Abstract
Previously, the authors proposed a formalization of renewable resources rational use problem based on the representation of controlled system as a discrete dynamical system. In the particular case of structured ecosystem described by Leslie’s binary model, despite its non-linearity, it turned out that all optimal controls preserving this system belong to the certain hyperplane. This paper explores the conditions under which the positive boundary of a feasible set of problem with so-called quasi-preserving controls also contain a part of some hyperplane. In the process, we used a generalization of classical concept of map irreducibility—the concept of local irreducibility. Statements about the influence of the irreducibility property of discrete dynamical system step operator on the properties of an feasible set positive boundary are proved.
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Smirnov, A.I., Mazurov, V.D. (2020). Feasible Set Properties of an Optimal Exploitation Problem for a Binary Nonlinear Ecosystem Model with Reducible Step Operator. In: Kochetov, Y., Bykadorov, I., Gruzdeva, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Communications in Computer and Information Science, vol 1275. Springer, Cham. https://doi.org/10.1007/978-3-030-58657-7_23
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