TY - JOUR

T1 - Output feedback exponential stabilization for one-dimensional unstable wave equations with boundary control matched disturbance

AU - Zholj, Hua Cheng

AU - Weiss, George

N1 - Publisher Copyright:
Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

PY - 2018

Y1 - 2018

N2 - We study the output feedback exponential stabilization of a one-dimensional unstable wave equation, where the boundary input, given by the Neumann trace at one end of the domain, is the sum of the control input and the total disturbance. The latter is composed of a nonlinear uncertain feedback term and an external bounded disturbance. Using the two boundary displacements as output signals, we design a disturbance estimator that does not use high gain. It is shown that the disturbance estimator can estimate the total disturbance in the sense that the estimation error signal is in L2[0, oo). Using the estimated total disturbance, we design an observer whose state is exponentially convergent to the state of original system. Finally, we design an observer-based output feedback stabilizing controller. The total disturbance is approximately canceled in the feedback loop by its estimate. The closed-loop system is shown to be exponentially stable while guaranteeing that all the internal signals are uniformly bounded.

AB - We study the output feedback exponential stabilization of a one-dimensional unstable wave equation, where the boundary input, given by the Neumann trace at one end of the domain, is the sum of the control input and the total disturbance. The latter is composed of a nonlinear uncertain feedback term and an external bounded disturbance. Using the two boundary displacements as output signals, we design a disturbance estimator that does not use high gain. It is shown that the disturbance estimator can estimate the total disturbance in the sense that the estimation error signal is in L2[0, oo). Using the estimated total disturbance, we design an observer whose state is exponentially convergent to the state of original system. Finally, we design an observer-based output feedback stabilizing controller. The total disturbance is approximately canceled in the feedback loop by its estimate. The closed-loop system is shown to be exponentially stable while guaranteeing that all the internal signals are uniformly bounded.

KW - Disturbance rejection

KW - Exponential stabilization

KW - Output feedback controller

KW - Unstable wave equation

UR - http://www.scopus.com/inward/record.url?scp=85055662271&partnerID=8YFLogxK

U2 - 10.1137/17M1133531

DO - 10.1137/17M1133531

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AN - SCOPUS:85055662271

SN - 0363-0129

VL - 56

SP - 4098

EP - 4129

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 6

ER -