions and Protocol Design
14.3.2 Partial-State Coupling–Solvability Conditions and Protocol Design
14.4 Numerical Examples
14.4.1 upper H Subscript normal infinityHinfty State Synchronization
14.4.2 upper H 2H2 State Synchronization
15 upper H Subscript normal infinityHinfty and upper H 2H2 Almost Output and Regulated Output Synchronization of Heterogeneous MAS
15.1 Problem Formulation
15.2 Scale-Free upper H Subscript normal infinityHinfty Almost Synchronization
15.2.1 Scale-Free upper H Subscript normal infinityHinfty Almost Output Synchronization
15.2.2 Scale-Free upper H Subscript normal infinityHinfty Almost Regulated Output Synchronization
15.3 Scale-Free upper H 2H2 Almost Synchronization
15.3.1 Scale-Free upper H 2H2 Almost Output Synchronization
15.3.2 Scale-Free upper H 2H2 Almost Regulated Output Synchronization
15.4 Numerical Examples
15.4.1 Example 1: upper H Subscript normal infinityHinfty Almost Output Synchronization
15.4.2 Example 2: upper H 2H2 Almost Output Synchronization
16 On Scalability in the Absence of Localized Information Exchange—Scale-Free Non-collaborative Protocol Design for Homogeneous MAS
16.1 Scale-Free Non-collaborative Linear Protocol Design
16.1.1 Problem Formulation
16.1.2 Scale-Free Non-collaborative Linear Protocol Design for Partial-State Coupling
16.1.3 Linear Protocol Design for Full-State Coupling
16.2 Scale-Free Non-collaborative Nonlinear Protocol Design
16.2.1 Problem Formulation
16.2.2 Protocol Design
16.3 Numerical Examples
16.3.1 Non-collaborative Linear Protocol Design
16.3.2 Non-collaborative Nonlinear Protocol Design
17 Distributed Cooperative Voltage Control of Multiterminal High Voltage DC Systems
17.1 Mathematical Modeling of Converters Dynamics
17.2 Problem Formulation
17.3 Scalable Regulated State Synchronization for MTDC System
17.4 Simulation Results
18 Distributed Cooperative Voltage Control of Inverter-Based Microgrids with General Time-Varying Communication Graphs
18.1 Modeling of Inverter-Interfaced Distributed Generator (IIDG) for Distributed Control
18.2 Problem Formulation
18.3 Distributed Cooperative Control of IIDGs
18.4 Simulation Results
Appendix A Some Useful Lemmas
A.1 Stability of Delayed Continuous-Time Systems
A.2 Stability of Delayed Discrete-Time Systems
A.3 Robustness of Low-Gain
Appendix References
