Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control

• Published in: European journal of control Vol. 39; pp. 39 - 52
• Main Authors: Zhou, Hua-Cheng, Guo, Bao-Zhu
• Format: Journal Article
• Language: English
• Published: Philadelphia Elsevier Ltd 01.01.2018; Elsevier Limited
• Subjects: Boundary control; Control theory; Disturbance rejection; Generators; Partial differential equations; Performance output tracking; stabilization; Tracking control; Uncertainty; Wave equation; Wave equations; Wave power; Well posed problems; Wave equation; Disturbance rejection; Performance output tracking; stabilization; 37L15; 93D15; Boundary control; 93B52; 93B51
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2017.10.006

In this paper, we consider performance output tracking for a boundary controlled one-dimensional wave equation with possibly unknown internal nonlinear uncertainty and external disturbance. We first show that the open-loop system is well-posed and then propose a disturbance estimator. It is shown that the disturbance estimator can estimate successfully the total disturbance that consists of internal uncertainty and external disturbance. An servomechanism based on the estimated total disturbance is then designed. It is shown that the closed-loop system is well-posed. Three control objectives are achieved: (a) the output is tracking the reference signal; (b) all the internal signals are uniformly bounded; (c) the closed-loop system is internally asymptotically stable if both the reference signal and the disturbance vanish or belong to the space H2(0, ∞) and L2(0, ∞), respectively. The unmatched performance output tracking control is first time applied to a system described by the partial differential equation for complete general disturbance rejection and reference tracking purpose. Another key feature of this paper is that we do not use the high-gain to estimate total disturbance for unmatched system. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.