Optimal control for fractional diffusion equations with incomplete data
In the paper, the optimal control of a time-fractional diffusion equation involving fractional derivative in the Riemann-Liouville sense where the boundary condition is missing or incomplete is studied. The authors use the no-regret control and the least (or low) regret control notions developed by Lions, according to which the least regret control problem ``consists in trying to find a control which optimizes the situation with the constraint of not making things too worse with respect to a known reference control, in presence of more or less significant perturbations. Its solution is called least (or low) regret control'' (see [\textit{J. L. Lions}, in: Environment, economics and their mathematical models. Papers from the Curso de Verano de la Universidad Complutense de Madrid held at Almeria, Spain, June 26-July 3, 1992. Paris: Masson. 101--123 (1994; Zbl 0862.49026)]). It is proved that the least regret control problem associated with the boundary fractional diffusion equation has a unique solution. It is also shown that this solution converges to the no-regret control which is characterized by a singular optimality system.
scientific article; zbMATH DE number 6800847
scientific article