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Optimization of the Values of the Right-Hand Sides of Boundary Conditions with Point and Integral Terms for the ODE System

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

In the paper, we investigate the problem of optimal control for a linear system of ordinary differential equations with linear boundary conditions. The boundary conditions include, as terms, the values of the phase variable both at separate intermediate points and their integral values over individual intervals of the independent variable. The values of the right sides of unseparated boundary conditions are optimizing in the problem. In the paper the necessary conditions for the existence and uniqueness of the solution to the boundary value problem, the convexity of the target functional, the necessary optimality conditions for the optimized parameters are obtained. Conditions contain constructive formulas of the gradient components of the functional. The numerical solution of an illustrative problem is considered.

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Author information

Authors and Affiliations

  1. Institute of Control Systems of Azerbaijan National Academy of Sciences, Str. B. Vahabzade 9, Baku, AZ1141, Azerbaijan

    Kamil Aida-zade & Vagif Abdullayev

  2. Institute of Mathematics and Mechanics of Azerbaijan National Academy of Sciences, Str. B. Vahabzade 9, Baku, AZ1141, Azerbaijan

    Kamil Aida-zade

  3. Azerbaijan State Oil and Industry University, Azadlig ave. 20, Baku, AZ1010, Azerbaijan

    Vagif Abdullayev

Authors
  1. Kamil Aida-zade
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  2. Vagif Abdullayev
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Corresponding author

Correspondence to Kamil Aida-zade .

Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Aida-zade, K., Abdullayev, V. (2020). Optimization of the Values of the Right-Hand Sides of Boundary Conditions with Point and Integral Terms for the ODE System. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_1

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