Skip to main content
SpringerLink
Log in

The p-order maximum principle for an irregular optimal control problem

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The general optimal control problem subject to irregular constraints is considered for which the factor of the objective functional in Pontryagin’s function may vanish. It turns out that, in the case of p-regular constraints, this drawback can be overcome and a constructive version of the p-order maximum principle can be formulated.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yu. G. Evtushenko, Optimization and Fast Automatic Differentiation (Vychisl. Tsentr, Ross. Akad. Nauk, Moscow, 2013) [in Russian].

    Google Scholar 

  2. V. M. Alekseev, V.M. Tikhomirov, and S. V. Fomin, Optimal Control (Nauka, Moscow, 1979) [in Russian].

    MATH  Google Scholar 

  3. U. Ledzewicz and H. Schättler, “High-order approximations and generalized necessary conditions for optimality,” SIAM J. Control Optim. 37, 33–53 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. A. Tret’yakov, “Necessary and sufficient optimality conditions of order p,” Zh. Vychisl. Mat. Mat. Fiz. 24, 203–209 (1984).

    MathSciNet  MATH  Google Scholar 

  5. A. A. Tret’yakov, “The implicit function theorem in singular problems,” Usp. Mat. Nauk 42 (5), 215–216 (1987).

    Google Scholar 

  6. A. Prusinska and A. Tret’yakov, “Necessary p-th order optimality conditions for irregular Lagrange problem in calculus of variations,” Math. Commun. 19, 561–572 (2014).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Siedlce University, Faculty of Science, Siedlce, 08-110, Poland

    A. Prusinska

  2. System Research Institute, Polish Acad. Scie, Warsaw, 01-447, Poland

    A. A. Tret’yakov

  3. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”, Russian Academy of Sciences, Moscow, 119333, Russia

    A. A. Tret’yakov

Authors
  1. A. Prusinska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Tret’yakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Tret’yakov.

Additional information

Original Russian Text © A. Prusinska, A.A. Tret’yakov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 9, pp. 1471–1476.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prusinska, A., Tret’yakov, A.A. The p-order maximum principle for an irregular optimal control problem. Comput. Math. and Math. Phys. 57, 1453–1458 (2017). https://doi.org/10.1134/S0965542517090111

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542517090111

Keywords

Search

Navigation