© 2016 IEEE. This paper presents a backstepping control design for a one-dimensional wave PDE with in-domain viscous damping, subject to a dynamical anti-damped boundary condition. Its main contribution is the design of an observer-based control law which stabilizes the wave PDE velocity, using only boundary mesurements. Numerical simulations on an oil-inspired example show the relevance of our result and illustrate the merits of this control design.
Roman, C., Bresch-Pietri, D., Cerpa, E., Prieur, C., & Sename, O. (2016). 2016 IEEE 55th Conference on Decision and Control, CDC 2016. 549-554. Paper presented at conference, . https://doi.org/10.1109/CDC.2016.7798326