Distributed linear quadratic optimal control:Compute locally and act globally

Abstract

In this letter we consider the distributed lin-ear quadratic (LQ) control problem for networks of agentswith single integrator dynamics. We first establish a generalformulation of the distributed LQ problem and show thatthe optimal control gain depends on global information onthe network. Thus, the optimal protocol can only be com-puted in a centralized fashion. In order to overcome thisdrawback, we propose the design of protocols that are com-puted in a decentralized way. We will write the global costfunctional as a sum of local cost functionals, each asso-ciated with one of the agents. In order to achieve “good”performance of the controlled network, each agent thencomputes its own local gain, using sampled informationof its neighboring agents. This decentralized computa-tion will only lead to suboptimal global network behavior.However, we will show that the resulting network will reachconsensus