System identification (SI) using small samples is a problem of interest in several applications. However, parameter estimation in these situations is a challenge since classical identification techniques (based on prediction-error methods) are guaranteed to be efficient and consistent only under asymptotic (large sample) conditions. In addition these techniques need the knowledge of delay and order of the process prior to estimation of parameters which is difficult to obtain especially when dealing with multi-input multi-output (MIMO) systems. This paper presents a method for identifying MIMO models which have auto-regressive with exogenous (ARX) input structure without the knowledge of delay and order of the process, using the ideas of sparse matrix optimization (SMO). The formulation of the proposed method consists of a constrained one norm minimization on the parameter matrix to induce sparsity. Three case studies, including one on real time data, are discussed to present the efficacy of the proposed method. Results show that the estimates obtained using the proposed algorithm have lower variance than the traditional least square estimates. © 2017 IEEE.

Arun K. Tangirala

Department Of Chemical Engineering

Satheesh K. Perepu

Identification (control systems)

MIMO systems

AUTO-REGRESSIVE

ESTIMATION OF PARAMETERS

Identification techniques

LEAST SQUARE ESTIMATES

MULTI-INPUT MULTI-OUTPUT SYSTEM

PARAMETER MATRICES

PREDICTION ERROR METHOD

SPARSE MATRICES

Parameter estimation

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IIT Madras

Identification of MIMO ARX models from small samples using sparse matrix optimization

2017 Indian Control Conference, ICC 2017 - Proceedings

System identification (SI), especially from small samples, is a challenging problem and of interest in several applications. Standard prediction-error minimization methods (PEM), under these conditions, generally result in estimates with higher variance. Moreover, in the identification of parametric models, one often needs prior knowledge of the input-output delay, obtaining estimates of which, is not possible using classical methods when the delay is either comparable or greater than the sample size. In this work, we develop a compressed sensing (CS)-based method for identifying sparse equation-error models that includes both auto-regressive eXogenous (ARX) and AR moving average eXogenous (ARMAX) structures with large delays, small orders and small delays with large orders, but with missing coefficients. The outcome is an iterative basis pursuit de noising (IBPDN) algorithm for solving non-linear CS problems. In addition, we propose a semi-rigorous method to lower the mutual coherence of the regressor matrix so as to obtain lower variance parameter estimates with the CS techniques. Errors in parameter estimates are computed using the bootstrapping method. Simulation studies on three diverse examples are presented to demonstrate the efficacy of the proposed methodology. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Fulltext

IFAC-PapersOnLine

Identification of equation error models from small samples using compressed sensing techniques

The delay estimation problem for open-loop single-input single-output (SISO) systems has been widely studied to the effect that well-established methods are available now. On the other hand, the delay estimation for MIMO systems remains a challenge to-date due to the presence of interactions among input and output variables. In this work, a method based on partial coherence functions (PCF) and Hilbert transform (HT) relation is presented to estimate time-delay for MIMO systems. The key step in the proposed method involves decoupling interactions using the PCF. The HT relation provides a platform for obtaining robust estimates of the time-delay by exploiting the causal nature of the relationship. The highlight of this method in contrast to conventional correlation-based techniques is that the problem formulation explicitly incorporates the delay parameter. In addition, the proposed method uses frequency-domain analysis which allows one to take into effects of noise in a straightforward way. Under closed-loop conditions, time-delay is estimated by introducing a dither signal at the controller output. Results from simulation and experimental studies are presented to demonstrate the effectiveness and potential of this method. © 2009 Elsevier Ltd. All rights reserved.

Chemical Engineering Science

Time-delay estimation in multivariate systems using Hilbert transform relation and partial coherence functions

Journal	Data powered by Typeset2017 Indian Control Conference, ICC 2017 - Proceedings
Publisher	Data powered by TypesetInstitute of Electrical and Electronics Engineers Inc.
Open Access	No