Anti-collocated observer-based output feedback control of wave equation with cubic velocity nonlinear boundary and Dirichlet control. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Ghaderi, Najmeh; Keyanpour, Mohammad
• Is Part Of: International journal of control. Volume 94:Issue 12(2021)
• Page Start: 3264
• Page End: 3274
• Publication Date: 2021-12-02
• Subjects: Backstepping control design -- cubic velocity nonlinear boundary condition -- observer design -- output feedback controller -- wave equation; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2020.1757761
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : This study focuses on the observer and observer-based output feedback control design for a one-dimensional wave equation with van der Pol type nonlinear boundary condition and Dirichlet boundary control. The contribution of this work is divided into two parts. Firstly, the anti-collocated backstepping observer design for the nonlinear wave system is investigated, and the well-posedness and the asymptotical stability analysis of the observer error are studied. Secondly, an output feedback observer-based controller is set up by using boundary displacement measurement only to stabilise the nonlinear wave system; also the asymptotical stability of the closed-loop system is shown. The validity of the theoretical results is demonstrated by numerical simulations.