Optimal Tracking of Time-varying Formation in Open Nonlinear Multiagent Systems

This paper addresses optimal tracking of time-varying formation in open nonlinear multiagent systems, where agents are allowed to arrive or depart at any moment. The objective of each agent is to minimize the cumulative local time-varying objective functions of all agents, while satisfying time-varying formation constraints. A distributed subgradient-based estimator utilizing signs of relative estimated formation references is proposed. Based on this estimation, a neural network-based adaptive tracking controller is developed to compensate for model nonlinearities and uncertainties. The convergence of the proposed protocol is analyzed using two regret measures: one representing the cumulative error between real trajectories and optimal trajectories, and the other representing the cumulative violation of formation constraints. The upper bounds of the regrets are derived and proven to be sublinear or linear under suitable parameter selections. Numerical examples complement the theoretical findings.