REGIONAL OPTIMAL NO-REGRET CONTROL FOR AN ELLIPTIC EQUATION WITH INCOMPLETE DATA IN A REGULAR STRATEGIC DOMAIN
Keywords:
problems with incomplete data, no-regret controlDOI:
https://doi.org/10.17654/0972111824001Abstract
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.
Received: November 18, 2023
Revised: December 16, 2023
Accepted: December 26, 2023
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