Sparse input matrix and state estimation for linear systems

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 ℓ
₁
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.