An analytic solution of the uncoupled multi-agent model and its benefit through optimal control system with attractor and repellant

This paper gives the analytic solution of the uncoupled multi-agent model. This solution describes the optimal path of each agent. In this exposition, the optimal control approach is used to model uncoupled multi-agent swarm with attractor and repellant. The special functional cost contains repellent cost functional is used to guarantee each agent never collides one to the others. The attractor term in the special functional cost makes each agent never mover far away to the others. This paper also gives the benefit of the agents moves in the multi-agent system.