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Russia Izhevsk
Section Mathematics
Title The characteristics of attainability set connected with invariancy of control systems on the finite time interval
Author(-s) Rodina L.I.a, Hammady A.H.a
Affiliations Udmurt State Universitya
Abstract We study the statistical characteristics of the attainability set $A(t,\sigma,X)$ of the control system which is parametrized by means of a topological dynamical system $(\Sigma,h^t).$ We obtain the lower estimates for characteristics connected with invariance of given set on a finite time interval. We also consider the following problem arising in many applications. Let numbers $\lambda_0\in (0,1]$ and $\vartheta>0$ are given. It is necessary to find the conditions which the control system and set $X$ should satisfy providing that for given $\sigma\in\Sigma$ relative frequency of containing of the attainability set $A(t,\sigma, X)$ in the given set $M $ on any interval of time length $\vartheta$ would be not less than $\lambda_0.$ Let's notice, that the characteristic $\vartheta$ is assumed given depending on an applying problems. In particular, if control process is periodic, then $\vartheta$ is the period of the process. Results are illustrated by examples of the control systems which describe different models of population growth.
Keywords control systems, dynamical systems, differential inclusions, statistically invariant sets
UDC 517.935, 517.938
MSC 34A60, 37N35, 49J15, 93B03
DOI 10.20537/vm130105
Received 12 November 2012
Language Russian
Citation Rodina L.I., Hammady A.H. The characteristics of attainability set connected with invariancy of control systems on the finite time interval, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 35-48.
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