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In this paper, a distributed convex optimization problem with swarm trackingbehavior is studied for continuous-time multi-agent systems. The agents' taskis to drive their center to track an optimal trajectory which minimizes the sumof local time-varying cost functions through local interaction, whilemaintaining connectivity and avoiding inter-agent collision. Each local costfunction is only known to an individual agent and the team's optimal solutionis time-varying. Here two cases are considered, single-integrator dynamics anddouble-integrator dynamics. For each case, a distributed convex optimizationalgorithm with swarm tracking behavior is proposed where each agent relies onlyon its own position and the relative positions (and velocities in thedouble-integrator case) between itself and its neighbors. It is shown that thecenter of the agents tracks the optimal trajectory, the the connectivity of theagents will be maintained and inter-agent collision is avoided. Finally,numerical examples are included for illustration.

Distributed Convex Optimization of Time-Varying Cost Functions with Swarm Tracking Behavior for Continuous-time Dynamics