Modeling random flocks through Generalized Factor Analysis

In this paper, we study modeling and identification of stochastic systems by Generalized Factor Analysis models. Although this class of models was originally introduced for econometric purposes, we present some possible applications of engineering interest. In particular, we show that there is a natural connection between Generalized Factor Analysis models and multi-agents systems. The common factor component of the model has an interpretation as a flocking component of the system behavior.

[1]  Gerardo Lafferriere,et al.  Flocks and Formations , 2005 .

[2]  Petre Stoica,et al.  Introduction to spectral analysis , 1997 .

[3]  Sandro Zampieri,et al.  Randomized consensus algorithms over large scale networks , 2007 .

[4]  P. Brazhnik,et al.  Gene networks: how to put the function in genomics. , 2002, Trends in biotechnology.

[5]  D. Aldous Exchangeability and related topics , 1985 .

[6]  Julius S. Bendat,et al.  Stationary Random Processes , 2012 .

[7]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[8]  Giulio Bottegal,et al.  A note on generalized factor analysis models , 2011, IEEE Conference on Decision and Control and European Control Conference.

[9]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[10]  R. Brockett On the control of a flock by a leader , 2010 .

[11]  Brian D. O. Anderson,et al.  Generalized linear dynamic factor models - An approach via singular autoregressions , 2009, ECC.

[12]  Aurel Wintner,et al.  THE SPECTRA OF TOEPLITZ'S MATRICES.* , 1950 .

[13]  J. Doob Stochastic processes , 1953 .

[14]  Gary Chamberlain,et al.  FUNDS, FACTORS, AND DIVERSIFICATION IN ARBITRAGE PRICING MODELS , 1983 .

[15]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1983 .

[16]  Alireza Tahbaz-Salehi,et al.  Consensus Over Ergodic Stationary Graph Processes , 2010, IEEE Transactions on Automatic Control.

[17]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[18]  I. M. Glazman,et al.  Theory of linear operators in Hilbert space , 1961 .

[19]  L. B. Rall Theory of Linear Operators in Hilbert Space. Vol. I (N. I. Akhiezer and I. M. Glazman) , 1962 .

[20]  M. Hallin,et al.  The Generalized Dynamic-Factor Model: Identification and Estimation , 2000, Review of Economics and Statistics.

[21]  Marco Lippi,et al.  THE GENERALIZED DYNAMIC FACTOR MODEL: REPRESENTATION THEORY , 2001, Econometric Theory.

[22]  H. Cramér On Some Classes of Nonstationary Stochastic Processes , 1961 .