Convergence of max–min consensus algorithms

• Guodong Shi ^[1] ; Weiguo Xia ^[2] ; Karl Henrik Johansson ^[3]
  1. [1] Australian National University

     Australian National University

     Australia

     
  2. [2] Dalian University of Technology

     Dalian University of Technology

     China

     
  3. [3] Royal Institute of Technology

     Royal Institute of Technology

     Suecia

     

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 62, 2015, págs. 11-17
• Idioma: inglés
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• Resumen

  • In this paper, we propose a distributed max–min consensus algorithm for a discrete-time nn-node system. Each node iteratively updates its state to a weighted average of its own state together with the minimum and maximum states of its neighbors. In order for carrying out this update, each node needs to know the positive direction of the state axis, as some additional information besides the relative states from the neighbors. Various necessary and/or sufficient conditions are established for the proposed max–min consensus algorithm under time-varying interaction graphs. These convergence conditions do not rely on the assumption on the positive lower bound of the arc weights