The natural phenomena of swarms, characterized by grouping of a large number of entities, can be observed in many living beings such as flocks of birds and schools of fish. The inspiring aspect of these phenomena is that although the intelligence of the individual members of the swarm is limited, a sophisticated and efficient group behavior is still achieved.;On the engineering side, in the last few years, distributed coordination control of a large scale multi-agent dynamical system has invoked increasing interest in the control community. A large group of mobile agents (e.g., mobile robots or mobile sensor nodes), geared with computing, sensing and communication devices can serve as a platform for a variety of civilian and military applications such as environmental monitoring, space exploration and battle-field mobile surveillance.;In this thesis, we use algebraic graphs to model the topologies of the swarm that embody the neighborhood, communication or the sensing relations among the members. We consider the general situation that the swarm's topology dynamically changes as the spacing among agents evolves with time. We study the underlying mechanisms in natural swarms, present a systematic methodology to analyze the behavior of a large group of mobile agents, and develop a unified framework for the controller design of a general range of coordinated motions of the swarm. By exploiting the presented framework as a guideline, we investigate and design decentralized controllers for two application scenarios of the coordinated motion of the swarm, namely, flocking in homogeneous environments and virtual leader tracking control. In addition, we examine the performance of the presented controllers under unknown but bounded disturbances. We show that with the presented controllers, the swarm can achieve the desired collective motion with bounded errors even in the presence of unknown disturbances.
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