Splitting of two-point boundary problem appearing in the theory of optimal control
In a Hilbert space a two-point boundary-value problem is considered that arises during the minimization of a linear quadratic functional on the trajectories of a linear equation with the operator A + εB invertible for sufficiently small ε >0 for the derivative, where A is a Fredholm opera...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7969 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | In a Hilbert space a two-point boundary-value problem is considered that arises during the minimization of a linear quadratic functional on the trajectories of a linear equation with the operator A + εB invertible for sufficiently small ε >0 for the derivative, where A is a Fredholm operator and all B-Jordan chains of the operator A have the same length. It is proved that we can asymptotically split the problem under consideration into a regularly perturbed boundary-value problem and two singularity perturbed Cauchy problems. |
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