Globally optimal distributed cooperative control for general linear multi-agent systems

Abstract

This paper aims to design distributed consensus protocols which satisfy two design requirements for identical general linear multi-agent systems on fixed, undirected graphs: meeting the global optimality and guaranteeing a prescribed convergence speed. By using inverse optimal approaches, the optimal partial stabilization is developed and the globally optimal distributed consensus problem for leader following and leaderless problems are solved. To obtain prescribed convergence speed of the multi-agent system, novel globally optimal distributed consensus design procedures are proposed. First, combining with the regional pole assignment, the optimal control can be found by solving a strict linear matrix inequality (LMI) problem. It turns out that the increasing number of the agent nodes will not increase the computational complexity. Then, a modified linear quadratic regulator (MLQR) design method is developed which leads to a model free design procedure by employing the adaptive dynamic programming (ADP) technique. Finally, a numerical example is given to illustrate the effectiveness of the proposed procedures.