The work uses the method of standard characteristic polynomials, based on the Lyapunov theorem on adaptive control systems, the theory of flexible and robust control, methods of the theory of nonlinear systems. When modeling an internal combustion engine, methods of identification theory were additionally involved. When obtaining theoretical results, the method of Lyapunov functions, the method of standard characteristic polynomials, methods of the theory of adaptive and robust control, methods of the theory of nonlinear systems were used. When constructing a model of an internal combustion engine, methods of identification theory were additionally involved. For the synthesis of control systems in conditions of uncertainty, one of the topical directions is adaptive systems. These are control systems that compensate for parametric, signal, functional, or structural uncertainties of the control object by automatically adjusting the controller during the system's working operation, i.e., adaptive systems make up for the lack of a priori information about the control object during operational operation. To solve the problem of managing undefined objects, for example, classical methods are used. In such methods, when state variables are immeasurable, it becomes necessary to use additional dynamic filters. Classical methods are more often used for a limited class of objects. In the case of class extension, the structure of the control algorithm becomes more complicated.

In article the method, allowing to use possibility of a neural(neuronic) network for forecasting of tax base of region is offered. The given method is suitable for working out of the positive shortterm forecast.