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Time-varying formation tracking for second-order multi-agent systems with switching directed topologies

Time-varying formation tracking problems for second-order multi-agent systems with switching and directed topologies are investigated, where the followers can not only form a predefined time-varying formation but also track the leader. A consensus based protocol is constructed using local neighboring information. An algorithm consisting of three steps is proposed to design the formation tracking control protocol. Then, based on the piecewise Lyapunov function theory, the stability of the proposed algorithm is proven and feasibility constraints as well as the threshold for the dwell time are also presented. Finally, a numerical simulation is presented to demonstrate the effectiveness of the theoretical results.