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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/1684637 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1687-9643 1687-9651 |