Solving the controllability problem for a nonlinear three-dimensional system

The controllability problem is solved for a nonlinear system of three differential equations that simulates aerated biological wastewater treatment using the thermal metabolism of thermophilic aerobic bacteria. Properties of the phase variables of such a system, bounded and continuable to a given segment, are established. The corresponding attainability set is parameterized by the switching instants of piecewise-constant controls. Parameterization helps reduce the controllability problem for the relevant system to finite dimensional conditional minimization of the auxiliary function. The results from numerical calculations for the solution to the initial problem are given.