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Section
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Mathematics
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Title
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About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls
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Author(-s)
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Rodina L.I.a,
Tonkov E.L.ab
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Affiliations
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Udmurt State Universitya,
Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesb
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Abstract
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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.
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Keywords
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statistically weakly invariant sets, controlled systems, attainability set, integral funnel, differential inclusion
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UDC
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517.977.5
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MSC
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35F15, 37G10
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DOI
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10.20537/vm120406
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Received
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7 September 2012
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Language
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Russian
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Citation
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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. 68-79.
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References
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