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Controllability of a Nonholonomic Macroeconomic System

Author

Listed:
  • C. Udrişte

    (University Politehnica of Bucharest)

  • M. Ferrara

    (University Mediterranea of Reggio Calabria)

  • D. Zugrăvescu

    (Institute of Geodynamics “Sabba S. Ştefanescu”)

  • F. Munteanu

    (Institute of Geodynamics “Sabba S. Ştefanescu”)

Abstract

This paper studies optimal control problems and sub-Riemannian geometry on a nonholonomic macroeconomic system. The main results show that a nonholonomic macroeconomic system is controllable either by trajectories of a single-time driftless control system (single-time bang–bang controls), or by nonholonomic geodesics or by sheets of a two-time driftless control system (two-time bang–bang controls). They are strongly connected to the possibility of describing a nonholonomic macroeconomic system via a Gibbs–Pfaff equation or by four associated vector fields, based on a contact structure of the state space and our isomorphism between thermodynamics and macroeconomics that praises three laws of a nonholonomic macroeconomic system.

Suggested Citation

  • C. Udrişte & M. Ferrara & D. Zugrăvescu & F. Munteanu, 2012. "Controllability of a Nonholonomic Macroeconomic System," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 1036-1054, September.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0021-x
    DOI: 10.1007/s10957-012-0021-x
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    References listed on IDEAS

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    1. C. Udrişte & I. Ţevy, 2010. "Multitime Dynamic Programming for Curvilinear Integral Actions," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 189-207, July.
    2. Sjak Smulders, 1995. "Entropy, environment, and endogenous economic growth," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 2(2), pages 319-340, August.
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    Cited by:

    1. Constantin Udriste & Massimiliano Ferrara & Ionel Tevy & Dorel Zugravescu & Florin Munteanu, 2018. "Phase Diagram for Roegenian Economics," Papers 1812.07959, arXiv.org.
    2. Constantin Udriste & Massimiliano Ferrara & Dorel Zugravescu & Florin Munteanu & Ionel Tevy, 2018. "Geobiodynamics and Roegenian Economic Systems," Papers 1812.07961, arXiv.org.
    3. Constantin Udriste & Vladimir Golubyatnikov & Ionel Tevy, 2018. "Economic Cycles of Carnot Type," Papers 1812.07960, arXiv.org.
    4. Dongya Li & Xiaoping Zhang & Shuang Wang & Fengxiang You, 2022. "Robust Synchronization of Fractional-Order Chaotic System Subject to Disturbances," Mathematics, MDPI, vol. 10(24), pages 1-15, December.

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