Modeling a generalized ecological–economic input–output balance with delay

  • M. V. Boichuk
  • N. M. Shmurygina

A solution is obtained for a generalized static model of input–output balance with delay with allowance for pollution control, the optimal trajectory being specified by a piecewise-differentiable function over [t 0, T], and the optimal control being described by a piecewise-continuous function over [t 0, T]. A solution algorithm is developed and results of computational modeling are presented.


delay input–output balance trajectory control 


  1. 1.
    I. M. Lyashenko, “Some generalizations of the input-output Leontief model,” in: Proc. Intern. Conf. on Dynamical System Modeling and Stability Investigation (May 27–30, 2003), Kyiv (2003).Google Scholar
  2. 2.
    I. M. Bogaenko, M. V. Boichuk, and N. M. Shmurygina, “Optimization of a generalized model of input–output balance with allowance for pollution control with lags,” Avtomatizatsiya Vyrobnychikh Protsessiv, No. 2, 53–61 (2006).Google Scholar
  3. 3.
    E. A. Andreeva, V. B. Kolmanovskii, and L. E. Shaikhet, Control of Systems with Aftereffect [in Russian], Nauka, Moscow (1992).Google Scholar
  4. 4.
    V. I. Fodchuk, Ya. J. Bigun, I. I. Klevchuk, I. M. Cherevko, and I. V. Yakimov, Regularly and Singularly Perturbed Differential-Functional Equations [in Ukrainian], Inst. Math. NASU, Kyiv (1996).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Yu. Fed’kovych National UniversityChernivtsiUkraine
  2. 2.B Bukovinskii UniversityChernivtsiUkraine

Personalised recommendations