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

TL;DR

This paper develops distributed algorithms for multi-agent systems with continuous-time dynamics to track optimal trajectories of time-varying cost functions, ensuring connectivity and collision avoidance.

Contribution

It introduces novel distributed convex optimization algorithms for both single- and double-integrator dynamics with swarm tracking behavior.

Findings

Agents' centers successfully track optimal trajectories.

Connectivity among agents is maintained.

Inter-agent collisions are avoided.

Abstract

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.