INFORMATION CHANGE THE WORLD

International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.6, No.9, Aug. 2014

Identification of Quality Indicators Dynamic System on Basis of Analysis Data "Input-Output"

Full Text (PDF, 1233KB), PP.1-11


Views:173   Downloads:1

Author(s)

Nikolay Karabutov

Index Terms

Equilibrium State Point, Spectrum of Eigenvalues, Identification, Structure, Lyapunov Exponents

Abstract

The problem of an estimation quality indicators of linear dynamic system in the conditions of uncertainty is considered. Quality indicators are a point of an equilibrium state and a spectrum of eigenvalues. We offer a method of an estimation a point of an equilibrium state. Method is based on identification of the particular solution system on a class of static models with the dynamic specification on an input. We offered on the basis of the general decision of system procedures and criteria of an estimation equilibrium state. After an estimation of equilibrium state system in work the problem of definition a spectrum eigenvalues of linear dynamic system is considered. We form the time series describing a modification of Lyapunov exponents. For identification of a spectrum eigenvalues we introduce special structures which describe a modification of the Lyapunov exponent. We apply a method of the secant structures and we receive spectrum tentative estimations. The special structure, allowing identifying the largest Lyapunov exponent, is offered. Generalization of the offered methods on linear non-stationary dynamic systems is given.

Cite This Paper

Nikolay Karabutov,"Identification of Quality Indicators Dynamic System on Basis of Analysis Data "Input-Output"", International Journal of Intelligent Systems and Applications(IJISA), vol.6, no.9, pp.1-11, 2014. DOI: 10.5815/ijisa.2014.09.01

Reference

[1]D.K. Arrowsmith, С.М. Place. Ordinary differential equa-tions. Chapman and Hall, London, New York, 1982.

[2]A. А. Andropov, E.A. Leontovich, I.I. Gordon, and A.G. Mayer. Qualitative theory of dynamic systems of second order. Nauka, Мoscow, 1968.

[3]R. Reissig, G. Sansone, and R. Conti. Qualitative theorie nichtlinearer differentialgleichungen. Edizioni cremonese, Roma, 1974.

[4]L. Cesari. Asymptotic behavior and stability problems in ordinary differential equations. Springer -Verlag, Berlin, Gottingen, Heidelberg. 1959.

[5]N.N. Bautin, and E.A. Leontovich. Methods and modes of qualitative research of dynamic systems on a plane. Nauka, Мoscow, 1990.

[6]L.N. Tikhonov, A.B. Vasil’eva, and A.G. Sveshnikov. Differential equations. Nauka, Мoscow, 1980.

[7]P.G. Akishin, P. Akritas, I.Antoniou, and V.V. Ivanov. Identification of discrete chaotic maps with singular points. Discrete dynamics in nature and society, 2001, Vol. 6: 147-156.

[8]J. Zhou, and F. Chen. A novel algorithm for detecting sin-gular points from fingerprint images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31, 7: 1239-1250.

[9]D. Parekh, and R. Vig. Survey on parameters of fingerprint classification methods based on algorithmic flow. Interna-tional Journal of Computer Science and Engineering Survey, 2011, 2, 3: 150-160.

[10]J.F. Foss, K.M. Bade, D.R. Neal, and R.J. Prevost. Topo-logical considerations in support of PIV vector field anal-yses. 10th international symposium on particle image ve-locimetry - PIV13. Delft, Netherlands, July 1-3, 2013: 1-12.

[11]N.N. Karabutov. Adaptive identification of systems: In-formational synthesis. URSS, Moscow, 2006.

[12]S. Ayasun, C.O. Nwankpa, and H.G. Kwatny. Computation of singular and singularity induced bifurcation points of differential-algebraic power system model. IEEE Trans-actions on Circuits and Systems I, 2004, 51, 8: 1525-1538.

[13]J. Meng, T. Zhu, X. Chen, and X. Yin. The nonlinear dy-namics characteristics of stock market and its variation. Proceedings of the 2nd International Conference on Com-puter Science and Electronics Engineering (ICCSEE 2013). Published by Atlantis Press, Paris, France. 2013: 0450-0455.

[14]P.B. Kuptsov. Calculation of Lyapunov indexes for the distributed systems: advantages and shortages of various numerical methods. Informations of High Schools. Applied Nonlinear Dynamics. 2010,18, 5: 93-112.

[15]N.D. Poljahov, A.V. Bespalov, and V.E. Kuznetsov. Esti-mation of a condition of engineering systems in real time on Lyapunov's first index. Conference materials «Control in engineering, erhatic, organizational network systems» (UTEOSS-2012). SCC the Russian Federation of Open Society "Concern TSNII "Electrodevice": Saint-Petersburg, 2012: 463-466.

[16]S. England. Quantifying dynamic stability of musculoskel-etal systems using Lyapunov exponents. Blacksburg, Vir-ginia. 2005.

[17]M.T. Rosenstein, J.J. Collins, C.J. De Luca. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. 1993, 65: 17-134.

[18]B.N. Datta, V.A. Yatsenko, and S.P. Nair. Model Updating and Simulation of Lyapunov Exponents. Proceedings of the European Control Conference 2007. Kos, Greece, July 2-5, 2007: 1094-1100.

[19]J.A. Scales, E.S. Van Vleck. Lyapunov exponents and localization in randomly layered media. journal of Compu-tational Physics, 1997, 133: 27–42.

[20]K. Slevin, Y. Asada, L.I. and Deych. Fluctuations of the Lyapunov exponent in two-dimensional disordered systems. Physical Review B, 2004, 70, 054201: 054201-1-054201-10.

[21]N.N. Karabutov. Structural Identification of Systems. The Analysis of Information Structures, URSS/ Librokom, Moscow, 2009.

[22]N.N. Karabutov. Deriving a dynamic-system eigenvalue spectrum under conditions of uncertainty by processing measurements. Measurement Techniques, Springer US, 2009, 52, 6: 572-579. DOI: 10.1007/ s11018-009-9309-0.

[23]L.E. Rejzin. Lyapunov's functions and a recognition prob-lem. Zinatne, Riga, 1986.

[24]E.N. Rozenvasser Periodically non-stationary control sys-tems. Nauka, Мoscow, 1973.

[25]B.F. Bylov, R.E. Vinograd, D.M. Grobman, and V.V. Ne-mytsky. Theory of Lyapunov's indexes and its application to stability problems. Nauka, Мoscow, 1966.

[26]P.K. Rashevsky. Course of differential geometry. State publishing house of the scientific and technical literature, Moscow, 1950.

[27]A.M. Lyapunov. General problem about movement stability. State publishing house of the scientific and technical literature, Moscow, 1950.

[28]N.N. Karabutov. Structural identification of systems: anal-ysis of dynamic structures. MSIU, Moscow, 2008.

[29]M.B. Fedorchuk. Ordinary differential equations. Nauka, Мoscow, 1985.