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On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

Author

Listed:
  • Manuel De la Sen

    (Department of Electricity and Electronics, Faculty of Science and Technology, Institute of Research and Development of Processes, Campus of Leioa, University of the Basque Country, 48940 Leioa, Spain)

  • Asier Ibeas

    (Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona (UAB), 08193 Barcelona, Spain)

  • Santiago Alonso-Quesada

    (Department of Electricity and Electronics, Faculty of Science and Technology, Institute of Research and Development of Processes, Campus of Leioa, University of the Basque Country, 48940 Leioa, Spain)

Abstract

This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable.

Suggested Citation

  • Manuel De la Sen & Asier Ibeas & Santiago Alonso-Quesada, 2021. "On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources," Mathematics, MDPI, vol. 9(17), pages 1-35, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2175-:d:630076
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    References listed on IDEAS

    as
    1. M. De la Sen, 2007. "On the Properties of Reachability, Observability, Controllability, and Constructibility of Discrete-Time Positive Time-Invariant Linear Systems with Aperiodic Choice of the Sampling Instants," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-23, August.
    2. Kashin Sugishita & Yasuo Asakura, 2021. "Vulnerability studies in the fields of transportation and complex networks: a citation network analysis," Public Transport, Springer, vol. 13(1), pages 1-34, March.
    3. Louis De Mesnard, 2009. "Is The Ghosh Model Interesting?," Journal of Regional Science, Wiley Blackwell, vol. 49(2), pages 361-372, May.
    4. Dobos, Imre & Floriska, Adel, 2007. "The resource conservation effect of recycling in a dynamic Leontief model," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 334-340, July.
    5. Louis de Mesnard, 2016. "Price consistency in the Leontief model [La cohérence des prix dans le modèle de Leontief]," Post-Print halshs-01338092, HAL.
    6. M. De La Sen & S. Alonso-Quesada, 2008. "Model-Matching-Based Control of the Beverton-Holt Equation in Ecology," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-21, February.
    7. Imre Dobos & Adel Floriska, 2005. "A Dynamic Leontief Model with Non-renewable Resources," Economic Systems Research, Taylor & Francis Journals, vol. 17(3), pages 317-326.
    8. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-995, May.
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