Solved was a number of the classical variational problems of control of the distributed-parameter dynamic systems constrained also by nondifferential and differential equations. The corresponding rules of the Lagrange multipliers were formulated and proved. For the generalized diffusion and generalized wave processes, the results obtained were applied to the conditional variational problems of distributed optimal control. Derivation of the Euler-Poisson and Euler equations as applied to the designed control system was substantiated for these problems.
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