Distributed Average Tracking in Multi-agent Systems

✍ Scribed by Fei Chen, Wei Ren

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 240
• Category: Library

✦ Synopsis

This book presents a systematic study of an emerging field in the development of multi-agent systems. In a wide spectrum of applications, it is now common to see that multiple agents work cooperatively to accomplish a complex task. The book assists the implementation of such applications by promoting the ability of multi-agent systems to track ― using local communication only ― the mean value of signals of interest, even when these change rapidly with time and when no individual agent has direct access to the average signal across the whole team; for example, when a better estimation/control performance of multi-robot systems has to be guaranteed, it is desirable for each robot to compute or track the averaged changing measurements of all the robots at any time by communicating with only local neighboring robots. The book covers three factors in successful distributed average tracking:

• algorithm design via nonsmooth and extended PI control;
• distributed average tracking for double-integrator, general-linear, Euler–Lagrange, and input-saturated dynamics; and
• applications in dynamic region-following formation control and distributed convex optimization.

The book presents both the theory and applications in a general but self-contained manner, making it easy to follow for newcomers to the topic. The content presented fosters research advances in distributed average tracking and inspires future research directions in the field in academia and industry.

✦ Table of Contents

Preface
Acknowledgements
Contents
Notation
Abbreviations
Part I Introduction
1 Overview
1.1 What is a Multi-agent System?
1.1.1 Agent
1.1.2 Autonomy
1.1.3 Multi-agent Systems
1.2 What is Distributed Average Tracking?
1.2.1 Formal Definition
1.2.2 Distributed Average Tracking Versus Dynamic (Average) Consensus
1.2.3 Two Kinds of Constraints in Distributed Average Tracking Design
1.3 Applications of Distributed Average Tracking
1.3.1 Visual Maps Merging
1.3.2 Multi-camera Tracking
1.3.3 Distributed Task Migration in Manycore Systems
1.3.4 Dynamic Region-Following Formation Control
1.4 Literature Review: Distributed Average Tracking
1.4.1 Quick Overview
1.4.2 Design via the Invariant-Sum Scheme
1.4.3 Design via the Sum-Tracking Scheme
1.5 Connections with Other Cooperative Control Problems
1.5.1 Average Consensus
1.5.2 Coordinated Tracking (Leader-Following Consensus)
1.5.3 Containment Control
1.6 Organization
References
2 Preliminaries
2.1 Graph Theory
2.1.1 Basic Definitions
2.1.2 Connectedness Notions
2.1.3 Matrices Associated with a Graph
2.2 Nonlinear Stability Theory
2.2.1 Nonlinear Models
2.2.2 Notions of Stability
2.2.3 Stability Theorems
2.2.4 Input-to-State Stability
2.3 Nonsmooth Analysis
References
Part II Algorithms
3 Distributed Average Tracking via Nonsmooth Feedback
3.1 Problem Description
3.2 Algorithm Design
3.3 Convergence Analysis
3.4 Initialization Errors, Time Delays, and Discrete-Time Implementation
3.4.1 Robustness to Initialization Errors
3.4.2 Robustness to Time Delays
3.4.3 Discrete-Time Implementation
3.5 Simulation
References
4 Distributed Average Tracking via an Extended PI Scheme
4.1 Problem Description
4.2 Challenges of Algorithm Design
4.3 Design Criteria Under an Extended PI Scheme
4.4 Smooth Distributed Average Tracking Algorithms
4.5 Simulation
References
Part III Dynamics
5 Distributed Average Tracking for Double-Integrator Dynamics
5.1 Problem Description
5.2 Distributed Average Tracking Under a Fixed Network Topology
5.2.1 Controllers Design
5.2.2 Algebraic Graph Results
5.2.3 Convergence Analysis
5.3 Distributed Average Tracking Under a Switching Network Topology
5.3.1 Controllers Design
5.3.2 Convergence Analysis
5.4 Velocity-Free Distributed Average Tracking in the Absence of Correct Initialization
5.5 Distributed Average Tracking in the Absence...
5.6 Simulation
References
6 Distributed Average Tracking for General Linear Dynamics
6.1 Problem Description
6.2 Robust Distributed Average Tracking Algorithm and Its Convergence
6.2.1 Algorithm Design
6.2.2 Convergence Analysis
6.3 Simulation
References
7 Distributed Average Tracking for Networked Euler–Lagrange Systems
7.1 Problem Description
7.2 Revisit of the Extended PI Algorithm
7.3 Distributed Average Tracking for Reference Signals with Steady States
7.3.1 Adaptive Control Algorithm Design
7.3.2 Convergence Analysis
7.4 Distributed Average Tracking for Reference Signals with Bounded Derivatives
7.4.1 Adaptive Control Algorithm Design
7.4.2 Convergence Analysis
7.5 Distributed Average Tracking for Reference Signals with a Common Time-Varying Velocity
7.5.1 Adaptive Control Algorithm Design
7.5.2 Convergence Analysis
7.6 Simulation
References
8 Distributed Average Tracking with Input Saturation
8.1 Problem Description
8.2 Distributed Average Tracking for References Without Inputs
8.2.1 Algorithm Design
8.2.2 Convergence Analysis
8.3 Distributed Average Tracking for Reference with Bounded Inputs
8.3.1 Algorithm Design
8.3.2 Convergence Analysis
8.4 Simulation
References
Part IV Applications
9 Distributed Average Tracking in Formation Control
9.1 Region-Following Formation Control Problem
9.2 Dynamic Region-Following Formation Control via Distributed Average Tracking
9.2.1 Single-Integrator Dynamics
9.2.2 Double-Integrator Dynamics
9.2.3 Higher-Order Linear Dynamics
9.3 Simulation
References
10 Distributed Average Tracking in Distributed Convex Optimization
10.1 Distributed Time-Varying Convex Optimization for Single-Integrator Dynamics
10.1.1 Centralized Time-Varying Convex Optimization
10.1.2 Distributed Time-Varying Convex Optimization Using Neighbors' Positions
10.1.3 Estimator-Based Distributed Time-Varying Convex Optimization
10.2 Distributed Time-Varying Convex Optimization for Double-Integrator Dynamics
10.2.1 Centralized Time-Varying Convex Optimization
10.2.2 Distributed Time-Varying Convex Optimization Using Neighbors' Positions and Velocities
10.2.3 Estimator-Based Distributed Time-Varying Convex Optimization
10.2.4 Distributed Time-Varying Convex Optimization Using Time-Varying Approximation of Signum Function
10.2.5 Distributed Time-Varying Convex Optimization Using Time-Invariant Approximation of Signum Function
10.3 Distributed Time-Varying Convex Optimization with Swarm Tracking Behavior
10.3.1 Distributed Time-Varying Convex Optimization with Swarm Tracking Behavior for Single-Integrator Dynamics
10.3.2 Distributed Time-Varying Convex Optimization with Swarm Tracking Behavior for Double-Integrator Dynamics
10.4 Simulation
References