Finite dimensional approximations for a class of infinite dimensional time optimal control problems

Marius Tucsnak (1) , Julie Valein (2, 3) , Chi-Ting Wu (2, 3)

1 IMB - Institut de Mathématiques de Bordeaux
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 IECL - Institut Élie Cartan de Lorraine

In this work we study the numerical approximation of the solutions of a class of abstract parabolic time optimal control problems with unbounded control operator. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the optimal time and the optimal controls of the approximate time optimal problems converge (in appropriate norms) to the optimal time and to the optimal controls of the original problem. In order to prove our main theorem, we provide a nonsmooth data error estimate for abstract parabolic systems.

Mots clés: distributed parameter systems; optimal control; numerical approximation AMS subject classifications 93C25

Domaines: Equations aux dérivées partielles [math.AP]

Marius Tucsnak, Julie Valein, Chi-Ting Wu. Finite dimensional approximations for a class of infinite dimensional time optimal control problems. International Journal of Control, 2019, 92 (1), pp.132-144. ⟨10.1080/00207179.2016.1228122⟩. ⟨hal-01393258⟩