Sparse Linear Time Invariant System Identification Using Weighted Lasso

Open Access
Author:
Tutuk, Fatih
Graduate Program:
Electrical Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
December 05, 2014
Committee Members:
  • Constantino Manuel Lagoa, Thesis Advisor
Keywords:
  • System Identification
  • Sparsity
  • Lasso
  • Reweighting
Abstract:
In this thesis, the identification of a single-input single-output (SISO) linear time invariant (LTI) dynamical system from a finite set of completely known input signals and noisy output signals is studied. The identification problem studied aims at estimating the transfer function coefficients, the order of the system, and the standard deviation of the measurement noise. Estimations are performed by employing an existing linear shrinkage method, which is the modified least absolute shrinkage and selection operator (LASSO). In the modified LASSO, the transfer function coefficients and the standard deviation of the measurement noise are estimated by minimizing the l2 norm of the error with an l1 norm penalty on the transfer function coefficients. Owing to the nature of the l1 norm penalty, the true order of the system is obtained by sparsifying the parameter vector, which contains the transfer function coefficients. An iterative algorithm is proposed to solve the modified LASSO optimization problem. We do not give the true order information of the system to the algorithm. This leads the problem of having a sparse and a correct parameter vector estimate at the same time, which causes wrong order estimation. In order to overcome this issue, we introduce the use of two types of weight matrices. The first weight type is the iterative reweighting for the LASSO, which is a well-known weighting for l1 norm minimization problems. The second weight type is a fixed weighting containing constant numbers. In this context, we show the applicability of the fixed weighting for sparsification. Finally, we test the validation of the proposed algorithm by synthetic randomly generated bounded-input bounded-output (BIBO) stable systems with noisy measurements.