Geodesic
About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2012), pp. 68-79

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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. 
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     author = {L. I. Rodina and E. L. Tonkov},
     title = {About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {68--79},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_4_a5/}
}
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L. I. Rodina; E. L. Tonkov. About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2012), pp. 68-79. http://geodesic.mathdoc.fr/item/VUU_2012_4_a5/