Computational methods for boundary optimal control and identification problems

0543695 - ÚGN 2022 RIV NL eng J - Journal Article
Axelsson, Owe - Béreš, Michal - Blaheta, Radim
Computational methods for boundary optimal control and identification problems.
Mathematics and Computers in Simulation. Roč. 189, November 2021 (2021), s. 276-290. ISSN 0378-4754. E-ISSN 1872-7166
R&D Projects: GA MŠMT LQ1602
EU Projects: European Commission(XE) 847593 - EURAD
Institutional support: RVO:68145535
Keywords : parameter identification * optimal control * iterative solution * preconditioning
OECD category: Applied mathematics
Impact factor: 3.601, year: 2021
Method of publishing: Limited access
https://www.sciencedirect.com/science/article/pii/S0378475421000586

The paper deals with boundary optimal control methods for partial differential equation (PDE) problems with both target and control variables on specified parts of the boundary of the problem domain. Besides the standard aim in approximation of the target variable the paper also addresses an inverse identification of conditions on an inaccessible part of the boundary by letting them play the role of a control variable function and by overimposing boundary conditions at another part of the boundary of the given domain. The paper shows the mathematical formulation of the problem, the arising (regularized) Karush–Kuhn–Tucker (KKT) system and introduces preconditioners for the solution of the regularized system. The spectral analysis of the preconditioner, analysis of the approximation of the target function and boundary condition on an inaccessible part of the boundary and numerical tests with the proposed preconditioning techniques are included.
Permanent Link: http://hdl.handle.net/11104/0320873