Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 80, pp. 1-14.

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

Authors: Yan-Na Jia (Taiyuan Normal Univ., Taiyuan Shanxi, China)
         Can Jin (Taiyuan Normal Univ., Taiyuan Shanxi, China)
         Xiu-Fang Yu (Taiyuan Normal Univ., Taiyuan Shanxi, China)
  
Abstract:
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. 

Submitted June 14, 2024. Published December 03. 2024.
Math Subject Classifications: 93C20, 35L05.
Key Words: Output tracking;  internal  model dynamic; error feedback; wave equation.