Optimal distributed cooperative control for multi-agent systems with constrains on convergence speed and control input

Abstract

This paper focuses on the distributed optimal cooperative control for multi-agent systems (MASs) over fixed communication graphs. Firstly, it is proved that the optimal distributed control for the local quadratic performance indexes of all agents is equivalent to solve a globally optimal problem, the resulting optimal Laplacian matrix associates with a complete graph hence the optimal distributed protocols do not exist. Consequently, we turn to solve the globally optimal distributed control problem for the candidate protocols with specified distributed structure. Furthermore, suboptimal fully distributed protocols can be designed when the Laplacian matrix and the initial states of all agents are unavailable. As a simple application, the minimum energy distributed cooperative control problem is addressed. Then, from a practical viewpoint, we solve the distributed optimal control problem with constrains on specified convergence speed and control input. Sufficient conditions for existence of the optimal solutions are derived. Finally, simulation examples are given to verify the effectiveness of the proposed results.