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Sufficient conditions for the control system local solvability

Annotation

A control system with mixed constraints, geometrical constraints for the control variable and set- valued dynamics is considered. The sufficient conditions for local solvability of the system are obtained.

Keywords

control system; set-valued mapping; covering mapping

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UDC

517.988.8, 517.929

Pages

45-53

References

1 Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskiy V.V. Vvedenie v teoriyu mnogoznachnykh otobrazheniy i differentsial'nykh vklyucheniy. M.: Fizmatlit, 2007. 2 Arutyunov A.V., Zhukovskiy S.E. Lokal'naya razreshimost' upravlyaemykh sistem so smeshannymi ogranicheniyami // Diff. uravneniya. 2010. T. 46. № 11. S. 1561-1570. 3. Arutyunov A.V., Zhukovskiy S.E. Existence of local solutions in constrained dynamic systems // Applicable Analysis. 2011. V. 90. Iss. 6. P. 889-898. 4 Arutyunov A.V. Nakryvayushchie otobrazheniya v metricheskikh prostranstvakh i nepodvizhnye tochki // Dokl. RAN. 2007. T. 416. № 2. S. 151-155. 5 Arutyunov A.V. Ustoychivost' tochek sovpadeniya i svoystva nakryvayushchikh otobrazheniy // Mat. zametki. 2009. T. 86. № 2. S. 163-169. 6 Arutyunov A.V., Gel'man B.D. O strukture mnozhestva tochek sovpadeniya // Mat. sbornik (prinyata k pechati, budet opublikovana v 2015 g.). 7 Arutyunov A.V., Avakov E.R., Zhukovskiy E.S. Nakryvayushchie otobrazheniya i ikh prilozheniya k differentsial'nym uravneniyam, ne razreshennym otnositel'no proizvodnoy // Diff. uravneniya. 2009. T. 45. № 5. S. 613-634. 8 Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. O korrektnosti differentsial'nykh uravneniy, ne razreshennykh otnositel'no proizvodnoy // Diff. uravneniya. 2011. T. 47. № 11. S. 1523-1537. 9 Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. Covering mappings and well-posedness of nonlinear Volterra equations // Nonlin. Anal.: TMA. 2012. V. 75. P. 1026-1044. 10 Arutyunov A., de Oliveira V.A., Pereira F.L., Zhukovskiy E., Zhukovskiy S. On the solvability of implicit differential inclusions // Appl. Anal. 2014. DOI: 10.1080/00036811.2014.891732.

Received

2014-11-10

Section of issue

Scientific articles

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