Optimal Consensus via Distributed Protocol for Second-Order Multiagent Systems

This article is devoted to the optimal protocol for the leader-following consensus of second-order multiagent systems. Remarkably, the global consensus cost functional and the directed topology are pregiven, and the optimal protocol to be sought is distributed. This makes the Riccati-based strategies inapplicable, by which merely centralized protocol can be derived. As the main contribution of this article, an effective strategy of seeking a distributed optimal protocol is proposed for second-order agents over the digraph of the directed tree. Detailedly, the feasibility of distributed optimal protocol is first affirmed, that is, the existence of optimal gain parameters can be guaranteed. Then, by recursively deriving the completely explicit formulas of the consensus errors of relative position and velocity, an online implementable algorithm is developed to achieve the parameterization of the cost functional, that is, to obtain the explicit formula of the cost functional with respect to gain parameters of all agents. Lastly, the desired optimal gain parameters are obtained by minimizing the explicit formula.