Skip to main content
SpringerLink
Log in

Optimality conditions for extremal controls in bilinear and quadratic problems

  • Brief communications
  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We consider the optimization problem for a bilinear functional with respect to a linear phase system with a modularly constrained control. On the base of exact formulas for the functional increment we establish sufficient optimality conditions for extremal controls. These conditions are stated as inequalities for one-dimensional functions on a time interval. They supplement the maximum principle, keeping the implementation complexity at the same level. The optimization problem for a quadratic functional is reduced to the bilinear case with the help of the matrix conjugate function.

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

References

  1. Srochko, V. A. Iterative Methods for Solving Optimal Control Problems (Fizmatlit, Moscow, 2000) [in Russian].

    Google Scholar 

  2. Arguchintsev, A.V., Dykhta, V. A., and Srochko, V. A. “Optimal Control: NonlocalConditions, Computational Methods, and the Variational Principle of Maximum”, Russian Mathematics (Iz. VUZ) 53, No. 1, 1–36 (2009).

    MathSciNet  MATH  Google Scholar 

  3. Strekalovskii, A. S. Elements of Nonconvex Optimization (Nauka, Novosibirsk, 2003) [in Russian].

    MATH  Google Scholar 

  4. Antipina, N. V. and Dykhta, V. A. Linear Lyapunov–Krotov Functions and Sufficient Conditions of Optimality in the Form of the Maximum Principle”, RussianMathematics (Iz. VUZ) 46, No. 12, 9–20 (2002).

    MathSciNet  MATH  Google Scholar 

  5. Srochko, V. A. and Antonik, V. G. “Sufficient Optimality Conditions for Extremal Controls Based on Functional Increment Formulas”, RussianMathematics (Iz. VUZ) 58, No. 8, 78–83 (2014).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Irkutsk State University, ul. K. Marksa 1, Irkutsk, 664003, Russia

    V. A. Srochko & V. G. Antonik

Authors
  1. V. A. Srochko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. G. Antonik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. A. Srochko or V. G. Antonik.

Additional information

Original Russian Text © V.A. Srochko, V.G. Antonik, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 5, pp. 86–92.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Srochko, V.A., Antonik, V.G. Optimality conditions for extremal controls in bilinear and quadratic problems. Russ Math. 60, 75–80 (2016). https://doi.org/10.3103/S1066369X1605008X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X1605008X

Keywords

Search

Navigation