Contributions by UCL

1
Contributions by UCL

• Multi-agent coordination and consensus
• Rigidity and persistence of formations

V. Blondel, R. Jungers, J. Hendrickx, R. Sepulchre
2
Multiagent coordination, consensus, and flocking

• Agents wish to reach agreement on a common value
  (some value in the range Min xi , Max xi, or
  the average of their values)
• Using a distributed algorithm
• Without assuming synchronization

3
Motivation

• Distributed computation and sensor networks
• Fusion of individual estimates (or of
  likelihood ratios)
• Load balancing
• Multiagent coordination and control
• Flocking, cooperative control.
• Agreement on a pending decision
• Social sciences
• Merging of expert opinions
• Formation of public consensus
• Modeling of jurors

4
Rigidity and persistence of formations
Each agent tries to maintain its distances toward
a pre-specied group of other agents constant. The
problem is to determine if one can guarantee that
the distance between every pair of agents remains
constant
5
Publications

• Vincent D. Blondel, Julien M. Hendrickx, Alex
  Olshevsky, and John N. Tsitsiklis, Convergence in
  Multiagent Coordination, Consensus, and Flocking,
  Proceedings of the 44th IEEE Conference on
  Decision and Control, Seville, Spain, 2005.
• Julien M. Hendrickx, Baris Fidan, Changbin Yu,
  Brian D. O. Anderson, Vincent D. Blondel,
  Rigidity and Persistence of Three and Higher
  Dimensional Formations. Proceedings of the First
  International Workshop on Multi-Agent Robotic
  Systems (MARS 2005), Barcelona, Spain, September
  13-14, 2005.
• Vincent D. Blondel, Yurii Nesterov, Stable sets
  of matrices and efficient approximations of the
  joint spectral radius, Oberwolfach reports,
  Mathematisches Forschungsinstitut Oberwolfach,
  Report 11/2005, p. 576, 2005. 
• Vincent D. Blondel, Julien M. Hendrickx, Alex
  Olshevsky, and John N. Tsitsiklis, Convergence in
  Multiagent Coordination, Consensus, and Flocking,
  Proceedings of the 44th IEEE Conference on
  Decision and Control, Seville, Spain, 2005.
• Changbin Yu, Julien M. Hendrickx, Baris Fidan,
  Brian D. O. Anderson, Vincent D. Blondel, Three
  and higher dimensional autonomous formations
  rigidity, persistence and structural persistence,
  submitted
• Julien M. Hendrickx, Baris Fidan, Changbin Yu,
  Brian D.O. Anderson, Vincent D. Blondel,
  Elementary operations for the reorganization of
  persistent formations, submitted.
• Julien M. Hendrickx, Brian D. O. Anderson,
  Jean-Charles Delvenne,Vincent D. Blondel,
  Directed graphs for the analysis of rigidity and
  persistence in autonomous agents systems. To
  appear in International Journal of Robust and
  Nonlinear Control.
• Vincent D. Blondel, Yurii Nesterov,
  Computationally efficient approximations of the
  joint spectral radius. SIAM Journal of Matrix
  Analysis, 271, pp. 256-272, 2005.
• Vincent D. Blondel, Yurii Nesterov and Jacques
  Theys, On the accuracy of the ellipsoid norm
  approximation of the joint spectral radius,
  Linear Algebra and its Applications, 3941, pp.
  91-107, 2005.