Model synthesis of dynamic process with non-stationary disturbances based on maximum of generalized power function
Matematičeskoe modelirovanie, Tome 28 (2016) no. 12, pp. 133-142.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new approach to model synthesis of dynamic process with non-stationary perturbations based on application of maximum condition of generalized power function is considered. A new stochastic filter is developed using this model and procedures of invariant embedding. Within the example it demonstrates the possibility of achieving the best precision characteristics by reducing the amount of computational effort in comparison with the Kalman filter in the traditional model of nonstationary process. This confirmed by the results of mathematical modeling.
Keywords: motion model, Hamilton–Ostrogradski principle, combined-maximum principle, invariant embedding, Kalman filter, shaping filter.
@article{MM_2016_28_12_a10,
     author = {A. A. Kostoglotov and A. A. Kuznetsov and S. V. Lazarenko},
     title = {Model synthesis of dynamic process with non-stationary disturbances based on maximum of generalized power function},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {133--142},
     publisher = {mathdoc},
     volume = {28},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_12_a10/}
}
TY  - JOUR
AU  - A. A. Kostoglotov
AU  - A. A. Kuznetsov
AU  - S. V. Lazarenko
TI  - Model synthesis of dynamic process with non-stationary disturbances based on maximum of generalized power function
JO  - Matematičeskoe modelirovanie
PY  - 2016
SP  - 133
EP  - 142
VL  - 28
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2016_28_12_a10/
LA  - ru
ID  - MM_2016_28_12_a10
ER  - 
%0 Journal Article
%A A. A. Kostoglotov
%A A. A. Kuznetsov
%A S. V. Lazarenko
%T Model synthesis of dynamic process with non-stationary disturbances based on maximum of generalized power function
%J Matematičeskoe modelirovanie
%D 2016
%P 133-142
%V 28
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2016_28_12_a10/
%G ru
%F MM_2016_28_12_a10
A. A. Kostoglotov; A. A. Kuznetsov; S. V. Lazarenko. Model synthesis of dynamic process with non-stationary disturbances based on maximum of generalized power function. Matematičeskoe modelirovanie, Tome 28 (2016) no. 12, pp. 133-142. http://geodesic.mathdoc.fr/item/MM_2016_28_12_a10/

[1] Y. Bar-Shalom, X. Rong Li, T. Kirubarajan, Estimation with Applications to Tracking and Navigation, John Wiley Sons, New York, 2001, 558 pp.

[2] R. A. Singer, “Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets”, IEEE Transactions on Aerospace and Electronic Systems, AES-6:4 (1970), 473–483 | DOI

[3] A. A. Kostoglotov, A. I. Kostoglotov, S. V. Lazarenko, “The Combined-Maximum Principle in Problems of Estimating the Motion Parameters of a Maneuvering Aircraft”, Journal of Communications Technology and Electronics, 54:4 (2009), 431–438 | DOI

[4] A. A. Kostoglotov, S. V. Lazarenko, “Nonsmooth Analysis in Measurement Processing”, Measurement Techniques, 2009, no. 2, 117–124 | DOI

[5] A. A. Kostoglotov, A. I. Kostoglotov, S. V. Lazarenko, B. M. Tsennix, “Method of Structural-Parametric Identification of Lagrangian Dynamic Systems in the Processing of Measurement Information”, Measurement Techniques, 2014, no. 2, 153–159 | DOI

[6] A. Majka, “Trajectory Management of the Unmanned Aircraft System in Emergency Situation”, Aerospace, 2 (2015), 222–234 | DOI

[7] H. L. Van Trees, Detection, Estimation, and Modulation Theory, v. 2, Nonlinear Modulation Theory, John Wiley Sons, New York, 1975, 344 pp.

[8] X. Rong Li, P. G. Vesselin, “Survey of Maneuvering Target Tracking. Part I: Dynamic Models”, IEEE Transactions on Aerospace and Electronic Systems, 2003, no. 4, 1333–1364 | DOI

[9] A. A. Krasovskii (red.), Spravochnik po teorii avtomaticheskogo upravleniia, Nauka, M., 1987, 712 pp.

[10] N. Nabaa, R. H. Bishop, “Validation and Comparison of Coordinated Turn Aircraft Maneuver Models”, IEEE Transactions on Aerospace and Electronic Systems, 2000, no. 1, 250–259 | DOI

[11] A. A. Kostoglotov, A. A. Kuznetsov, “Synthesis of Algorithm for Estimation of the Motion parameters of an Airplane on the Basis of Method of Steepest Decent”, Automatic Control and Computer Sciences, 2004, no. 4, 46–54

[12] A. I. Lure, Analiticheskaia mekhanika, Gos. izd. fiziko-matemat. literat., M., 1961, 824 pp.

[13] V. N. Orlov, L. I. Rozonoer, “Variatsionnyi printsip dlia uravnenii makroskopicheskoi dinamiki i ego prilozheniia v khimicheskoi kinetike”, ZVMiMF, 1981, no. 5, 1192–1205

[14] V. V. Velichenko, “O variatsionnom metode v probleme invariantnosti upravliaemykh sistem”, Avtomatika i telemekhanika, 1972, no. 4, 22–35

[15] A. A. Kostoglotov, A. I. Kostoglotov, S. V. Lazarenko, “Joint Maximum Principle in the Problem of Synthesizing an Optimal Control of Nonlinear Systems”, Automatic Control and Computer Sciences, 2007, no. 5, 274–281 | DOI

[16] S. V. Lazarenko, “Metod sinteza optimalnogo upravleniia s ispolzovaniem printsipa Gaussa”, Informatsionno-izmeritelnye i upravliaiushchie sistemy, 2013, no. 12, 37–43

[17] A. A. Kostoglotov, A. I. Kostoglotov, S. V. Lazarenko, D. S. Andrashitov, “Mnogoparametricheskaia variatsionnaia identifikatsiia dinamicheskikh sistem na osnove obieedinennogo printsipa maksimuma”, Informatsionno-izmeritelnye i upravliaiushchie sistemy, 2012, no. 4, 68–76

[18] A. P. Sage, J. L. Melsa, System Identification, Academic Press, New York–London, 1971, 221 pp. | MR | Zbl

[19] K. V. Gardiner, Stokhasticheskie metody v estestvennykh naukakh, Mir, M., 1986, 539 pp. | MR

[20] G. E. Norman, V. V. Stegailov, “Stochastic theory of the classical molecular dynamics method”, Mathematical Models and Computer Simulations, 5:4 (2013), 305–333 | DOI | MR | Zbl

[21] A. Farina, F. Studer, Radar Data Processing, v. 1, Introduction and Tracking, Research Studies Press John Wiley Sons, New York, 1985, 320 pp.