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We consider the general approach to studying differential models of hierarchical control systems. The model is considered over a finite time interval. Our approach is based on passing to the discrete counterpart of the model and, consequently, from functionals to objective functions in the criteria. We introduce the notion of Stakelberg equilibriums accounting for stable evolution requirements. The solution is then constructed with the method of Lagrange multipliers; in the general case, with imitational modeling. As an example, we consider a quality control system for river water and show the results.