Optimal strategies in the average consensus problem

2007/08/23 by Jean‐Charles Delvenne, Jean-Charles Delvenne, Ruggero Carli +4 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Distributed Control Multi-Agent Systems #Game Theory and Applications #Optimization and Search Problems #cs.MA #cs.NI #math.OC

paper · pdf · doi:10.48550/arxiv.0708.3220

9 pages; extended preprint with proofs of a CDC 2007 (Conference on decision and Control) paper

arxiv created 2007/08/23 · arxiv updated 2013/09/18

Abstract

We prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely many steps. A more general family of strategies, constructed by block Kronecker products, is investigated and compared to Cayley strategies.

Citations

• Consensus Problems in Networks of Agents With Switching Topology and Time-Delays

Cited by

• Consensus Networks over Finite Fields

Related

• On Distributed Average Consensus Algorithms
• Average-Consensus Algorithms in a Deterministic Framework
• Average Consensus on General Strongly Connected Digraphs
• Consensus with Ternary Messages
• Consensus with Output Saturations