Active parametric identification of Gaussian linear discrete system based on experiment design

V. M. Chubich   ; O. S. Chernikova   ; E. A. Beriket

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 90-102

Résumé

The application of methods of theory of experiment design for the identification of dynamic systems allows the researcher to gain more qualitative mathematical model compared with the traditional methods of passive identification. In this paper, the authors summarize results and offer the algorithms of active identification of the Gaussian linear discrete systems based on the design inputs and initial states. We consider Gaussian linear discrete systems described by state space models, under the assumption that unknown parameters are included in the matrices of the state, control, disturbance, measurement, covariance matrices of system noise and measurement. The original software for active identification of Gaussian linear discrete systems based on the design inputs and initial states are developed. Parameter estimation is carried out using the maximum likelihood method involving the direct and dual procedures for synthesizing A- and D- optimal experiment design. The example of the model structure for the control system of submarine shows the effectiveness and appropriateness of procedures for active parametric identification.

Détail

Keywords: parameter estimation; maximum likelihood method; Kalman filter; experiment design; (Fisher) information matrix.

Bibliographie

[1] Kash'jap R.L., Construction of Dynamic Stochastic Models Based on Experimental Data, Nauka, M., 1983, 384 pp.

[2] L'jung L., System Identification: Theory User, Nauka, M., 1991, 432 pp. | MR

[3] Cypkin Ja.Z., Information Theory of Identification, Nauka, M., 1995, 336 pp. | MR

[4] Walter E., Pronzato L., Identification of Parametric Models from Experimental Data, Springer-Verlag, Berlin, 1997, 413 pp. | MR | Zbl

[5] Mehra R.K., “Optimal Input Signals for Parameter Estimation in Dynamic Dystems: Durvey and New Results”, IEEE Trans. on Automat. Control, 19:6 (1974), 753–768 | DOI | MR | Zbl

[6] Krug G.K., Sosulin Ju.A., Fatuev V.A., Planning Experiment in Problems of Identification and Extrapolation, Nauka, M., 1977, 208 pp. | MR

[7] Ovcharenko V.N., “Planning of Identifies Input Signals in Linear Dynamic Systems”, Automation and Remote Control, 62:2 (2001), 236–247 | DOI | MR | Zbl

[8] Jauberthie C., Denis-Vidal L., Coton P., Joly-Blanchard G., “An Optimal Input Design Procedure”, Automatica, 42 (2006), 881–884 | DOI | MR | Zbl

[9] Voevoda A.A., Troshina G.V., “Using the Fisher Information Matrix when Selecting a Control Signal for Estimating the Parameters of Dynamic Models and Observation of Objects of Low Order”, Collection of Scientific Works NSTU, 2006, no. 3(45), 19–24 (in Russian)

[10] Alexandrov A.G., “Finite-Frequency Method of Identification”, Preprints of 10th IFAC Symposium on System Identification, v. 2, 1994, 523–527

[11] Aleksandrov A.G., Orlov Ju.F., “Finite-Frequency Identification: Dynamic Algorithm”, Problems of Control, 2009, no. 4, 2–8 (in Russian)

[12] Denisov V.I., Chubich V.M., Chernikova O.S., “Active Identification of Stochastic Linear Discrete Systems in the Time Domain”, Journal of Applied and Industrial Mathematics, 6:3 (2003), 70–87 (in Russian) | MR | Zbl

[13] Denisov V.I., Chubich V.M., Chernikova O.S., “Active Identification of Stochastic Linear Discrete Systems in the Frequency Domain”, Journal of Applied and Industrial Mathematics, 10:1 (2007), 183–200 | DOI | MR

[14] Denisov V.I., Chubich V.M., Chernikova O.S., Bobyleva D.I., Active Parametric Identification of Stochastic Linear Systems, Monograph, NGTU, Novosibirsk, 2009, 192 pp.

[15] Chubich V.M., Chernikova O.S., “Optimal Parameter Estimation for Gaussian Models of Linear Discrete Systems Based on the Planning of the Initial Conditions”, Scientific Bulletin of NSTU, 2013, no. 3(36), 15–22 (in Russian)

[16] Chubich V.M., “Computation the Fisher Information Matrix for the Problem of Active Parametric Identification of Stochastic Nonlinear Discrete Systems”, Scientific Bulletin of NSTU, 2009, no. 1(34), 23–40 (in Russian)

[17] Chubich V.M., “Information Technology Active Parametric Identification of Quasi-Linear Discrete Systems”, Informatics and Applications, 5:1 (2011), 46–57 (in Russian)

[18] Chubich V.M., “Planning the Initial Conditions in the Problem of Active Parametric Identification of Gaussian Linear Discrete Systems”, Scientific Bulletin of NSTU, 2011, no. 1(42), 39–46 (in Russian)

[19] Ermakov S.M., Zhigljavskij A.A., Mathematical theory of optimal experiment, Nauka, M., 1987, 320 pp.

[20] Veremej E.I., Linear Systems with Feedback, Lan', St. Petersburg, 2013, 448 pp.

[21] Chubich V.M., Chernikova O.S., Filippova E.V., “Software System Active Parametric Identification of Stochastic Dynamical Systems APIS”, XI International Conference on Actual Problems of Electronic Instrument Engineering APEIE-2012 (Novosibirsk, 2012), v. 6, 66–73 (in Russian) [В.М. Чубич, О.С. Черникова, Е.В. Филиппова, “Программная система активной параметрической идентификации стохастических динамических систем APIS”, XI Междунар. конф. «Актуальные проблемы электронного приборостроения АПЭП-2012», т. 6, 2012, 66–73]