Abstract:
The problem of controlling the process of cleaning a reservoir from impurity using rivers flowing from it is considered. The controlled variable is the vector of impurity concentrations that enter each river from the reservoir. The spread of impurity in the river is described by the convection-diffusion equation. This equation includes a term that is determined by other sources of impurity entering the river. The exact value of this term is unknown, but the limits of its change are given. The goal of the choice of control is to lead the vector consisting of the average concentrations of impurities in rivers and the remaining amount of impurity mass in the reservoir to a given compact at a fixed moment in time. After replacing the variables, the formulated problem is reduced to the problem of controlling a system of ordinary differential equations in the presence of uncertainty. Using an approximate algorithm, a solvability set is constructed for this problem.
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