Sufficient optimality conditions for bilinear optimal control of the linear damped wave equation

Franz Bethke (1) , Axel Kröner (1, 2)

1 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems

In this paper we discuss sufficient optimality conditions for an optimal control problem for the linear damped wave equation with the damping parameter as the control. We address the case that the control enters quadratic in the cost function as well as the singular case that the control enters affine. For the non-singular case we consider strong and weak local minima , in the singular case we derive sufficient optimality conditions for weak local minima. Thereby, we take advantage of the Goh transformation applying techniques recently established in Aronna, Bonnans, and Kröner [Math. Program. 168(1):717–757, 2018] and [INRIA research report, 2017]. Moreover, a numerical example for the singular case is presented.

Domaines: Optimisation et contrôle [math.OC]

Franz Bethke, Axel Kröner. Sufficient optimality conditions for bilinear optimal control of the linear damped wave equation . [Research Report] Humboldt Universität Berlin. 2018. ⟨hal-01807699⟩