Skip to main content
SpringerLink
Log in

Invariance Property in Approaching Problem on a Finite Time Interval

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8353))

Included in the following conference series:

  • 1279 Accesses

Abstract

The problem of approaching a target set in the phase state space by controlled system at the fixed time moment is under consideration. Algorithm for solving this problem is described in the paper. This method is based on weak invariance property of problem solvability sets.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Krasovskii, N.N.: Control of Dynamical System, 520 p. Nauka, Moscow (1985)

    Google Scholar 

  2. Krasovskii, N.N.: The basic game problem of approach. Target absorption. Extremal strategy. Lectures on control theory. 4 Uralstate university, 96 p. Sverdlovsk (1970)

    Google Scholar 

  3. Krasovskii, N.N., Subbotin, A.I.: Positional Differential Games, 456 p. Nauka, Moscow (1974)

    Google Scholar 

  4. Pontryagin, L.S.: On linear differential games. I. Dokl. Acad. Nauk USSR 156(4), 738–741 (1964)

    Google Scholar 

  5. Ushakov, V.N., Matviychuk, A.R., Ushakov, A.V., Parshikov, G.V.: Invariance of sets in approach problem solution construction. Proc. IMM Ur. Br. RAS 19(1), 134–145 (2013)

    Google Scholar 

  6. Guseinov, KhG, Moiseev, A.N., Ushakov, V.N.: On control systems attainability sets approximation. Prikl. Math. Mech. 62(2), 179–187 (1998)

    MathSciNet  Google Scholar 

  7. Ushakov, V.N., Matviychuk, A.R., Ushakov, A.V.: Approximation of attainability sets and integral funnels. Vestn. Udm. Univ. (Math., Mech., Comp. Sci.) 4, 23–39 (2011)

    Google Scholar 

  8. Nikolskii, M.S.: On differential inclusion attainability set approximation. Vestn. Mos. Univ. (Ser. 15. Vychisl. Mat. Kibernet) 4, 31–34 (1987)

    Google Scholar 

  9. Kurzhanski, A.B., Valyi, I.: Ellipsoidal Calculus for Estimation and Control. Birkhauser, Boston (1997)

    Book  MATH  Google Scholar 

  10. Cardaliaguet, P., Quincampoix, M., Saint-Pierre, P.: Numerical schemes for discontinuous value functions of optimal control. Set-valued Anal. 8(1–2), 111–126 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Falcone, M., Saint-Pierre, P.: Algorithms for constrained optimal control problem: a link between viability and dynamic programming. University of Rome (1995) (Preprint)

    Google Scholar 

  12. Chernousko, F.L.: Dynamical System Phase State Estimation: Method of Ellipsoids. Nauka, Moscow (1988)

    Google Scholar 

  13. Gusev, M.I.: Estimation of attainability sets of multidimensional control systems with nonlinear crossing connections. Proc. IMM Ur. Br. RAS 15(4), 82–94 (2009)

    Google Scholar 

  14. Filippova, T.F.: Differential equations for ellipsoidal estimates of attainability sets of nonlinear dynamical controlled system. Proc. IMM Ur. Br. RAS 16(1), 223–232 (2010)

    Google Scholar 

  15. Lempio, F., Veliov, M.V.: Discrete approximations of differential inclusions. Bayereuther Math. Schr. 54, 149–232 (1998)

    MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The research was supported by RFBR grants 11-01-00427 and 12-01-00290, grant of the President of the Russian Federation for support of leading scientific schools SS-5927.2012.1 and project 12-P-1-1002 “Control under uncertainty. Positional strategies and Hamiltonian structures in control problems”.

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Russian Academy of Sciences, 16 S. Kovalevskaya str., Ekaterinburg, 620990, Russia

    Vladimir Ushakov, Alexander Matviychuk & Sergey Brykalov

  2. Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia

    Alexander Matviychuk

Authors
  1. Vladimir Ushakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Matviychuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergey Brykalov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Ushakov .

Editor information

Editors and Affiliations

  1. Inst. of Info. & Comm. Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

  3. Dept. of Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ushakov, V., Matviychuk, A., Brykalov, S. (2014). Invariance Property in Approaching Problem on a Finite Time Interval. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43880-0_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43879-4

  • Online ISBN: 978-3-662-43880-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation