  In this paper, we propose an approach for solving an energy-optimal goal
assignment problem to generate the desired formation in multi-agent systems.
Each agent solves a decentralized optimization problem with only local
information about its neighboring agents and the goals. The optimization
problem consists of two sub-problems. The first problem seeks to minimize the
energy for each agent to reach certain goals, while the second problem entreats
an optimal combination of goal and agent pairs that minimizes the energy cost.
By assuming the goal trajectories are given in a polynomial form, we prove the
solution to the formulated problem exists globally. Finally, the effectiveness
of the proposed approach is validated through the simulation.
