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Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications

Author

Listed:
  • Liviu Popescu

    (Department of Statistics and Economic Informatics, University of Craiova, 200585 Craiova, Romania)

  • Daniel Militaru

    (Independent Researcher, 200585 Craiova, Romania)

  • Gabriel Tică

    (Department of Statistics and Economic Informatics, University of Craiova, 200585 Craiova, Romania)

Abstract

In the present paper, two optimal control problems are studied using Lie geometric methods and applying the Pontryagin Maximum Principle at the level of a new working space, called Lie algebroid. It is proved that the framework of a Lie algebroid is more suitable than the cotangent bundle in order to find the optimal solutions of some driftless control affine systems with holonomic distributions. Finally, an economic application is given.

Suggested Citation

  • Liviu Popescu & Daniel Militaru & Gabriel Tică, 2022. "Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:545-:d:745983
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    References listed on IDEAS

    as
    1. Caputo,Michael R., 2005. "Foundations of Dynamic Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521842723, October.
    2. Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, April.
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    Cited by:

    1. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.

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