The problem of an optimal control system describing a general boundary value problem for $2b$-elliptic levels is investigated. The cases of constrained internal and boundary control are considered. The quality criterion is given by the sum of the volume and surface integrals. Using the integral representation, with the help of the Green's function, solutions of the boundary value problem for $2b$-elliptic levels and the Taylor formula, the provided and sufficient conditions for ensuring the optimal solution of the system describing the general boundary value problem for elliptic levels are found.

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