American Institute of Mathematical Sciences

Advanced
November  2008, 2(4): 411-426. doi: 10.3934/ipi.2008.2.411

Missing boundary data reconstruction via an approximate optimal control

Rajae Aboulaϊch 1, , Amel Ben Abda 2, and  Moez Kallel 3,

1. 

Ecole Mohammadia d’Ingénieurs, LERMA, Avenue Ibn Sina, BP 765, Agdal-Rabat, Morocco
2. 

Ecole Nationale d’Ingénieurs de Tunis, LAMSIN, BP 37, 1002 Tunis Belvédère, Tunisia
3. 

Institut Préparatoire aux Etudes d’Ingénieur de Tunis & ENIT-LAMSIN, BP 37, 1002 Tunis Belvédère, Tunisia

Received  December 2007 Revised  July 2008 Published  November 2008

An approximate optimal control formulation of the Cauchy problem for elliptic equations is considered. A cost functional adding a fading through the iterations regularizing term borrowed from the domain decomposition communauty is proposed. Convergence of the descretized finite elements solution to the continuous one is proved. Numerical experiments involving smooth, non-smooth geometries as well as anisotropy highlight the capability of the present missing boundary data recovering process.
Keywords: Cauchy problem, regularization, optimal control, inverse problem.
Mathematics Subject Classification: Primary: 35J20, 49J20; Secondary: 74S05.
Citation: Rajae Aboulaϊch, Amel Ben Abda, Moez Kallel. Missing boundary data reconstruction via an approximate optimal control. Inverse Problems & Imaging, 2008, 2 (4) : 411-426. doi: 10.3934/ipi.2008.2.411
[1]

Lili Chang, Wei Gong, Guiquan Sun, Ningning Yan. PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem. Inverse Problems & Imaging, 2015, 9 (3) : 791-814. doi: 10.3934/ipi.2015.9.791
[2]

Luca Rondi. On the regularization of the inverse conductivity problem with discontinuous conductivities. Inverse Problems & Imaging, 2008, 2 (3) : 397-409. doi: 10.3934/ipi.2008.2.397
[3]

Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial & Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967
[4]

Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469
[5]

Abderrahmane Habbal, Moez Kallel, Marwa Ouni. Nash strategies for the inverse inclusion Cauchy-Stokes problem. Inverse Problems & Imaging, 2019, 13 (4) : 827-862. doi: 10.3934/ipi.2019038
[6]

Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. An optimal control problem in HIV treatment. Conference Publications, 2013, 2013 (special) : 311-322. doi: 10.3934/proc.2013.2013.311
[7]

Andrea Bacchiocchi, Germana Giombini. An optimal control problem of monetary policy. Discrete & Continuous Dynamical Systems - B, 2021, 26 (11) : 5769-5786. doi: 10.3934/dcdsb.2021224
[8]

Shuli Chen, Zewen Wang, Guolin Chen. Cauchy problem of non-homogenous stochastic heat equation and application to inverse random source problem. Inverse Problems & Imaging, 2021, 15 (4) : 619-639. doi: 10.3934/ipi.2021008
[9]

V. Varlamov, Yue Liu. Cauchy problem for the Ostrovsky equation. Discrete & Continuous Dynamical Systems, 2004, 10 (3) : 731-753. doi: 10.3934/dcds.2004.10.731
[10]

Mauro Garavello, Paola Goatin. The Cauchy problem at a node with buffer. Discrete & Continuous Dynamical Systems, 2012, 32 (6) : 1915-1938. doi: 10.3934/dcds.2012.32.1915
[11]

Adrien Dekkers, Anna Rozanova-Pierrat. Cauchy problem for the Kuznetsov equation. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 277-307. doi: 10.3934/dcds.2019012
[12]

Jussi Korpela, Matti Lassas, Lauri Oksanen. Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation. Inverse Problems & Imaging, 2019, 13 (3) : 575-596. doi: 10.3934/ipi.2019027
[13]

Xiaoqiang Dai, Shaohua Chen. Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data. Discrete & Continuous Dynamical Systems - S, 2021, 14 (12) : 4201-4211. doi: 10.3934/dcdss.2021114
[14]

V.N. Malozemov, A.V. Omelchenko. On a discrete optimal control problem with an explicit solution. Journal of Industrial & Management Optimization, 2006, 2 (1) : 55-62. doi: 10.3934/jimo.2006.2.55
[15]

Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129
[16]

Lijuan Wang, Qishu Yan. Optimal control problem for exact synchronization of parabolic system. Mathematical Control & Related Fields, 2019, 9 (3) : 411-424. doi: 10.3934/mcrf.2019019
[17]

Akram Kheirabadi, Asadollah Mahmoudzadeh Vaziri, Sohrab Effati. Solving optimal control problem using Hermite wavelet. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 101-112. doi: 10.3934/naco.2019008
[18]

Renzhao Chen, Xuezhang Hou. An optimal osmotic control problem for a concrete dam system. Communications on Pure & Applied Analysis, 2021, 20 (6) : 2341-2359. doi: 10.3934/cpaa.2021082
[19]

M. Teresa T. Monteiro, Isabel Espírito Santo, Helena Sofia Rodrigues. An optimal control problem applied to a wastewater treatment plant. Discrete & Continuous Dynamical Systems - S, 2022, 15 (3) : 587-601. doi: 10.3934/dcdss.2021153
[20]

Yujing Wang, Changjun Yu, Kok Lay Teo. A new computational strategy for optimal control problem with a cost on changing control. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 339-364. doi: 10.3934/naco.2016016

2020 Impact Factor: 1.639

Tools

Metrics

  • PDF downloads (115)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy