Explicit solutions to the optimum boundary control problem of a vibrating string

Abstract

A non-homogeneous vibrating string of finite length is considered. The control function, which acts on one end of the string, is to be chosen so that a quadratic cost functional involving an infinite time interval is minimized. Explicit exact solutions to the corresponding Riccati operator equation are determined directly, i.e. without reference to the underlying control problem. From these solutions both optimum open-loop and closed-loop control are derived.

Notes

This research has been sponsored by Deutsche Forschungsgemeinschaft.