Is it possible to stabilize an Infinite-dimensional system by stabilization of the corresponding approximated finite-dimensional system?

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In stochastic systems(SDEs), Most of the time we assumed that the disturbance and noise vanish at the equilibrium point, is it reasonable assumption?

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Konstantin Petrovich Lovetskiy

May be that artical Article Tikhonov regularization of optimal control problems governed...

could help to solve your problem...

Mohamed-Mourad Lafifi

Dear Ali,

Also i suggest you to see links and attached files may be you can found a solution for your problem .

https://core.ac.uk/download/pdf/82475668.pdf

http://archive.schools.cimpa.info/anciensite/NotesCours/PDF/2006/Zuazua.pdf

https://pdf.sciencedirectassets.com/272578/1-s2.0-S0022247X00X05483/

https://www.rug.nl/research/portal/files/3176978/thesis.pdf

Best regards

Kabir Sadeghi

As in the finite-dimensional case, a state-space based controller for the infinite dimensional H∞ disturbance-attenuation problem may be calculated by solving two Riccati equations. These operator Riccati equations can rarely be solved exactly. It can be approximated the original infinite-dimensional system by a sequence of finite-dimensional systems. The solutions to the corresponding finite-dimensional Riccati equations can be shown to converge to the solution of the infinite-dimensional Riccati equations. Furthermore, the corresponding finite-dimensional controllers yield performance arbitrarily close to that can be obtained with the infinite-dimensional controller.

I hope it is helpful to you.

All the best.

Ali Namadchian

Dear Kabir Sadeghi

Thank you very much

could you please introduce me a reference about what you have said in your answer

Dear Ali Namadchian

You are most welcome.

In my page of ReseachGate, or by googling my name you can find all of them easily. If you do not succeed let me know.