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The Optimal Control Problem with Fixed-End Trajectories for a Three-Sector Economic Model of a Cluster

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10751))

Abstract

For the mathematical model of a three-sector economic cluster, the problem of optimal control with fixed ends of trajectories is considered. An algorithm for solving the optimal control problem for a system with a quadratic functional is proposed. Control is defined on the basis of the principle of feedback. The problem is solved using the Lagrange multipliers of a special form, which makes it possible to find a synthesising control.

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References

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkre-lidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes. Interscience Publishers, New York (1962)

    Google Scholar 

  2. Pontryagin, L.S.: The maximum principle in optimal control, Moscow (2004). (in Russian)

    Google Scholar 

  3. Bellman, R., Kalaba, R.: Dynamic Programming and Modern Control Theory. Academic Press, New York (1965)

    MATH  Google Scholar 

  4. Krotov, V.F., Gurman, V.I.: Methods and Problems of Optimal Control. Nauka, Moscow (1973). (in Russian)

    Google Scholar 

  5. Kolemayev, V.A.: Economic-Mathematical Modeling. UNITY, Moscow (2005). (in Russian)

    Google Scholar 

  6. Dzhusupov, A.A., Kalimoldayev, M.N., Malishevsky, E.V., Murzabekov, Z.N.: Solution of a problem of stabilization of three-sector model of branch. Inf. Prob. 1, 20–27 (2011). (in Russian)

    Google Scholar 

  7. De, S.: Intangible capital and growth in the ‘new economy’: implications of a multi-sector endogenous growth model. Struct. Change Econ. Dynam. 28, 25–42 (2014)

    Article  Google Scholar 

  8. Dobrescu, L., Neamtu, M., Opris, D.: Deterministic and stochastic three-sector dynamic growth model with endogenous labour supply. Econ. Rec. 89(284), 99–111 (2013)

    Article  Google Scholar 

  9. Zhang, J.: The analytical solution of balanced growth of non-linear dynamic multi-sector economic model. Econ. Model. 28(1), 410–421 (2011)

    Article  Google Scholar 

  10. Zhou, S., Xue, M.: A model of optimal allocations of physical capital and human capital in three sectors. Wuhan Univ. J. Nat. Sci. 12(6), 997–1002 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sen, P.: Capital accumulation and convergence in a small open economy. Rev. Int. Econ. 21(4), 690–704 (2013)

    Article  Google Scholar 

  12. Aseev, S.M., Besov, K.O., Kryazhimskii, A.V.: Infinite-horizon optimal control problems in economics. Russ. Math. Surv. 67(2), 195–253 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Shnurkov, P.V., Zasypko, V.V.: Analytical study of the problem of optimal investment management in a closed dynamic model of a three-sector economy. Bull. MSTU 2, 101–115 (2014). (in Russian)

    Google Scholar 

  14. Aipanov, S., Murzabekov, Z.: Analytical solution of a linear quadratic optimal control problem with control value constraints. Comput. Syst. Sci. Int. 53(1), 84–91 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Murzabekov, Z.N., Milosz, M., Tussupova, K.B.: Solution of steady state search problem in three-sector economic model of a cluster. Actual Probl. Econ. 3(165), 443–452 (2015)

    Google Scholar 

  16. Klamka, J.: Constrained controllability of dynamics systems. Int. J. Appl. Math. Comput. Sci. 9(2), 231–244 (1999)

    MathSciNet  MATH  Google Scholar 

  17. Klamka, J.: Controllability of nonlinear discrete systems. Int. J. Appl. Math. Comput. Sci. 12(2), 173–180 (2002)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Kamshat Tussupova .

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Murzabekov, Z., Miłosz, M., Tussupova, K. (2018). The Optimal Control Problem with Fixed-End Trajectories for a Three-Sector Economic Model of a Cluster. In: Nguyen, N., Hoang, D., Hong, TP., Pham, H., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2018. Lecture Notes in Computer Science(), vol 10751. Springer, Cham. https://doi.org/10.1007/978-3-319-75417-8_36

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  • DOI: https://doi.org/10.1007/978-3-319-75417-8_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75416-1

  • Online ISBN: 978-3-319-75417-8

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