An Introduction and Summary of Use of Optimal Control Methods for PDE's

0559292 - ÚGN 2023 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Axelsson, Owe
An Introduction and Summary of Use of Optimal Control Methods for PDE's.
Large-Scale Scientific Computing : 12th International Conference, LSSC 2019. Cham: Springer, 2020 - (Lirkov, I.; Margenov, S.), s. 275-283. ISBN 978-3-030-41031-5. ISSN 0302-9743. E-ISSN 1611-3349.
[International Conference on Large-Scale Scientific Computing 2019 /12./. Sozopol (BG), 10.06.2019-14.06.2019]
Grant CEP: GA MŠMT LQ1602
Institucionální podpora: RVO:68145535
Klíčová slova: optimal control * preconditioner * inner product free
Obor OECD: Applied mathematics
https://link.springer.com/book/10.1007/978-3-030-41032-2

Optimal control problem formulation are fundamental for the construction and test of many equipments in engineering and elsewhere. In a mathematical formulation of them, one considers a domain of definition, Ω which covers the machine or other equipment. The main idea is to control the performance of the machine by use of a control function. This can be a distributed control, (v) that is, defined on the whole of Ω or only on part (ΩC) of Ω, frequently (part of) the boundary ∂Ω. The solution (u) is normally a solution of a partial differential equation defined on the whole of Ω, but frequently measured, i.e. observed only on a subdomain, Ω0 or part of the boundary ∂Ω. One has then a target solution defined there and wants to compute the control function so that the computed solution is as close as possible to that desired function. Since such a problem is of inverse type, i.e. ill-posed, it must be regularized, i.e. a Tichonov type of penalty term is added to the functional to be minimized. One uses then mostly the square of the L2(ΩC) - norm of the control function. The paper is structured as follows. In Sect. 2 the optimal control framework is presented followed by the preconditioning method in Sect. 3. Inner product free acceleration methods are then shortly presented in Sect. 4 and the paper ends with some concluding remarks.
Trvalý link: https://hdl.handle.net/11104/0332627