Welcome

Welcome to our comprehensive course on Complex Network Systems and Control!

In this course, we will delve into the fascinating world of cooperative control of complex network systems over directed switching communication topologies.

Introduction: Our journey begins with an exploration of recent research progress in cooperative control. We’ll investigate how various scientific communities, from applied mathematics to sociology, have contributed to understanding the dynamics of complex network systems (CNSs) and multi-agent systems (MASs).

Outline of Contents: To guide you through this course, here’s an outline of the topics we’ll cover:

1. Introduction to Multi-Agent Systems and Complex Network Systems
   • Understanding CNSs and MASs
   • Exploring synchronization and consensus
   • Reviewing recent research progress
2. Foundations of Dynamical and Network Systems
   • Understanding basic concepts of dynamical systems
   • Introduction to network theory and graph theory
   • Exploring key properties of complex networks
   • Reviewing fundamental principles of control theory applied to networks

Conclusion: By the end of this course, you’ll have gained a solid understanding of cooperative control principles applied to complex network systems. You’ll be equipped to tackle real-world challenges in various fields, from engineering to biology.

We’re excited to embark on this learning journey with you!

Best regards,

Welcome

Introduction

Multi-agent systems (MASs) have emerged as a dynamic research domain over the last two decades, finding applications in diverse fields such as mobile robotics, unmanned aerial vehicles (UAVs), autonomous underwater vehicles, and satellites. Among the myriad challenges in MASs, the consensus tracking problem stands out as particularly significant. In practical scenarios, the velocities of maneuvering agents are subject to change over time, and the communication radius of each agent is limited. Consequently, the communication topology between agents can vary, making the tracking problem under time-varying topologies a critical area of study.

An Overview of Multi-agent Systems

Drawing inspiration from human group activities and collective behaviors observed in nature, researchers have dedicated significant efforts to understanding MASs. Over the past two decades, MASs have garnered widespread attention across various disciplines, yielding numerous advancements in areas such as consensus tracking with switching topologies, disturbance-rejection consensus, finite-time tracking control, pinning adaptive-impulsive control, and optimal coordination.

MASs consist of multiple autonomous agents capable of sensing the environment, movement, and information processing. Agents can take various forms, including UAVs, unmanned ground vehicles (UGVs), spacecraft, autonomous trains, and robots. The collaborative nature of MASs enables efficient, cost-effective, and reliable solutions to complex tasks by distributing them among individual agents.

Cooperative control of MASs encompasses various categories, including consensus control, formation control, and tracking control. Consensus control, in particular, has garnered significant attention due to its fundamental nature. Consensus in MASs refers to the agreement among agents regarding a certain quantity of interest, typically dependent on the state of all agents. Formulating consensus problems as leaderless or leader-following scenarios has been a common approach, where agents aim to reach a common value or follow a virtual leader’s objective, respectively.

Formation control involves guiding a group of interconnected agents to cooperatively move in a desired formation pattern, which can be either time-invariant or time-varying. Tracking control, on the other hand, focuses on guiding agents to track a target, akin to a leader-following consensus problem.

Consensus:

Since consensus of MASs is a fundamental problem in this research area, it has attracted increasing attention of researchers from various disciplines of engineering, biology, and science. In networks of agents, consensus means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents. A consensus algorithm is an interaction rule that specifies the information exchange between an agent and all of its neighbors on the network. The consensus problems have been formulated as consensus of leaderless problems or leader-following problems . For a cooperative MAS, leaderless consensus means that each agent updates its state based on local information of its neighbors such that all agents eventually reach an agreement on a common value, while leader-following consensus means that there exists a virtual leader that specifies an objective for all agents to follow.

Given a agent

\dot{ x_{i}}(t)  = u_{i}(t) 

Formation control:

Formation control is another hot topic, where a group of interconnected agents is controlled to cooperatively move with a desired formation pattern. The desired formation could be time invariant or time varying. Specifically, Lu et al. obtain sufficient conditions guaranteeing the exponentially converging speeds for both time-invariant and time- varying formation problems of MASs with directed graph interconnection topologies and time-varying coupling delays. Wang et al. design a novel event-triggered integral sliding mode control strategy that makes sure the high-order agents achieve a time-varying formation.

Tracking control :

Tracking control is a typical issue of MASs [7,9,11,13,28]. Many researchers have achieved significant results [13,29
32] on the tracking problem as it is an important topic in MASs’ research area. Consensus track- ing of a target can be regarded as leader-following consensus problem. For example, Hajshirmohamadi et al. [33] propose unified event-triggered frame- work that requires the agents to transmit their information when the trigger- ing condition is satisfied. In Ref. [34], two adaptive event-triggered communication schemes are presented for the consensus tracking control of MASs with stochastic actuator failures. Linear and dynamic-gain-based non- linear observers are designed for solving the consensus tracking problem of second-order MASs with disturbance in Ref. [35].

Chapter 2: Dynamics and Control Strategies

The diverse forms of agents in MASs lead to varying mathematical models for their dynamics, broadly categorized into linear and nonlinear dynamics. Recent research efforts have also delved into MASs with integer dynamics, owing to their simplicity and analytical tractability. Additionally, studies have explored MASs with nonlinear dynamics and switching topologies, reflecting the complexity and diversity of real-world MAS scenarios.

In subsequent chapters, we will delve deeper into the methodologies and techniques employed in consensus tracking under switching topologies, exploring both theoretical frameworks and practical applications in MASs.

Stay tuned for an insightful journey into the world of consensus tracking in multi-agent systems with switching topologies!