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For the singularly perturbed parabolic problem, a regularized asymptotics of the solution of the problem of optimal control was constructed. The solution asymptotics involves parabolic boundary-layer functions obeying a special function called the “complementary probability integral.
The problem of minimum-energy control in the integro-differential linear systems with Fredholm integral was solved using the N.N. Krasovskii method of the problem of moments. An explicit solution of the boundary problem for the integro-differential equation was established using the K.A. Kasymov method.