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Approximation of the Solution Set of Optimal Control Problems

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Large-Scale Scientific Computing (LSSC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3743))

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Abstract

We investigate approximation in W 1,2 topology of the solution set of a differential inclusion with Kamke Lipschitz right-hand side. The results are then applied to Bolza optimal control problem in form of differential inclusions. Namely it is shown that the optimal solution is the limit of optimal solution of appropriately defined finite dimensional nonlinear programming problems.

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References

  1. Clarke, F., Yu, L., Stern, R., Wolenski, P.: Nonsmooth Analysis and Control Theory. Springer, New York (1998)

    MATH  Google Scholar 

  2. Donchev, T.: Generic properties of differential inclusions and control problems. In: Li, Z., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2004. LNCS, vol. 3401, pp. 266–271. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Donchev, T., Farkhi, E.: Euler approximation of discontinuous one-sided Lipschitz convex differential inclusions. In: Ioffe, A., Reich, S., Shafrir, I. (eds.) Calculus of Variations and Differential Equations, pp. 101–118. Chapman & Hall/CRC Boca Raton, New York (1999)

    Google Scholar 

  4. Dontchev, A., Farkhi, E.: Error estimates for discretized differential inclusions. Computing 41, 349–358 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dontchev, A., Lempio, F.: Difference methods for differential inclusions: a survey. SIAM Rev 34, 263–294 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Grammel, G.: Towards fully discretized differential inclusions. Set Valued Analysis 11, 1–8 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ioffe, A.: Euler–Lagrange and Hamiltonian formalisms in dynamical optimization. Trans. Amer. Math. Soc. 349, 2871–2900 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lempio, F., Veliov, V.: Discrete approximations of differential inclusions. Bayreuter Mathematische Schiften, Heft 54, 149–232 (1998)

    MATH  MathSciNet  Google Scholar 

  9. Mordukhovich, B.: Discrete approximations and refined Euler-Lagrange conditions for differential inclusions. SIAM J. Control. Optim. 33, 882–915 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mordukhovich, B.: Approximation Methods in Problems of Optimization and Control. Nauka, Moskow (1988) (in Russian)

    Google Scholar 

  11. Pianigiani, G.: On the fundamental theory of multivalued differential equations. J. Differential Equations 25, 30–38 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pshenichniy, B.: Convex Analysis and Extremal Problems. Nauka, Moskow (1980) (in Russian)

    Google Scholar 

  13. Rurenko, E.: Approximate calculation of the attainability set for a differential inclusions. Vestn. Mosk. Univ. Ser, Vych. Math. Kibern. 15, 81–83 (1989)

    MathSciNet  Google Scholar 

  14. Tolstonogov, A.: Differential Inclusions in a Banach Space. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Architecture and Civil Engineering, 1 Hr. Smirnenski, 1046, Sofia, Bulgaria

    Tzanko Donchev

Authors
  1. Tzanko Donchev
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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Donchev, T. (2006). Approximation of the Solution Set of Optimal Control Problems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_23

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  • DOI: https://doi.org/10.1007/11666806_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31994-8

  • Online ISBN: 978-3-540-31995-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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