Output tracking for a 1-D wave equations with spatially varying coefficients and subject to unknown disturbances

In this article, we study the output tracking problem for a wave equation with variable coefficients, and subject to boundary control matched disturbances. Both the disturbances and the reference signal are unknown harmonic signal. The performance output is non-collocated with the control input. Initially, we establish an undisturbed auxiliary system and devise an appropriate internal model dynamic to reformulate the tracking error. Subsequently, we introduce an error-based feedback controller, leveraging an invertible transformation to achieve output tracking. The well-posedness and stability of the closed-loop system are established by applying semigroup theory approach. Finally, we illustrate the effectiveness of these theoretical results with numerical simulations. For more information see https://ejde.math.txstate.edu/Volumes/2024/80/abstr.html