We consider the optimal control of a nonlinear elliptic problem with missing data (so-called ill-posed problems). Using the notion of no-regret and low-regret control, we give a characterization of the control for ill-posed problems. More precisely, we study the control  of Cauchy evolution problems via a regularization approach which generates incomplete information. We obtain a singular optimality system characterizing the no-regret control for the Cauchy evolution problems.

optimal control, no-regret, low-regret, adapted low-regret control.

Received: December 14, 2022; Revised: February 7, 2023; Accepted: April 4, 2023; Published: April 24, 2023

How to cite this article: Thomas TINDANO, Mifiamba SOMA, Sadou TAO and Somdouda SAWADOGO, Optimal control of a nonlinear elliptical evolution problem with missing data, Advances in Differential Equations and Control Processes 30(2) (2023), 135-150. http://dx.doi.org/10.17654/0974324323009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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