Low-regret control of a nonlinear parabolic problem with missing data
DOI:
https://doi.org/10.24193/subbmath.2026.2.10Keywords:
Nonlinear, parabolic problem, no-regret, low-regret, adapted low regret controlAbstract
In this paper, we study the optimal control of a nonlinear parabolic problem with missing data. Using the concepts of no-regret control, low-regret control and adapted low-regret control, we give a characterization of the con trol for ill-posed problems. More precisely, we study the control of a nonlinear parabolic problem using a regularization approach that generates incomplete information. We obtain a singular optimality system characterizing the no-regret control for the nonlinear parabolic problem.
Mathematics Subject Classification (2010): 35Q93, 49J20, 93C10, 93C41.
Received 24 November 2025; Accepted 18 February 2026.
References
[1] Gabay, D., Lions, J.-L., Least regrets strategic decisions, C. R. Math. Acad. Sci. Paris, 319(10)(1994), 1049–1056.
[2] Lions, J.-L., Some methods in the mathematical analysis of systems and their control, Science Press, Beijing, 1981.
[3] Lions, J.-L., Méthodes Mathématiques de l'Informatique, Gauthier-Villars, Bordas, Paris, vol. 13, 1983.
[4] Lions, J.-L., Optimal control of non well posed distributed systems, Banach Center Publ., 14(1)(1985), 299–311.
[5] Lions, J.-L., Contrôle de pareto de systèmes distribués. le cas stationnaire, C. R. Math. Acad. Sci. Paris, 302(6)(1986), 223–227.
[6] Lions, J.-L., Contrôle à moindres regrets des systèmes distribués, C. R. Math. Acad. Sci. Paris, 315(1992), 1253–1257.
[7] Lions, J.-L., Duality arguments for multi agents least-regret control, Institut de France, 1999.
[8] Lions, J.-L., Least regret control, virtual control and decomposition methods, ESAIM Math. Model. Numer. Anal., M2AN, 32(2)(2000), 409–418.
[9] Picart, D., Ozier-Lafontaine, H. O., Abdennebi, L., Modeling plant nutrient uptake: Mathematical analysis and optimal control, Evol. Equ. Control Theory, 4(2)(2015), 193–203.
[10] Nakoulima, O., Omrane, A., Velin, J., Perturbations à moindres regrets dans les systèmes distribués à données manquantes, C. R. Math. Acad. Sci. Paris, 330(9)(2000), 801–806.
[11] Nakoulima, O., Omrane, A., Velin, J., On the pareto control and no-regret control for distributed systems with incomplete data, SIAM J. Control Optim., 42(4)(2003), 1167–1184.
[12] Savage, L. J., The foundations of statistics, 2nd rev. ed., Dover Publications, New York, 1972, pp. 310.
[13] Smoller, J., Shock Waves and Reaction–Diffusion Equations, Springer-Verlag, New York, 1983.
[14] Tindano, T., Tao, S., Sawadogo, S., Optimal control of a nonlinear elliptic problem with missing data, Journal of Mathematics Research, 14(6)(2022), 46–55.
[15] Thomas, T., Mifiamba, S., Tao, S., Somdouda, S., Optimal control of a nonlinear elliptical evolution problem with missing data, 30(2)(2023), 135–150.
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