Optimal control of an elastic string with viscous damping

Abstract

We study bilinear optimal control of a wave equation with one spatial dimension. The problem describes oscillations of an elastic string with viscous damping, and the damping coefficient is taken as the control. The objective functional involves driving the state solution close to a desired profile and incurring a cost on the control. The optimal control is characrerized in terms of an optimality system.

Keywords:

• Wave equation
• bilinear optimal control

AMS:

• 35L10
• 49J20