Sufficient approximate optimality condition for the inverse one-phase Stefan problem

• Autorzy: Lipnicka Marta , Lipnicki Artur , Nowakowski Andrzej

Identyfikatory

DOI

10.2478/candc-2024-0010

• Języki publikacji: EN

Abstrakty

EN

We investigate the identification problem for the onephase Stefan problem. As the inverse Stefan problem is not well posed, an optimal control problem is considered instead. In the paper we develop a dual dynamic programming approach to derive sufficient approximate optimality conditions for that optimal control problem. As a next step we formulate and prove a verification theorem for approximate solution. The verification Theorem 4.1 is the basis for the development of a numerical algorithm. Having the verification theorem we do not need the convergence of our algorithm.

Słowa kluczowe

EN

sufficient approximate optimality condition; inverse one-phase Stefan problem; computational algorithm; verification theorem

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2024
• Tom: Vol. 53, No. 1
• Strony: 231--246
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Lipnicka Marta

• University of Łódź, Faculty of Mathematics and Computer Science Banacha 22, 90-238 Łódź, Poland

autor

Lipnicki Artur

• University of Łódź, Faculty of Mathematics and Computer Science Banacha 22, 90-238 Łódź, Poland

autor

Nowakowski Andrzej

• University of Łódź, Faculty of Mathematics and Computer Science Banacha 22, 90-238 Łódź, Poland

Bibliografia

• Abdulla, U. G. (2013) On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems and Imaging, 7: 307–340.
• Abdulla, U. G. (2016) On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems and Imaging, 10: 869–898.
• Abdulla, U. G. and Goldfarb, J. (2024) Fréchet differentability in Besov spaces in the optimal control of parabolic free boundary problems. arxiv: 1604.00057, to appear in Inverse and Ill-posed Problems, URL https://arxiv.org/abs/1604.00057.
• Abdulla, U. G., Cosgrove, E. and Goldfarb, J. (2017) On the Fréchet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations and Control Theory doi:10.3934/eect.2017017, 6: 319–344.
• Budak, B. M. and Vasileva, V. N. (1972) On the solution of the inverse Stefan problem. Soviet Mathematics Doklady, 13: 811–815.
• Budak, B. M. and Vasileva, V. N. (1973) On the solution of Stefans converse problem II. USSR Computational Mathematics and Mathematical Physics, 13: 97–110.
• Budak, B. M. and Vasileva, V. N. (1974) The solution of the inverse Stefan problem. USSR Computational Mathematics and Mathematical Physics, 13: 130–151.
• Goldman, N. L. (1997) Inverse Stefan Problems. Kluwer Academic Publishers Group, Dodrecht.
• Lipnicka, M. and Nowakowski, A. (2018) On dual dynamic programming in shape optimization of coupled models. Structural and Multidisciplinary Optimization, doi: 10.1007/s00158-018-2057-5.
• Lipnicka, M. and Nowakowski, A. (2018) Sufficient ε-Optlmality Conditions for Navier-Stokes Flow. Numerical Algorithm. IEEE Conference on Decision and Control (CDC), Miami Beach, FL, 2484–2489, doi: 10.1109/CDC.2018.8619266.
• Lipnicka, M. and Nowakowski, A. (2022a) Optimal control using to approximate probability distribution of observation set. Math. Methods Appl. Sci. 1-16, doi: https://doi.org/10.1002/mma.8391.
• Lipnicka, M. and Nowakowski, A. (2022b) Optimal Control in Learning Neural Network. In: H. A. Le Thi, T. Pham Dinh and H. M. Le, eds., Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO. Lecture Notes in Networks and Systems, 363. Springer, Cham. https://doi.org/10.1007/978-3-030-92666-3 26.
• Lipnicka, M. and Nowakowski, A. (2023) Learning of neural network with optimal control tools. Engineering Applications of Artificial Intelligence, 121, https://doi.org/10.1016/j.engappai.2023.106033.