Distributed LQR design for multi-agent systems on directed graph topologies

In this paper, the inverse optimal approach is employed to design distributed cooperative control protocols for identical linear systems that guarantee consensus and global optimality with respect to a positive (semi-) definite quadric performance index. Cooperative control and pinning control problems are considered, where the communication graphs are assumed to be directed and have fixe topology. Simple sufficient conditions are established, which indicate that the global optimality is achieved using local distributed protocols which are designed by the linear quadric regulator (LQR) based optimal control method. Examples are given to show the effectiveness of the proposed methods.