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Erschienen in:
2015 | OriginalPaper | Buchkapitel
On the Solvability of a Nonlinear Optimal Control Problem for the Thermal Processes Described by Fredholm Integro-Differential Equations
verfasst von : Akylbek Kerimbekov
Erschienen in: Current Trends in Analysis and Its Applications
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Abstract
The problem of nonlinear optimal control of the thermal process described by Fredholm integro-differential equation was investigated. The concept of a weak generalized solution of the boundary problem was introduced and the algorithm for its construction was indicated. It was established that the optimal control is defined as a solution of a nonlinear integral equation satisfying the additional condition in the form of inequality. Sufficient conditions for unique solvability of nonlinear optimization were found and the algorithm for constructing approximate solutions was developed. The convergence of approximate solutions with respect to control, optimal process and functional was investigated.