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Русская версия

**G. V. SHEVCHENKO**

Russia, 630090, Novosibirsk,

Ave. of acad. Koptyug, 4,

S.L.Sobolev Institute of Mathematics, Siberian

Branch of the Russian Academy of Sciences,

We suggest an iterative method for solving a nonlinear problems of a resources consumption minimization. The suggested method is a generalization of the method for solving linear problems of a resources consumption minimization on a class of nonlinear systems with the right part divided by state and control, linear with respect control. The mathematical description of the controlled process specifies also the structure of controlling device. The device is chosen to belong to the class of wise constant controllers (widespread and easily realizable). Optimal control for nonlinear systems with linearly selected control appears to be piece constant, which essentially simplifies the computing. It is proved that the sequence of controls converges to the epsilon-optimal control in the finite number of iterations. The computing algorithm is given. Ref. 12 items.