Active wave suppression in the interior of a one-dimensional domain

We consider the problem of creating an absorber in the interior of a system that supports one-dimensional wave propagation, such as a waveguide, using active control. The control goal is suppression of wave propagation beyond a prescribed region of the waveguide, but without perturbing the propagation within that region. Unlike boundary control, achieving full absorption in the interior introduces a challenge of creating both a non-transmitting and a non-reflecting sink. We overcome this challenge by introducing a near uni-directional control wave which is accomplished by using two concentrated actuators. The residual back-action wave is minimized based on the available control energy. We employ this control wave in two algorithms, a feed-forward and a feedback one, which we denote by Interior Wave Suppression. We illustrate the theoretical results through numerical simulation of an acoustic waveguide example.