Identification of Equation Error Models from Small Samples using Compressed Sensing Techniques

Perepu, Satheesh K.; Tangirala, Arun K.

doi:10.1016/j.ifacol.2015.09.066

“…(2) During-Estimation: This class of methods tries to estimate the model structure along with model parameters. The core idea is to utilize regularization or sparsity constraints in compressed sensing techniques for model structure determination (Perepu and Tangirala, 2015).…”

Section: Introductionmentioning

confidence: 99%

ARX Model Identification using Generalized Spectral Decomposition

Maurya¹,

Tangirala²,

Narasimhan³

2020

Preprint

Self Cite

0

View full text Add to dashboard Cite

This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the estimation of ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay. In this paper, we propose a novel automated framework which recovers orders, delay, output noise distribution along with parameter estimates. The primary tool utilized in the proposed framework is generalized spectral decomposition. The proposed algorithm systematically estimates all the parameters in two steps. The first step utilizes estimates of the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the efficacy of the proposed method and are observed to deliver consistent estimates even at low signal to noise ratio (SNR).

show abstract

“…(2) During-Estimation: This class of methods tries to estimate the model structure along with model parameters. The core idea is to utilize regularization or sparsity constraints in compressed sensing techniques for model structure determination (Perepu and Tangirala, 2015). (3) Post-Estimation: In these approaches, a certain model structure is assumed, and its correctness is checked after estimation.…”

Section: Introductionmentioning

confidence: 99%

Identification of Output-Error (OE) Models using Generalized Spectral Decomposition

Maurya

¹

,

Tangirala

²

,

Narasimhan

³

2019

2019 Fifth Indian Control Conference (ICC)

Self Cite

0

View full text Add to dashboard Cite

This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the estimation of ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay. In this paper, we propose a novel automated framework which recovers orders, delay, output noise distribution along with parameter estimates. The primary tool utilized in the proposed framework is generalized spectral decomposition. The proposed algorithm systematically estimates all the parameters in two steps. The first step utilizes estimates of the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the efficacy of the proposed method and are observed to deliver consistent estimates even at low signal to noise ratio (SNR).

show abstract

“…Over the last few years considerable progress has been made in the precise reconstruction of the zero and nonzero elements in an unknown sparse parameter vector of a stochastic dynamics system based on its input and output observations, for example, the compressed sensing (CS) based identification methods [29] [34] and the corresponding adaptive/online algorithms [10] [20] [23], the variable selection algorithms [12] [22] [38], etc. The basic idea of CS theory is to obtain a sparsest estimate of the parameter vector by minimizing the L 0 norm, i.e., the number of nonzero elements, with L 2 constraints [7] [14].…”

Section: Introductionmentioning

confidence: 99%

“…the dynamics of systems, in [29] [34] [37] the CS method is applied to the parameter estimation of linear systems and in [10] [20] [23] the adaptive algorithms such as least mean square (LMS), Kalman filtering (KF), Expectation Maximization (EM), and projection operator are introduced. The variable selection problem aims to find the true but unknown contributing variables of a system among many alternative ones.…”

Section: Introductionmentioning

confidence: 99%

Sparse System Identification for Stochastic Feedback Control Systems

Zhao,

Yin,

Bai

2019

Preprint

0

View full text Add to dashboard Cite

Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector θ of a stochastic dynamic system under feedback control, for which the current input may depend on the past inputs and outputs, system noises as well as exogenous dithers. First, a sparse parameter identification algorithm is introduced based on L 2 norm with L 1 regularization, where the adaptive weights are adopted in the optimization variables of L 1 term. Second, estimates generated by the algorithm are shown to have both set and parameter convergence. That is, sets of the zero and nonzero elements in the parameter θ can be correctly identified with probability one using a finite number of observations, and estimates of the nonzero elements converge to the true values almost surely. Third, it is shown that the results are applicable to a large number of applications, including variable selection, open-loop identification, and closed-loop control of stochastic systems. Finally, numerical examples are given to support the theoretical analysis.

show abstract

Identification of Equation Error Models from Small Samples using Compressed Sensing Techniques

Cited by 14 publications

References 12 publications

ARX Model Identification using Generalized Spectral Decomposition

ARX Model Identification using Generalized Spectral Decomposition

Identification of Output-Error (OE) Models using Generalized Spectral Decomposition

Sparse System Identification for Stochastic Feedback Control Systems

Contact Info

Product

Resources

About