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