экономическая модель,
вариационное исчисление,
оптимальное управление,
принцип инвариантности,
чувствительность динамических систем
Abstract
The problems of modeling processes and systems of the economy are considered, the optimal control problem is posed, the system of nonlinear differential equations representing the economy and the optimized target functional are determined; a variational method for solving the problem is chosen, the principle of invariance of nonlinear systems and the possibilities provided by them for modeling dynamic, including economic, systems are described. A critical analysis of the state in the field of economic modeling is given. The features and properties of the invariance principle of linear systems are considered in terms of the Laplace transform. Sensitivity functions of nonlinear systems and Gato and Frechet derivatives defining them are obtained. The application of sensitivity theory in problems of optimal control of nonlinear systems is shown by the example of a fairly simple problem.
