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Controllability of a Nonholonomic Macroeconomic System

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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.

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References

  1. Udrişte, C.: Thermodynamics versus economics. UPB Sci. Bull, Series A 69(3), 89–91 (2007)

    Google Scholar 

  2. Udrişte, C., Ferrara, M., Zugrăvescu, D., Munteanu, F.: Geobiodynamics and Roegen type economy. Far East J. Math. Sci. (FJMS) 28(3), 681–693 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Udrişte, C.: Geometric Dynamics. Kluwer, Amsterdam (2000)

    Book  MATH  Google Scholar 

  4. Udrişte, C., Dogaru, O., Ţevy, I.: Extrema with Nonholonomic Constraints. Monographs and Textbooks, vol. 4. Geometry Balkan Press, Bucharest (2002)

    MATH  Google Scholar 

  5. Udrişte, C., Ferrara, M., Opriş, D.: Economic Geometric Dynamics. Monographs and Textbooks, vol. 6. Geometry Balkan Press, Bucharest (2004)

    MATH  Google Scholar 

  6. Udrişte, C., Ferrara, M.: Black hole models in economics. Tensor NS 70(1), 53–62 (2008)

    MATH  Google Scholar 

  7. Stamin, C., Udrişte, C.: Nonholonomic geometry of Gibbs contact structure. U.P.B. Sci. Bull., Series A 72(1), 153–170 (2010)

    MATH  Google Scholar 

  8. Liu, W., Sussmann, H.: Abnormal sub-Riemannian minimizers. IMA Preprint Series # 1059 (1992)

  9. Udrişte, C.: Multitime controllability, observability and bang–bang principle. J. Optim. Theory Appl. 139(1), 141–157 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Udrişte, C.: Simplified multitime maximum principle. Balkan J. Geom. Appl. 14(1), 102–119 (2009)

    MathSciNet  MATH  Google Scholar 

  11. Udrişte, C.: Nonholonomic approach of multitime maximum principle. Balkan J. Geom. Appl. 14(2), 111–126 (2009)

    Google Scholar 

  12. Udrişte, C., Ţevy, I.: Multitime linear-quadratic regulator problem based on curvilinear integral. Balkan J. Geom. Appl. 14(2), 127–137 (2009)

    Google Scholar 

  13. Udrişte, C., Ţevy, I.: Multitime dynamic programming for curvilinear integral actions. J. Optim. Theory Appl. 146(1), 189–207 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Udrişte, C.: Equivalence of multitime optimal control problems. Balkan J. Geom. Appl. 15(1), 155–162 (2010)

    MathSciNet  MATH  Google Scholar 

  15. Udrişte, C.: Multitime maximum principle for curvilinear integral cost. Balkan J. Geom. Appl. 16(1), 128–149 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Udrişte, C., Bejenaru, A.: Multitime optimal control with area integral costs on boundary. Balkan J. Geom. Appl. 16(2), 138–154 (2011)

    MathSciNet  MATH  Google Scholar 

  17. ShankarSastry, S., Montgomery, R.: The structure of optimal controls for steering problem. In: NOLCOS, Conf Proc., Bordeaux, France (1992)

    Google Scholar 

  18. Chernavski, D.S., Starkov, N.I., Shcherbakov, A.V.: On some problems of physical economics. Phys. Usp. 45(9), 977–997 (2002)

    Article  Google Scholar 

  19. Georgescu-Roegen, N.: The Entropy Law and Economic Process. Harvard University Press, Cambridge (1971)

    Google Scholar 

  20. Ruth, M.: Insights from thermodynamics for the analysis of economic processes. In: Kleidon, A., Lorenz, R. (eds.) Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond, pp. 243–254. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Smulders, S.: Entropy, environment and endogenous economic growth. Journal of International Tax and Public Finance 2, 317–338 (1995)

    Google Scholar 

  22. Sergeev, V.: The thermodynamical approach to market (translated from Russian and edited by Leites, D.). Max Planck Institute, Preprint no: 76, (2006); arXiv:0803.3432v1 [physics.soc-ph] 24 Mar (2008)

  23. Nardini, F.: Technical Progress and Economic Growth. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  24. Vrănceanu, G.: Lectures of Differential Geometry Vol. I (in Romanian). Didactical and Pedagogical Editorial House, Bucharest (1962). Vol. II, (1964)

    Google Scholar 

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Acknowledgements

The authors are grateful to the referees and the editors of JOTA for their comments and suggestions on the previous versions of the manuscript. Partial support is given by the University Politehnica of Bucharest, and by Academy of Romanian Scientists, Bucharest, Romania.

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Authors and Affiliations

  1. Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, Bucharest, 060042, Romania

    C. Udrişte

  2. Department SSGES, University Mediterranea of Reggio Calabria, Via dei Bianchi, 2-Palazzo Zani, 89100, Reggio Calabria, Italy

    M. Ferrara

  3. Institute of Geodynamics “Sabba S. Ştefanescu”, Dr. Gerota 19-21, Bucharest, 020032, Romania

    D. Zugrăvescu & F. Munteanu

Authors
  1. C. Udrişte
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  2. M. Ferrara
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  3. D. Zugrăvescu
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  4. F. Munteanu
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Corresponding author

Correspondence to C. Udrişte.

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Udrişte, C., Ferrara, M., Zugrăvescu, D. et al. Controllability of a Nonholonomic Macroeconomic System. J Optim Theory Appl 154, 1036–1054 (2012). https://doi.org/10.1007/s10957-012-0021-x

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  • DOI: https://doi.org/10.1007/s10957-012-0021-x

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