Sparse input matrix and state estimation for linear systems

Laetitia Chapel (1) , Douglas J. Leith (1)

1 Hamilton Institute [NUI]

This paper addresses the problem of sparse identification of the input matrix parameters in linear systems. A filter that combines state and sparse input matrix estimation is developed. This takes advantage of the connections between Kalman filtering and least squares estimation to formulate the problem as a ℓ1 regularised least squares optimisation, i.e. as a LASSO problem. The solution consistency is discussed and the technique is applied to experimental measurements from a production web server with promising results.

Mots clés: Kalman filtering; LASSO problem; linear systems; production web server; regularised least squares optimisation; sparse identification; sparse input matrix estimation; state estimation; Kalman filters; least squares approximations; matrix algebra; optimisation

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Systèmes dynamiques [math.DS]

Laetitia Chapel, Douglas J. Leith. Sparse input matrix and state estimation for linear systems. Decision and Control (CDC), 2010 49th IEEE Conference on, Dec 2010, United States. pp.4441-4446, ⟨10.1109/CDC.2010.5718016⟩. ⟨hal-00616734⟩