Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866914950226640896 |
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| author | Khlopin, Dmitry V. |
| author_facet | Khlopin, Dmitry V. |
| contents | We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the the weakly overtaking criterion and the overtaking criterion, necessary boundary conditions on co-state arcs are deduced, these conditions need no assumptions about the asymptotic behavior of the motion, co-state arc, cost functional, and its derivatives. In the absence of an asymptotic terminal constraint, these boundary conditions with the Pontryagin Maximum Principle allow raising the co-state arcs, corresponding to some asymptotic subdifferentials of the cost functional (fixing the optimal control) at infinity. If this set is a singleton, these conditions coincide with the co-state arc representation proposed by Aseev and Kryazhimskii. These results are illustrated by several examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1910_12092 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions Khlopin, Dmitry V. Optimization and Control 49K15, 49J53, 93C15, 91B62 We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the the weakly overtaking criterion and the overtaking criterion, necessary boundary conditions on co-state arcs are deduced, these conditions need no assumptions about the asymptotic behavior of the motion, co-state arc, cost functional, and its derivatives. In the absence of an asymptotic terminal constraint, these boundary conditions with the Pontryagin Maximum Principle allow raising the co-state arcs, corresponding to some asymptotic subdifferentials of the cost functional (fixing the optimal control) at infinity. If this set is a singleton, these conditions coincide with the co-state arc representation proposed by Aseev and Kryazhimskii. These results are illustrated by several examples. |
| title | Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions |
| topic | Optimization and Control 49K15, 49J53, 93C15, 91B62 |
| url | https://arxiv.org/abs/1910.12092 |