In this paper, we study a problem of optimal control for an elliptic equation with incomplete data (unknown source) in a strategic regular subdomain. By using the concepts of no-regret, low-regret control, a null-controllability approach and Carleman estimate, we prove null-controllability of our system. Then, we define no-regret control which is hard to characterize. To avoid this problem, we relax our definition by a quadratic perturbation to get a low-regret control sequence converging to no-regret control to obtain an optimality system. By this optimality system, we establish the null controllability.

problems with incomplete data, no-regret control, Carleman estimates.

Received: November 18, 2023; Revised: December 16, 2023; Accepted: December 26, 2023; Published: March 12, 2024

How to cite this article: Cheikh SECK, Mouhamadou NGOM and Lamine NDIAYE, Regional optimal no-regret control for an elliptic equation with incomplete data in a regular strategic domain, Far East Journal of Dynamical Systems 37(1) (2024), 1-12. http://dx.doi.org/10.17654/0972111824001

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

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