On solvability of the tracking problem in nonlinear vector optimization of oscillation processes

The tracking problem is investigated in the nonlinear vector optimization of oscillation processes described by integro-differential partial differential equations when the scalar function of external and boundary influence depends nonlinearly on several controls. It is established that this problem has some specific features; in particular, the components of the distributed and boundary vector controls satisfy a system of equal relations and are defined as a solution to a system of two nonlinear integral equations. A method for solving this system is developed. Sufficient conditions are found for the unique solvability of the tracking problem, and an algorithm is developed for constructing a complete solution to the nonlinear optimization problem.