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

Manuel De la Sen, Asier Ibeas and Santiago Alonso-Quesada
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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

Mathematics, 2021, vol. 9, issue 17, 1-35

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.

Keywords: Leontief economic model; Ghosh model; controllability; equilibrium points; singular systems; stability; positive systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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