Marion Gilson

Refined instrumental variable methods for identification of LPV Box-Jenkins models

The identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.

Instrumental variable methods for closed-loop system identification

In this paper, several instrumental variable (IV) and instrumental variable-related methods for closed-loop system identification are considered and set in an extended IV framework. Extended IV methods require the appropriate choice of particular design variables, as the number and type of instrumental signals, data prefiltering and the choice of an appropriate norm of the extended IV-criterion. The optimal IV estimator achieves minimum variance, but requires the exact knowledge of the noise model. For the closed-loop situation several IV methods are put in an extended IV framework and characterized by different choices of design variables. Their variance properties are considered and illustrated with a simulation example.

Refined Instrumental Variable Identification of Continuous-time Hybrid Box-Jenkins Models

This chapter describes and evaluates a statistically optimal method for the identification and estimation3 of continuous-time (CT) hybrid Box-Jenkins (BJ) transfer function models from discrete-time, sampled data. Here, the model of the basic dynamic system is estimated in continuous-time, differential equation form, while the associated additive noise model is estimated as a discrete-time, autoregressive moving average (ARMA) process. This refined instrumental variable method for continuous-time systems (RIVC) was first developed in 1980 by Young and Jakeman [52] and its simplest embodiment, the simplified RIVC (SRIVC) method, has been used successfully for many years, demonstrating the advantages that this stochastic formulation of the continuous-time estimation problem provides in practical applications (see, e.g., some recent such examples in [16, 34, 40, 45, 48]).

Brief On the relation between a bias-eliminated least-squares (BELS) and an IV estimator in closed-loop identification

A bias-correction method for closed-loop identification, introduced in the literature as the bias-eliminated least-squares (BELS) method (Zheng & Feng, Automatica 31 (1995) 1019), is shown to be equivalent to a basic instrumental variable estimator applied to a predictor for the closed-loop system. This predictor is a function of the plant parameters and the known controller. Corresponding to the related method using a least-squares criterion, the method is referred to as the tailor-made IV method for closed-loop identification. The indicated equivalence greatly facilitates the understanding and the analysis of the BELS method.

Developments for the matlab contsid toolbox

Abstract The CONtinuous-Time System IDentification (CONTSID) toolbox is a successful implementation of the methods developed over the last twenty years for estimating continuous-time transfer function or state-space models directly from sampled data. This paper gives a short overview of the toolbox, describes the latest developments and illustrates them on a few examples. Finally, the future plans are briefly summarized.

A bias-eliminated least-squares method for continuous-time model identification of closed-loop systems

Schemes for system identification based on closed-loop experiments have attracted considerable interest lately. However, most of the existing approaches have been developed for discrete-time models. In this paper, the problem of continuoustime model identification is considered. A bias correction method without noise modelling associated with the Poisson moment functionals approach is presented for indirect identification of closed-loop systems. To illustrate the performances of the proposed method, the bias-eliminated least-squares algorithm is applied to the parameter estimation of a simulated system via Monte Carlo simulations.

Third-order cumulants based methods for continuous-time errors-in-variables model identification

In this paper, the problem of identifying stochastic linear continuous-time systems from noisy input/output data is addressed. The input of the system is assumed to have a skewed probability density function, whereas the noises contaminating the data are assumed to be symmetrically distributed. The third-order cumulants of the input/output data are then (asymptotically) insensitive to the noises, that can be coloured and/or mutually correlated. Using this noise-cancellation property two computationally simple estimators are proposed. The usefulness of the proposed algorithms is assessed through a numerical simulation.

Instrumental variable scheme for closed-loop LPV model identification

Identification of real-world systems is often applied in closed loop due to stability, performance or safety constraints. However, when considering Linear Parameter-Varying (LPV) systems, closed-loop identification is not well-established despite the recent advances in prediction error approaches. Building on the available results, the paper proposes the closed-loop generalization of a recently introduced instrumental variable scheme for the identification of LPV-IO models with a Box-Jenkins type of noise model structures. Estimation under closed-loop conditions with the proposed approach is analyzed from the stochastic point of view and the performance of the method is demonstrated through a representative simulation example.

Refined instrumental variable methods for identification of Hammerstein continuous-time Box-Jenkins models

This article presents instrumental variable methods for direct continuous-time estimation of a Hammerstein model. The non-linear function is a sum of known basis functions and the linear part is a Box-Jenkins model. Although the presented algorithm is not statistically optimal, this paper further shows the performance of the presented algorithms and the advantages of continuous-time estimation on relevant simulations.

LATEST DEVELOPMENTS FOR THE MATLAB CONTSID TOOLBOX

This paper describes the latest developments for the CONTSID toolbox which includes time-domain identification methods for estimating continuous-time transfer function or state-space models directly from sampled data. The main additions to the new version aim at extending the optimal instrumental variable method to handle wider practical situations in order to enhance the application field of the CONTSID toolbox. The toolbox now includes: (1) a recursive version of the optimal instrumental variable method, (2) a version for multiple input system identification where the denominators of the transfer functions associated with each input are not constrained to be identical, (3) a version for identifying hybrid models of the general Box-Jenkins transfer function form, where a continuous-time plant model with a discrete-time noise model is estimated.