Skip to main content
SpringerLink
Log in

On the nonlinear dependence of the optimal boundary control on the initial and terminal conditions

  • Short Communications
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider the optimal boundary control of string vibrations and study the case of boundary force control at one end of the string, the other end being free. We show that if the initial and terminal data are arbitrary, then the dependence of the optimal boundary control on these data may be nonlinear. Conditions under which the dependence is linear are indicated. An example is considered in which the optimal control can be found in closed form.

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. Il’in, V.A. and Moiseev, E.I., Optimization of Boundary Controls of String Vibrations, Uspekhi Mat. Nauk, 2005, vol. 60, no. 6, pp. 89–114.

    MathSciNet  Google Scholar 

  2. Il’in, V.A. and Moiseev, E.I., Optimal Boundary Control by an Elastic Force at One End of a String with the Other End Free over an Arbitrary Sufficiently Large Time Interval, Differ. Uravn., 2007, vol. 43, no. 12, pp. 1655–1663.

    MathSciNet  Google Scholar 

  3. Moiseev, E.I., Optimal Boundary Control by a Displacement in W 1p of a String with a Free End, Differ. Uravn., 2008, vol. 44, no. 5, pp. 709–711.

    MathSciNet  Google Scholar 

  4. Moiseev, E.I. and Kholomeeva, A.A., Optimal Boundary Control by a Force at One End of a String with a Given Force Mode at the Other End, Differ. Uravn., 2011, vol. 47, no. 10, pp. 1492–1497.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    E. I. Moiseev

Authors
  1. E. I. Moiseev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © E.I. Moiseev, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 11, pp. 1653–1657.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moiseev, E.I. On the nonlinear dependence of the optimal boundary control on the initial and terminal conditions. Diff Equat 47, 1675–1679 (2011). https://doi.org/10.1134/S0012266111110140

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266111110140

Keywords

Search

Navigation