Consensus rate regulation for general linear multi-agent systems under directed topology

摘要

Recently, optimization in distributed multi-agent coordination has been studied concerning convergence speed. The optimal convergence speed of consensus for multi-agent systems consisting of general linear node dynamics is still an open problem. This paper aims to design optimal distributed consensus protocols for general identical linear continuous time cooperative systems which not only minimize some local quadric performances, but also regulate the consensus rate (including convergence rate and damping rate) for the multi-agent systems. The graph topology is assumed to be fixed and directed. The inverse optimal design method is utilized and the resulting optimal distributed protocols place part of close-loop poles of the global disagreement systems at specified locations asymptotically, while the remains far from the imaginary axis enough. It turns out that for the identical linear continuous time multi-agent systems, the convergence speed has no upper bound. The main advantages of the developed method over the LQR design method are that the resulting multi-agent systems can achieve specified consensus rate asymptotically and the resulting protocols have the whole right half complex plane as its asymptotical consensus region. Numerical examples are given to illustrate the effectiveness of the proposed design procedures.