Analytical Study of Optimal Investments Control Problem of in Closed-Form Dynamic Model of Three-Sector Economics

The research of a math problem of the optimum control, formulated based on closed form dynamic model of three-sector economy is continued. State of the system is described by set of specific capital functions in each sector; control parameter is a value characterizing the amount of specific investments of fund-generating sector, which is the key factor in economic system. Solution of assigned problem of optimal control is based on usage of Pontryagin’s maximum principle. For the main types of control functions, satisfying maximum condition, obvious analytical representations for the solution of simultaneous equations of differential constraint concerning functions of conditions are received. They are also valid for the simultaneous interfaced equations. Taking into account analytical results the definition procedure of optimum control was developed. The procedure can be realized by numerical techniques.

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