Distributed LQR Optimal Protocol for Leader-Following Consensus.

This paper addresses the linear quadratic regulator optimal leader-following consensus for multiagent systems in a single-integrator form. Substantially different from the existing related works, the cost function, a global one, and the topology structure are both pregiven, and the optimal protocol to be sought is distributed (which merely depends on relative state information). This violates the optimal protocol design based on the algebraic Riccati equation, although a centralized protocol can be derived. To solve the problem, a novel design strategy of distributed optimal protocol is proposed for the multiagent systems over the digraph of a directed tree. Specifically, the dynamics of the consensus error is explicitly obtained, by which an online-implementable algorithm is given to achieve the parameterization of the cost function. Namely, the completely explicit formula with respect to the gain parameters of all agents is derived for the cost function. Based on this, the existence of optimal gain parameters is rigorously proven, which means the existence of the desired distributed optimal protocol. Furthermore, the optimal gain parameters are derived by minimizing the explicit formula. Two simulation examples are provided to illustrate the effectiveness of the theoretical results.