Identification of parsimonious continuous time LTI models with applications. (September 2018) - Varanasi, Santhosh Kumar; Jampana, Phanindra
Highlights: For all existing methods, model order is obtained using statistical estimates which essentially solve identification problem at every predefined order. We propose a sparse optimization method which estimates best possible model order and parameters simultaneously without repeated simulations. Theoretical analysis of the convergence is given and it is noted that the estimates are likely consistent. The proposed method is able to identify accurately the non-zero coefficients in case of marginally stable systems. Tanks in series experimental setup demonstrates the practical applicability of proposed method. Abstract: Identifying lower order models is desirable both for control design and prediction purposes. In a few cases, a lower order model can be further reduced so that it contains the fewest number of parameters. In this paper, a sparsity seeking optimization method is proposed to identify such parsimonious continuous time (CT) linear time invariant (LTI) models. Theoretical analysis of convergence of estimates is presented. Numerical results on a variety of systems show that the algorithm accurately estimates the model parameters. Further, Monte Carlo simulations are used to verify the statistical convergence properties of the parameter estimates. Identification of a reduced order CT LTI model of tanks in series system demonstrates the practical applicability of the proposed method.