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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.27 No.3
- 발행연도
- 2017.1
- 수록면
- 361 - 372 (12page)
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This article presents a numerical solution to the optimal control problem governed by linear parabolic differential equation (PDE), generally solved by direct numerical method. It consists in choosing the controls in a finite dimension space (piecewise constants) by the discretization of the time interval. The optimal control problem is approached by an optimisation problem under constraints. To solve this problem, two combined mathematical methods are used : the Adomian decomposition method and the Alienor method. Firstly, the Adomian method is used to solve the PDE by explicitly expressing the solution as convergence series; depending on controls and requires no discretization in space and in time, contrary to numerical methods. Secondly, the Alienor method reduces the problem of minimization of a function with several variables to a function with one variable, unlike the iterative optimisation methods which require initialization of the initial vector. An application of this Adomian /Alienor combined model to solve the PDE is performed, and results are compared with those obtained by Adomian/Levenberg-Marquardt method.
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참고문헌 (16)
참고문헌 신청
Lions, J.L. / 1968 / Controle optimal des systemes gouvernes par des equations aux derivees partielles
Joshi, H, R. / 2005 / Optimal control of the convective velocity coefficient in parabolic problem / Non linear Analysis 63:1383~1390
Mampassi, B. / 2005 / New challenges for computing optimal control of distributed parameter systems / Kybernetes 34(7/8)
Trelat,E. / 2005 / Controle optimal : theorie et applications
Cherruault, Y. / 1998 / Modeles et methodes mathematiques pour les sciences du vivant / Presses Universitaires de France (P.U.F)
Joshi, H, R. / 2005 / Optimal control of the convective velocity coefficient in parabolic problem / Non linear Analysis 63:1383~1390
Mampassi, B. / 2005 / New challenges for computing optimal control of distributed parameter systems / Kybernetes 34(7/8)
Trelat,E. / 2005 / Controle optimal : theorie et applications
Cherruault, Y. / 1998 / Modeles et methodes mathematiques pour les sciences du vivant / Presses Universitaires de France (P.U.F)
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