Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions
We consider the problem of optimal control in which the state of the controlled system is described by impulsive differential equations under nonlocal boundary conditions, which is a natural generalization of the Cauchy problem. Using the principle of contracting mappings, we prove the existence and...
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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2621 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider the problem of optimal control in which the state of the controlled system is described by impulsive differential
equations under nonlocal boundary conditions, which is a natural generalization of the Cauchy problem. Using the principle
of contracting mappings, we prove the existence and uniqueness of a solution of a nonlocal boundary-value problem with
pulse action with fixed admissible controls. Under certain conditions for the initial data of the problem, we calculate the
gradient of a functional and obtain necessary optimality conditions. |
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