Nikolay Karabutov

Structural Methods of Estimation Lyapunov Exponents Linear Dynamic System

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Author(s)

1. Dept. of Problems Control, Moscow state engineering university of radio engineering, electronics and automation, Financial University under the government of the Russian Federation, Moscow, Russia

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2015.10.01

Received: 20 Feb. 2015 / Revised: 2 May 2015 / Accepted: 15 Jul. 2015 / Published: 8 Sep. 2015

Index Terms

Identification, Lyapunov exponent, struc-ture, secant, coefficient of structural properties system, dynamic system, structurally-frequency method

Abstract

The problem of structural identification linear dynamic systems on the basis of the analysis Lyapunov exponent in the conditions of uncertainty is considered. The method of estimation the general solution system on the basis of application static model is developed. Defini-tion of Lyapunov exponent (LE) on the analysis of a coefficient structural properties system is grounded. On the basis of a coefficient of structural properties the special structures reflecting change LE are introduced. The criterion of estimation an order system on the basis of the analysis behaviour these structures are offered. The decision-making method about type of roots dynamic system on the basis of the analysis of time series and the structures reflecting change LE is developed. Two approaches to an estimation of the largest LE and the Perron bottom indexes are offered. The first approach to identification of a change in a coefficient of structural properties with the help secant method for various classes of roots is grounded. The second approach is the structurally-frequency method grounded on definition of estimations LE by means of the analysis of local minima of structures offered in work. The frequency method which is a modification of a method a bar graph in the statistical theory is applied to a validation of the obtained estimations. Results of simulation confirm effectiveness of the offered methods, structures and procedures.

Cite This Paper

Nikolay Karabutov,"Structural Methods of Estimation Lyapunov Ex-ponents Linear Dynamic System", International Journal of Intelligent Systems and Applications(IJISA), vol.7, no.10, pp.1-11, 2015. DOI:10.5815/ijisa.2015.10.01

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International Journal of Intelligent Systems and Applications (IJISA)