Abstract.
In this paper, a nonlinear dynamical controlled system of differential equations describing the process of production and sales of a perishable consumer good is studied. The price of the good is the control parameter. Attainable sets of the system are investigated. It is proved that only bang-bang controls with at most one switching can lead trajectories to the boundary of an attainable set. Thus, this boundary is formed by the union of two one-parameter curves; the parameter is the moment of switching. Attainable sets for different parameters of the model are constructed with the use of a computer program written in MAPLE. Possible economic applications are discussed.
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This work was partially supported by the Russian Foundation for Basic Research (project No. 01-03-00737) and the RFBR Support Grant for Leading Scientific Schools (project No. SS-1846.2003.1).
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Grigorieva, E., Khailov, E. Attainable Set of a Nonlinear Controlled Microeconomic Model. J Dyn Control Syst 11, 157–176 (2005). https://doi.org/10.1007/s10883-005-4168-8
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DOI: https://doi.org/10.1007/s10883-005-4168-8