| Summary: | In this article, the formation control problem has been considered for second-order multi-agent system with time delay. The involved controller is divided into two parts. The first part is to design the leader-following and adaptive control strategies that are utilized to achieve the specified formation shape. Based on a potential field function, the second part is applied to realizing the collision avoidance of the agents communicating with each other. By using the Lyapunov theory, some sufficient criteria are derived to ensure the specified formation shape of all agents and collision avoidance of any pair of agents. The derived criteria are formulated in terms of algebraic conditions, in which the control gains play an important role. Finally, a numerical simulation is given to illustrate the effectiveness of the derived results.
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