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Russia Izhevsk; Yekaterinburg
Section  Mathematics 
Title  About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls 
Author(s)  Rodina L.I.^{a}, Tonkov E.L.^{ab} 
Affiliations  Udmurt State University^{a}, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{b} 
Abstract  We investigate the conditions under which the control system $\dot x=f(t,x,u),$ $u\in U (t,x)$ together with closure of set of shifts (concerning time $t$) of control system possesses property of uniform local or uniform global attainability on the given time interval. We do not suppose that function $(t,x)\to U(t,x),$ setting geometrical restrictions on admissible controls $u(t,x)\in U(t,x),$ has convex compact images and we do not suppose that differential inclusion corresponding to control system has convex images. 
Keywords  statistically weakly invariant sets, controlled systems, attainability set, integral funnel, differential inclusion 
UDC  517.977.5 
MSC  35F15, 37G10 
DOI  10.20537/vm120406 
Received  7 September 2012 
Language  Russian 
Citation  Rodina L.I., Tonkov E.L. About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 4, pp. 6879. 
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