Sensitivity analysis of hyperbolic optimal control problems

Adam Kowalewski (1) , Irena Lasiecka (2) , Jan Sokolowski (3)

1 Institute of Automatics [Cracow]
2 Department of Mathematics
3 IECN - Institut Élie Cartan de Nancy

The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration. The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth domain. The imperfection is replaced by its approximation defined by a suitable Steklov's type differential operator. For approximate optimal control problems the well-posedness is shown. One term asymptotics of optimal control are derived and justified for the approximate model. The key role in the arguments is played by the so called "hidden regularity" of boundary traces generated by hyperbolic solutions.

Mots clés: Linear partial differential operators; Hyperbolic boundary value problems; Optimal control problems; Kondratiev weighted spaces; Steklov-Poincaré operator; Sensitivity analysis

Domaines: Equations aux dérivées partielles [math.AP]

Adam Kowalewski, Irena Lasiecka, Jan Sokolowski. Sensitivity analysis of hyperbolic optimal control problems. Computational Optimization and Applications, 2012, 52 (1), pp.147-179. ⟨10.1007/s10589-010-9375-x⟩. ⟨hal-00530949⟩