Geodesic
The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and statistically invariant sets of control systems
Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 217-226.

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

We obtain conditions that allow one to evaluate the relative frequency of occurrence of the reachable set of a control system in a given set. If the relative frequency of occurrence in this set is $1$, then the set is said to be statistically invariant. It is assumed that the images of the right-hand side of the differential inclusion corresponding to the given control system are convex, closed, but not necessarily compact. We also study the basic properties of the space $\mathrm{clcv}(\mathbb R^n)$ of nonempty closed convex subsets of $\mathbb R^n$ with the Hausdorff–Bebutov metric. 
@article{TRSPY_2012_278_a19,
     author = {L. I. Rodina},
     title = {The space $\mathrm{clcv}(\mathbb R^n)$ with the {Hausdorff--Bebutov} metric and statistically invariant sets of control systems},
     journal = {Informatics and Automation},
     pages = {217--226},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a19/}
}
TY  - JOUR
AU  - L. I. Rodina
TI  - The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and statistically invariant sets of control systems
JO  - Informatics and Automation
PY  - 2012
SP  - 217
EP  - 226
VL  - 278
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a19/
LA  - ru
ID  - TRSPY_2012_278_a19
ER  - 
%0 Journal Article
%A L. I. Rodina
%T The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and statistically invariant sets of control systems
%J Informatics and Automation
%D 2012
%P 217-226
%V 278
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a19/
%G ru
%F TRSPY_2012_278_a19
L. I. Rodina. The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and statistically invariant sets of control systems. Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 217-226. http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a19/

[1] Rodina L.I., Tonkov E.L., “Statisticheskie kharakteristiki mnozhestva dostizhimosti upravlyaemoi sistemy, nebluzhdaemost i minimalnyi tsentr prityazheniya”, Nelineinaya dinamika, 5:2 (2009), 265–288

[2] Panasenko E.A., Rodina L.I., Tonkov E.L., “Asimptoticheski ustoichivye statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 5, 2010, 135–142 | MR

[3] Rodina L.I., Tonkov E.L., “Statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Vestn. Udm. un-ta. Matematika. Mekhanika. Kompyut. nauki, 2011, no. 1, 67–86

[4] Panasenko E.A., Tonkov E.L., “Invariantnye i ustoichivo invariantnye mnozhestva differentsialnykh vklyuchenii”, Tr. MIAN, 262, 2008, 202–221 | MR | Zbl

[5] Panasenko E.A., Tonkov E.L., “Rasprostranenie teorem E.A. Barbashina i N.N. Krasovskogo ob ustoichivosti na upravlyaemye dinamicheskie sistemy”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15, no. 3, 2009, 185–201

[6] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR

[7] Panasenko E.A., Rodina L.I., Tonkov E.L., “Prostranstvo $\mathrm {clcv}(\mathbb R^n)$ s metrikoi Khausdorfa–Bebutova i differentsialnye vklyucheniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 1, 2011, 162–177

[8] Nemytskii V.V., Stepanov V.V., Kachestvennaya teoriya differentsialnykh uravnenii, Gostekhteorizdat, M., 1949

[9] Filippov A.F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR

[10] Blagodatskikh V.I., Filippov A.F., “Differentsialnye vklyucheniya i optimalnoe upravlenie”, Tr. MIAN, 169, 1985, 194–252 | MR | Zbl

[11] Perov A.I., “Neskolko zamechanii otnositelno differentsialnykh neravenstv”, Izv. vuzov. Matematika, 1965, no. 4, 104–112 | MR | Zbl

[12] Chaplygin S.A., “Novyi metod priblizhennogo integrirovaniya differentsialnykh uravnenii”, Izbrannye trudy. Mekhanika zhidkosti i gaza. Matematika. Obschaya mekhanika, Nauka, M., 1976, 307–360 | MR

[13] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl