IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p545-d745983.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/545/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/545/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Caputo,Michael R., 2005. "Foundations of Dynamic Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521842723, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    2. Pierre Bernhard & Marc Deschamps, 2017. "Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter," Working Papers 2017-10, CRESE.
    3. Alice Issanchou & Karine Daniel & Pierre Dupraz & Carole Ropars-Collet, 2018. "Soil resource and the profitability and sustainability of farms: A soil quality investment model," Working Papers SMART 18-01, INRAE UMR SMART.
    4. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    5. Caputo, Michael R. & Dragone, Davide, 2022. "Rational agents might be overweight, underweight, or the physiologically optimal weight," Economics Letters, Elsevier, vol. 210(C).
    6. Alagoz, B. Baykant & Kaygusuz, Asim & Akcin, Murat & Alagoz, Serkan, 2013. "A closed-loop energy price controlling method for real-time energy balancing in a smart grid energy market," Energy, Elsevier, vol. 59(C), pages 95-104.
    7. Angel Sanchis-Cano & Luis Guijarro & Massimo Condoluci, 2018. "Dynamic capacity provision for wireless sensors’ connectivity: A profit optimization approach," International Journal of Distributed Sensor Networks, , vol. 14(4), pages 15501477187, April.
    8. Thomas A. Weber, 2017. "Global Optimization on an Interval," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 684-705, February.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    10. Chen Ling & Michael Caputo, 2012. "The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 313-334, September.
    11. Jan Zabojnik, 2011. "Subjective Evaluations With Performance Feedback," Working Paper 1283, Economics Department, Queen's University.
    12. Caputo, Michael R., 2007. "The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 198-224, November.
    13. Thomas A. Weber, 2016. "A robust resolution of Newcomb’s paradox," Theory and Decision, Springer, vol. 81(3), pages 339-356, September.
    14. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    15. Thanh Tran & Kanghyun Yoon & Stefan Genchev, 2017. "Lump‐Sum versus Pay‐As‐You‐Go: The Moderating Effect of Contract Types on the Optimal Logistics Decisions," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 38(4), pages 547-555, June.
    16. Silvia Bertarelli & Chiara Lodi & Stefania Ragni, 2022. "An optimal strategy to control mining and recycling of non-renewable resources," Working Papers 2202, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2022.
    17. Bolin, Kristian & Lindgren, Björn, 2014. "Non-monotonic health behaviours - implications for individual health-related behaviour in a demand-for-health framework," Working Papers in Economics 588, University of Gothenburg, Department of Economics.
    18. Eli Fenichel & Timothy Richards & David Shanafelt, 2014. "The Control of Invasive Species on Private Property with Neighbor-to-Neighbor Spillovers," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(2), pages 231-255, October.
    19. Jean-Bernard Chatelain & Bruno Tinel & Karim Azizi & Nicolas Canry, 2012. "Are the No-Ponzi Game and the Transversality Conditions Relevant for Public Debt? A Keynesian Appraisal," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00686788, HAL.
    20. Cesar Tamayo, 2015. "Investor protection and optimal contracts under risk aversion and costly state verification," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 547-577, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:545-:d:745983. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.