Approximate Controllability of Semilinear Control System Using Tikhonov Regularization
For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arb...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/1684637 |
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| _version_ | 1832558465787101184 |
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| author | Ravinder Katta N. Sukavanam |
| author_facet | Ravinder Katta N. Sukavanam |
| author_sort | Ravinder Katta |
| collection | DOAJ |
| description | For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial state x0 to an ϵ neighbourhood of the target state xτ at time τ>0 under the assumption that the nonlinear function f is Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that the target state corresponding to the regularized control is close to the actual state to be attained. |
| format | Article |
| id | doaj-art-8c242fa6dfd146aeb36f0a1d2ad95a23 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-8c242fa6dfd146aeb36f0a1d2ad95a232025-02-03T01:32:18ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/16846371684637Approximate Controllability of Semilinear Control System Using Tikhonov RegularizationRavinder Katta0N. Sukavanam1Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, IndiaDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, IndiaFor an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial state x0 to an ϵ neighbourhood of the target state xτ at time τ>0 under the assumption that the nonlinear function f is Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that the target state corresponding to the regularized control is close to the actual state to be attained.http://dx.doi.org/10.1155/2017/1684637 |
| spellingShingle | Ravinder Katta N. Sukavanam Approximate Controllability of Semilinear Control System Using Tikhonov Regularization International Journal of Differential Equations |
| title | Approximate Controllability of Semilinear Control System Using Tikhonov Regularization |
| title_full | Approximate Controllability of Semilinear Control System Using Tikhonov Regularization |
| title_fullStr | Approximate Controllability of Semilinear Control System Using Tikhonov Regularization |
| title_full_unstemmed | Approximate Controllability of Semilinear Control System Using Tikhonov Regularization |
| title_short | Approximate Controllability of Semilinear Control System Using Tikhonov Regularization |
| title_sort | approximate controllability of semilinear control system using tikhonov regularization |
| url | http://dx.doi.org/10.1155/2017/1684637 |
| work_keys_str_mv | AT ravinderkatta approximatecontrollabilityofsemilinearcontrolsystemusingtikhonovregularization AT nsukavanam approximatecontrollabilityofsemilinearcontrolsystemusingtikhonovregularization |