Chapter 1
Introduction

Yue Wang1, Eloy Garcia2, David Casbeer2 and Fumin Zhang3

1Department of Mechanical Engineering, Clemson University, Clemson, SC, USA

2The Control Science Center of Excellence, Air Force Research Laboratory, Wright-Patterson AFB, OH, USA

3School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA

1.1 Introduction

Many military and civilian applications require a team of agents to coordinate with each other to perform specific tasks without human intervention. In those systems, individual agents (e.g., unmanned underwater/ground/aerial vehicles) have limited capabilities due to short sensing and communication ranges, and small computational power. However, their collective behavior exhibits significant advantages compared to a single sophisticated agent, including large-scale spatial distribution, robustness, high scalability, and low cost [1]. The deployment of large-scale multi-agent systems with constrained costs and smaller sizes can thus achieve tasks that are otherwise unable to be finished by a single agent. Teams of engineered multi-agent systems can collect and process data and perform tasks cooperatively [2-8]. Multi-agent systems play an important role in a wide range of applications such as search and rescue [9], tracking/classification [10-14], surveillance [15, 16], space exploration [17], and radiation shielding and site clearing [18]. Multi-agent systems have also been considered and utilized in fields such as cooperative mobile robotics [19], distributed artificial intelligence and computing [20-22], wireless sensor networks [23], biology [24], social study [25], smart grids [26], traffic management [27, 28], and supply-chain management [29]. Therefore, the use of multi-agent system technologies in both everyday modern society and national defense and homeland security is bound to tremendously increase. In this book, we aim to provide an overview of recent progresses made in the cooperative control of multi-agent systems on both fundamental theory development as well as applications.

In the control community, multi-agent system theory has focused on developing vehicle motion control laws for various tasks including consensus and formation control [2, 30-43], coverage control [44-48], target search and tracking [3-5, 49, 50], task allocation problems [25, 51-53], sensor management problems [14], output regulation [54, 55], optimization [56], and estimation. Three types of control schemes for multi-agent systems have been proposed in the open literature, that is, centralized [57], decentralized [58], and distributed multi-agent control [1]. The centralized control scheme assumes global knowledge of the multi-agent system and seeks to achieve some control objective considering all agents' states, which inevitably suffers from the scalability issue. The decentralized control scheme computes control actions based only on an agent's local information while the more popular distributed control scheme takes both the agent's own information and neighboring agents' information into account to calculate the control action. Both the decentralized and distributed control algorithms provide scalable solutions and can be implemented under minimal connectivity properties. On the other hand, connectivity preserving protocols are developed for multi-agent systems to keep connected and hence guarantee motion stability [59, 60]. The problem has been considered in scenarios such as flocking [61, 62], rendezvous [59, 63], and formation control [64, 65]. The control hierarchy for multi-agent systems can be categorized into two classes, that is, top-down and bottom-up methodologies [66]. The top-down scheme assigns an overarching objective for the multi-agent system and designs control action for each individual agent to achieve this objective. The top-down multi-agent task decomposition is often difficult. While the bottom-up scheme directly defines each individual agent's local control action and their cooperation protocol, which however cannot guarantee any global objective. The paper [67] provides an overview of progresses made in the distributed multi-agent coordination. The books [64, 68] provide an introduction to the distributed control of multi-agent systems. The book [1] discusses the distributed control of multi-agent systems from four main themes, or dimensions: distributed control and computation, adversarial interactions, uncertain evolution, and complexity management. A special category of multi-agent systems, multi-robot systems, has become one of the most important areas of research in robotics [19]. Significant advance has been made in distributed control and collaboration of multi-robot systems in control theory and artificial intelligence [68-70]. There are a considerable amount of works on multi-agent consensus and formation control, and synchronization. We briefly summarize the main results as follows.

The multi-agent consensus control problem ensures that a group of mobile agents stays connected and reaches agreement while achieving some performance objective [64]. The papers [71, 72] provide a good survey of consensus problems in multi-agent cooperative control. In [64], the consensus problem is considered over dynamic interaction graphs by adding appropriate weights to the edges in the graphs. Theoretical results regarding consensus seeking under both time-invariant and dynamically changing information exchange topologies are summarized. Applications of consensus protocols to multi-agent coordination are investigated. In [73, 74], consensus algorithms are extended for second-order nonlinear dynamics in a dynamic proximity network. Necessary and sufficient conditions are given to ensure second-order consensus. In [75], leader-following consensus algorithms are developed for a linear multi-agent system on a switching network, where the input of each agent is subject to saturation. In [76], multi-agent consensus based on the opinion dynamics introduced by Krause is studied. A new proof of convergence is given with all agents in the same cluster holding the same opinion (represented by a real number). Lower bounds on the inter-cluster distances at a stable equilibrium are derived. In [33], multi-agent consensus is considered for an active leader-tracking problem under variable interconnection topology. The effects of delays on multi-agent consensus have been considered in [77].

The paper [78] provides a survey of formation control of multi-agent systems. The existing results are categorized into position-, displacement-, and distance-based control. The finite-time formation control for nonlinear multi-agent systems is investigated in [43]. A small number of agents navigate the whole team based on the global information of the desired formation while the other agents regulate their positions by the local information in a distributed manner. A class of nonlinear consensus protocols is first ensured and then applied to the formation control. In [79], a model-independent coordination strategy is proposed for multi-agent formation control in combination with tracking control for a virtual leader. The authors show that the formation error can be stabilized if the agents can track their respective reference points perfectly or if the tracking errors are bounded. In [80], a decentralized cooperative controller for multi-agent formation control and collision avoidance is developed based on the navigation function formalism. The control law is designed as the gradient of a navigation function whose minimum corresponds to the desired formation. Multi-agent formation control with intermittent information exchange is considered in [81]. Energy-based analysis is utilized to derive stability conditions. The paper [82] investigates rotating consensus and formation control problems of second-order multi-agent systems based on Lyapunov theory. Both theoretical and experimental results are presented in [42] on multi-agent decentralized control that achieves leader-follower formation control and collision avoidance for multiple nonholonomic robots.

In [83], synchronization approach is developed for trajectory tracking of multiple mobile robots while maintaining time-varying formations. In [84], synchronization algorithms are designed in a leader-follower cooperative tracking control problem where the agents are modeled as identical general linear systems on a digraph containing a spanning tree. The control framework includes full-state feedback control, observer design, and dynamic output feedback control. In [54], a distributed control scheme is adopted for robust output regulation in a multi-agent system where both the reference inputs and disturbances are generated by an exosystem. In [55], the output regulation problem is extended to multi-agent systems where a group of subsystems cannot access the exogenous signal. In [85], output consensus algorithms are developed for heterogeneous agents with parametric uncertainties. The multi-agent output synchronization problem is also studied in [86] where the coupling among the agents is nonlinear and there are communication delays. In [87], a general result for the robust output regulation problem has been studied for linear uncertain multi-agent systems. In [88], finite-time synchronization is proposed for a class of second-order nonlinear homogenous multi-agent systems with a leader-follower architecture. A finite-time convergent observer and an observer-based finite-time output feedback controller are developed to achieve the goal.

In [89], distributed tracking control is developed for linear multi-agent...