Construction of nonlinear regulators in economic growth models

  • A. A. Krasovskii
  • A. M. Taras’ev


An infinite-horizon optimal control problem is considered which arises in an economic growthmodel with exhaustible energy resources. The Hamiltonian system in the Pontryagin maximum principle is analyzed and nonlinear regulators are constructed for the dynamical system under consideration. The presented results of synthetic economic growth trajectories generated by nonlinear regulators of the system are based on real-life data.


nonlinear control systems optimal stabilization economic modeling 


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  1. 1.
    M. Intriligator, Mathematical Optimization and Economic Theory (Prentice-Hall, Englewood Cliffs, NJ, 1971; Airis-Press, Moscow, 2002).Google Scholar
  2. 2.
    K. J. Arrow, Collected Papers, Vol. 5: Production and Capital (Harvard Univ. Press, Cambridge, MA, 1985).Google Scholar
  3. 3.
    L. V. Kantorovich and V. L. Makarov, in Long-Term Planning and Forecasting, Proc. Conf. (Macmillan, London, 1976).Google Scholar
  4. 4.
    K. Shell, in Mathematical Systems Theory and Economics (Springer-Verlag, New York, 1969), Vol. 1, pp. 241–292.Google Scholar
  5. 5.
    R. M. Solow, Growth Theory: An Exposition (Clarendon, Oxford, 1970).Google Scholar
  6. 6.
    R. U. Ayres and K. Martinás, On the Reappraisal of Microeconomics: Economic Growth and Change in a Material World (Edward Elgar, Cheltenham, 2005).Google Scholar
  7. 7.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1961; Pergamon, Oxford, 1964).Google Scholar
  8. 8.
    S. M. Aseev and A. V. Kryazhimskii, Tr. Mat. Inst. Steklova 257, 5 (2007).MathSciNetGoogle Scholar
  9. 9.
    E. J. Balder, J. Math. Anal. Appl. 95, 195 (1983).zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    A. A. Krasovskii and A. M. Taras’ev, Tr. Mat. Inst. Steklova 262, 127 (2007).MathSciNetGoogle Scholar
  11. 11.
    A. M. Tarasyev and C. Watanabe, Nonlinear Analysis 47(4), 2309 (2001).zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    N. N. Krasovskii, Some Problems in the Theory of Motion Stability (Fizmatgiz, Moscow, 1959) [in Russian].Google Scholar
  13. 13.
    A. M. Letov, Avtomat. i Telemekh. 22(4), 425 (1961).MathSciNetGoogle Scholar
  14. 14.
    I. G. Malkin, Theory of Motion Stability (Nauka, Moscow, 1966) [in Russian].zbMATHGoogle Scholar
  15. 15.
    N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].zbMATHGoogle Scholar

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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsUral Division of the Russian Academy of SciencesYekaterinburgRussia

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