Simulating two-dimensional optimal control problem of fractional partial differential equations
In this work, a novel method for simulating the fractional two-dimensional linear-quadratic optimal control problem of fractional partial differential equations is introduced. Here, the fractional two-dimensional optimal control problems are transformed into a quadratic programing framework by which...
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| Vydané v: | Advances in Computational Science and Engineering Ročník 1; číslo 3; s. 271 - 297 |
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| Jazyk: | English |
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01.09.2023
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| ISSN: | 2837-1739, 2837-1739 |
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| Abstract | In this work, a novel method for simulating the fractional two-dimensional linear-quadratic optimal control problem of fractional partial differential equations is introduced. Here, the fractional two-dimensional optimal control problems are transformed into a quadratic programing framework by which we can use many quadratic programming solvers. There is no need to find the optimality conditions and no need to use any multiplier. The optimal control problem involves a two-dimensional performance index and the control of problem depends on both spatial and temporal variables. Some illustrative examples with complicated and challenging situations are investigated. |
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| AbstractList | In this work, a novel method for simulating the fractional two-dimensional linear-quadratic optimal control problem of fractional partial differential equations is introduced. Here, the fractional two-dimensional optimal control problems are transformed into a quadratic programing framework by which we can use many quadratic programming solvers. There is no need to find the optimality conditions and no need to use any multiplier. The optimal control problem involves a two-dimensional performance index and the control of problem depends on both spatial and temporal variables. Some illustrative examples with complicated and challenging situations are investigated. |
| Author | Malmir, Iman |
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| Cites_doi | 10.1080/00207179.2016.1178807 10.1515/jaa-2020-2011 10.1002/oca.2861 10.22034/cmde.2021.37458.1669 10.3934/math.20221061 10.4310/PAMQ.2022.v18.n3.a7 10.19139/soic-2310-5070-1228 10.1016/j.apm.2019.12.011 10.2298/TSCI180825254Y 10.3934/naco.2021007 10.1007/s00211-022-01290-3 10.1016/bs.hna.2020.10.003 10.1137/070679703 10.3934/naco.2020011 10.3390/math9212672 10.1177/1077546311408471 10.1109/TSMC.1981.4308749 10.1016/j.rico.2023.100251 10.1080/00207160.2017.1417591 10.1093/imamci/dnac031 |
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| Issue | 3 |
| Keywords | multi-order fractional two-dimensional optimal control fractional Robin condition numerical methods in engineering Two-dimensional fractional optimal control two-dimensional constrained optimal control of PDEs state or control constrained optimization of partial differential equations fractional partial differential equations quadratic programming |
| Language | English |
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