A sub-optimal consensus design for multi-agent systems based on hierarchical LQR

This paper presents a new and systematic procedure to design sub-optimal hierarchical feedback controllers for the leader-follower consensus problem in homogeneous multi-agent systems. First, the given multi-agent system is treated as a two-layer hierarchical system where the agents perform local actions in the lower layer and interact with others in the upper layer to achieve some global goals. Then the consensus controller design is formulated as a hierarchical state feedback control problem. Employing LQR approach with an appropriately selected performance index, an optimal hierarchical state feedback controller is derived which includes two terms namely local and global terms. Consequently, by removing the local term, the remaining global term is proved to make the multi-agent system consensus which results in a sub-optimal hierarchical consensus controller. Finally, some numerical examples are introduced to illustrate the effectiveness of the proposed method.