Sensitivity analysis of hyperbolic optimal control problems
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- Kowalewski, A., Lasiecka, I. & Sokołowski, J. Comput Optim Appl (2012) 52: 147. doi:10.1007/s10589-010-9375-x
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.