Brief paper: On H∞ and H2 performance regions of multi-agent systems

  • Authors:

  • Zhongkui Li;Zhisheng Duan;Guanrong Chen

  • Affiliations:

  • School of Automation, Beijing Institute of Technology, Beijing 100081, China;State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China;Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

This paper addresses the distributed H"2 and H"~ control problems for multi-agent systems with linear or linearized dynamics. An undirected multigraph with loops is used to represent the communication topology of a multi-agent network. A distributed controller is designed, based on the relative states of neighboring agents and a subset of absolute states of the networked agents. The notions of H"~ and H"2 performance regions are introduced and analyzed, respectively. A necessary and sufficient condition for the existence of a controller yielding an unbounded H"~ performance region is derived. A multi-step procedure for suboptimal H"~ controller synthesis is presented. It is also shown that the H"~ performance limit of the network under the distributed controller is equal to the minimal H"~ norm of a single agent achieved by using the state feedback controller. It is finally shown that, contrarily to the H"~ case, the H"2 performance limit scales with the number of agents in the network.