Linear Quadratic Regulator for Containment Control in Multi-Agent Systems over Directed Graphs

This study applies a design method called linear quadratic regulator to tackle the containment control problem of discrete-time linear multi-agent systems over directed graphs. By solving an algebraic Riccati equation, the study establishes both necessary and sufficient conditions required to achieve consensus. The researchers introduce an innovative distributed control law for information transmission between leaders and followers. This control law allows the following agents to move within the convex hull formed by the navigation agent, and effectively enables them to converge quickly and then follow again by introducing position error adjustment parameters. The effectiveness of the proposed algorithms is demonstrated through a simulation example.