Distributed time-varying formation optimal tracking for uncertain Euler–Lagrange systems with time-varying cost functions

This article studies the distributed formation optimal tracking problems for Euler–Lagrange systems, where each agent only has access to local cost function and other relative state information with its neighbors. Different from existing works, the effects of time-varying formation, parametric uncertainties, external disturbances and optimal performance of Euler–Lagrange systems are all considered simultaneously. Under the proposed distributed formation optimal tracking protocol, all agents are able to asymptotically track an optimal reference trajectory, while maintain the given time-varying formation. Firstly, a dynamic system is introduced for each agent to generate optimal reference signal, which uses only the individual's own state and the neighboring relative measurements with no extra exchange of virtual states needed. Then, an optimal tracking control strategy is proposed, with which zero optimum-tracking error can be achieved. Thirdly, sufficient conditions are given to guarantee that the agents' states asymptotically converge to the optimal solution in the desired formation under the proposed algorithm. At last, numerical simulation is designed to verify the strategies.