ON NONLINEAR OPTIMIZATION OF OSCILLATORY PROCESSES UNDER CONTROL CONSTRAINTS

Authors

Saltanat Bayzbekovna Doulbekova Kyrgyz-Russian Slavic University named after the first President of the Russian Federation B.N. Yeltsin
Akylbek Kerimbekov Kyrgyz-Russian Slavic University named after the first President of the Russian Federation B.N. Yeltsin

Keywords:

boundary value problem, generalized solution, energy integral, functional, boundary control, optimal control.

Abstract

The article investigates the solvability of the problem of nonlinear optimization of oscillatory processes described by integro-differential equations in partial derivatives with the integral Fredholm operator. The studies are carried out when the function of external forces is nonlinear and depends on the control functions and on which restrictions are imposed. The integral functional of a general form is chosen as an assessment of the quality of control. It is established that the desired optimal control should be sought among the solutions of an infinite system of nonlinear Fredholm equations of the first kind, the solvability of which is studied by operator methods. It is proved that the operator equation has infinitely many solutions. Sufficient conditions for the existence of a solution to the nonlinear optimization problem are found.

References

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