Abstract
This work is devoted to solving the time optimal control problem of a mathematical model describing the process of biological waste water treatment and is given as a three-dimensional nonlinear control system of differential equations. For analysis of this problem, the Pontryagin maximum principle is used and the corresponding two-point boundary value problem is formulated. In order to investigate the uniqueness of a solution to this problem, the properties of the corresponding attainable set and the multivalued mapping associated with it are studied. The basis of analysis of this set is its parametric description by moments of switching of piecewise constant controls. A scheme for the approximate solution of the time optimal control problem for the original system is proposed, and results of numerical calculations are presented.
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