Adaptive stabilization of Kirchhoffs non-linear strings by boundary displacement feedback

This paper is concerned with adaptive global stabilization of an undamped non-linear string in the case where any velocity feedback is not available. The linearized system may have an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The adaptive stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by adaptive boundary control.