In the class of linear optimal control problems, a new approach to finding a solution to the boundary value problem of the maximum principle is proposed. The approach is based on the maximum principle expressed as fixed point problems, which makes it possible to construct new methods for finding extremal controls and determine solutions to the boundary value problem of the maximum principle. The efficiency of fixed point methods is illustrated by a model example.
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Buldaev, A., Kazmin, I. Fixed Point Methods for Solving Boundary Value Problem of the Maximum Principle. J Math Sci 279, 763–775 (2024). https://doi.org/10.1007/s10958-024-07058-4
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DOI: https://doi.org/10.1007/s10958-024-07058-4