Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model
In this paper, we present the numerical solution for the optimal control problem of monodomain model with Rogersmodified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
Scientific Research Publishing
2012
|
| Subjects: |
| _version_ | 1796856825407078400 |
|---|---|
| author | Kin, Wei Ng Ahmad, Rohanin |
| author_facet | Kin, Wei Ng Ahmad, Rohanin |
| author_sort | Kin, Wei Ng |
| collection | ePrints |
| description | In this paper, we present the numerical solution for the optimal control problem of monodomain model with Rogersmodified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem. Our control objective is to dampen the excitation wavefront of the transmembrane potential in the observation domain using optimal applied current. Various conjugate gradient methods have been applied by researchers for solving this type of optimal control problem. For the present paper, we adopt the modified Fletcher-Reeves method and modified Dai-Yuan method for computing the optimal applied current. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current when the modified Fletcher-Reeves method is used. However, this is not the case when the modified Dai-Yuan method is employed. Numerical results indicate that the modified Dai-Yuan method failed to converge to the optimal solution when the Armijo line search is used. |
| first_indexed | 2024-03-05T18:48:51Z |
| format | Article |
| id | utm.eprints-31112 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T18:48:51Z |
| publishDate | 2012 |
| publisher | Scientific Research Publishing |
| record_format | dspace |
| spelling | utm.eprints-311122019-03-31T08:23:15Z http://eprints.utm.my/31112/ Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model Kin, Wei Ng Ahmad, Rohanin Q Science In this paper, we present the numerical solution for the optimal control problem of monodomain model with Rogersmodified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem. Our control objective is to dampen the excitation wavefront of the transmembrane potential in the observation domain using optimal applied current. Various conjugate gradient methods have been applied by researchers for solving this type of optimal control problem. For the present paper, we adopt the modified Fletcher-Reeves method and modified Dai-Yuan method for computing the optimal applied current. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current when the modified Fletcher-Reeves method is used. However, this is not the case when the modified Dai-Yuan method is employed. Numerical results indicate that the modified Dai-Yuan method failed to converge to the optimal solution when the Armijo line search is used. Scientific Research Publishing 2012-08 Article PeerReviewed Kin, Wei Ng and Ahmad, Rohanin (2012) Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model. Applied Mathematics, 3 (8). pp. 864-872. ISSN 2152-7393 http://dx.doi.org/10.4236/am.2012.38128 DOI:10.4236/am.2012.38128 |
| spellingShingle | Q Science Kin, Wei Ng Ahmad, Rohanin Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| title | Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| title_full | Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| title_fullStr | Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| title_full_unstemmed | Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| title_short | Modified fletcher-reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| title_sort | modified fletcher reeves and dai yuan conjugate gradient methods for solving optimal control problem of monodomain model |
| topic | Q Science |
| work_keys_str_mv | AT kinweing modifiedfletcherreevesanddaiyuanconjugategradientmethodsforsolvingoptimalcontrolproblemofmonodomainmodel AT ahmadrohanin modifiedfletcherreevesanddaiyuanconjugategradientmethodsforsolvingoptimalcontrolproblemofmonodomainmodel |