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On-line parameter and delay estimation of continuous-time dynamic systems

Kozłowski J., Kowalczuk Z.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 2

223--232

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.

Nonparametric instrumental variables for identification of block-oriented systems

Mzyk G.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 3

521--537

A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.

Zastosowanie metody zmiennych instrumentalnych do identyfikacji systemów Hammersteina-Wienera

Mzyk G.

Pomiary Automatyka Kontrola

2001

R. 47, nr 7/8

35--39

W pracy rozpatruje się zastosowanie metody najmniejszych kwadratów i metody zmiennych instrumentalnych do estymacji parametrów blokowo zorientowanych, nieliniowych systemów dynamicznych. Dla systemu o strukturze Hammersteina-Wienera zaproponowano algorytm identyfikacji metodą zmiennych instrumentalnych i porównano go z algorytmem najmniejszych kwadratów. Udowodniono zgodność zaproponowanego estymatora, nawet dla przypadku występowania skorelowanych zakłóceń. Rozwiązano problem optymalnej generacji zmiennych instrumentalnych.

Application of least squares and instrumental variables to recovering parameters of nonlinear complex dynamic block-oriented systems is examined. For a system with the Hammerstein-Wiener structure the instrumental variable algorithm is designed and compared with the least squares algorithm for estimating system parameters. The advantages of the proposed estimator are discussed and in particular its weak consistency, even in the presence of correlated noise is shown. The problem of generating optimal values of instruments is analysed.