Multiscale consensus for decentralized estimation and its application to building systems

Multiscale approaches to accelerate the convergence of decentralized consensus problems are introduced. Consecutive consensus iterations are executed on several scales to achieve fast convergence for networks with poor connectivity. As an example the proposed algorithm is applied to the decentralized Kalman filtering problem for estimation of contaminants in building systems. Two conventional observers are designed and convergence is compared with respect to the number of communications necessary, which is an effective measure of system complexity. It is demonstrated that the proposed multiscale scheme substantially accelerates the decentralized consensus. Future extentions and directions are briefly summarized.

[1]  Stephen P. Boyd,et al.  Fastest Mixing Markov Chain on a Graph , 2004, SIAM Rev..

[2]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[3]  N E Manos,et al.  Stochastic Models , 1960, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[4]  Jason Speyer,et al.  Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[5]  Stephen P. Boyd,et al.  A space-time diffusion scheme for peer-to-peer least-squares estimation , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[6]  William L. Briggs,et al.  A multigrid tutorial, Second Edition , 2000 .

[7]  Andrzej Banaszuk,et al.  Stochastic multiscale approaches to consensus problems , 2008, 2008 47th IEEE Conference on Decision and Control.

[8]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[9]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[10]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[11]  R. Olfati-Saber.  Ultrafast consensus in small-world networks , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  Irad Yavneh,et al.  Why Multigrid Methods Are So Efficient , 2006, Computing in Science & Engineering.

[13]  H. F. Durrant-Whyte,et al.  Fully decentralised algorithm for multisensor Kalman filtering , 1991 .