No-regret distributed control of system governed by quasilinear elliptic equations with incomplete data: the degenerate case (Q1887201)

An optimal control problem governed by a quasilinear equation with incomplete or perturbed data is considered. The author studies the regularity property (continuity and differentiability) between the data (control-perturbation) and the state. He establishes a relation between the data and the first-order derivatives of the state. The existence of a sequence of optimal controls is proved. A family of singular optimal control systems characterizing the optimal control is emphasized. Passing to the limit, an optimal control for the problem considered is obtained.