Geodesic
The statistically weak invariant sets of control systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 67-86

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

We obtain the conditions that allow to estimate the relative frequency of occurrence of the attainable set of a control system in some given set. The set is called statistically invariant if the relative frequency of occurrence in this set is equal to one. We also derive the conditions of the statistically weak invariance of the given set with respect to controllable system, that is, for every initial point from this set, at least one solution of the control system is statistically invariant. We suggest that the images of the right hand part of the differential inclusions corresponding for the given control system are closed but may be not compact. The main results are formulated in the terms of Lyapunov functions, metric of Hausdorff–Bebutov and the dynamical system of shifts that attended in the right hand part of the differential inclusion.
Keywords: controllable systems, dynamical systems, differential inclusions, weakly invariant and statistically weakly invariant sets. 
@article{VUU_2011_1_a7,
     author = {L. I. Rodina and E. L. Tonkov},
     title = {The statistically weak invariant sets of control systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {67--86},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_1_a7/}
}
TY  - JOUR
AU  - L. I. Rodina
AU  - E. L. Tonkov
TI  - The statistically weak invariant sets of control systems
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 67
EP  - 86
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_1_a7/
LA  - ru
ID  - VUU_2011_1_a7
ER  - 
%0 Journal Article
%A L. I. Rodina
%A E. L. Tonkov
%T The statistically weak invariant sets of control systems
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 67-86
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2011_1_a7/
%G ru
%F VUU_2011_1_a7
L. I. Rodina; E. L. Tonkov. The statistically weak invariant sets of control systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 67-86. http://geodesic.mathdoc.fr/item/VUU_2011_1_a7/