Distributed Optimization for Uncertain Linear Multi-agent Systems by Integral Control

In this paper, we consider a distributed optimization problem for a group of linear high-order multi-agent systems. All agents are allowed to possess parametric uncertainties that range over an arbitrarily large compact set. The goal is to collectively minimize a sum of local costs in a distributed fashion and finally guarantee an output consensus on this optimal point using only output information of agents. By adding an optimal signal generator to generate the global optimal point, a distributed integral control is constructively given to solve this problem under mild assumptions. The efficacy of this control is verified by a numerical example.