Distributed LQR design for multi-agent formations

In this paper we study the optimal formation control of multiple agents whose communication topology as well as the interaction parameters is tunable upon a cost function consisting of both control energy and formation indicator. The determination of interaction parameters is accompanied by the design of linear quadratic regulation(LQR) controllers which are distributed ones. When extending the results to systems with multiple agents, it is sufficient that the underlying graph of the cost matrix has an unrooted tree or the directed underlying graph is persistent. Numerical examples are provided to illustrate the effectiveness of the method.