Adaptive boundary stabilization of a nonlinear axially moving string

Abstract

AbstractIn this paper, we are interested in stabilizing a nonlinear axially moving string by an adaptive boundary control. The existence and uniqueness of a solution of the closed loop system is dealt with in the framework of the nonlinear semigroup theory by using a theorem due to Crandall‐Liggett. The control is constructed through a low‐gain adaptive velocity feedback. It is shown that the formulated control is capable of stabilizing exponentially the closed loop system.