2010/11/29 by Alain Sarlette, Sarlette, Alain, Christian Lageman +1
Computer Science · #34H15 #51F25 #93A14 #93B27 #93C10 #93D20 #Distributed Control Multi-Agent Systems #FOS: Mathematics #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1011.6171
openalex publication_date 2010/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies autonomous synchronization of k agents whose states evolve on SO(n), but which are only coupled through the action of their states on one "reference vector" in Rn for each link. Thus each link conveys only partial state information at each time, and to reach synchronization agents must combine this information over time or throughout the network. A natural gradient coupling law for synchronization is proposed. Extensive convergence analysis of the coupled agents is provided, both for fixed and time-varying reference vectors. The case of SO(3) with fixed reference vectors is discussed in more detail. For comparison, we also treat the equivalent setting in Rn, i.e. with states in Rn and connected agents comparing scalar product of their states with a reference vector.