Observer-based global output feedback controller design for an unstable wave PDE with nonlinear boundary condition. (22nd January 2022)

• Record Type: Journal Article
• Authors: Ghaderi, Najmeh; Keyanpour, Mohammad
• Is Part Of: IMA journal of mathematical control and information. Volume 39:Number 1(2022)
• Page Start: 295
• Page End: 321
• Publication Date: 2022-01-22
• Subjects: output feedback control and observers -- van der Pol boundary condition -- distributed parameter systems -- unstable wave PDE -- backstepping control design; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnab045
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: In this work, an observer-based output feedback controller for a one-dimensional wave equation with van der Pol type nonlinear boundary conditions is considered. The uncontrolled system with the energy injection and the cubic velocity nonlinearity reveals different kinds of dynamical behaviours, for example, chaotic acoustic vibration, period-doubling bifurcation, square wave and some other dynamical patterns. Firstly, an observer is designed, and next, we propose an observer-based output feedback controller using the backstepping approach. We prove well-posedness and globally asymptotic stability of the observer error and corresponding closed-loop system. To this purpose, pre-compactness of the trajectories is shown for the large-time analysis. The validity of the theoretical results is illustrated by some numerical simulations.