Nonlinear Analysis 61 (2005) 671 – 693 www.elsevier.com/locate/na Stabilization and parameter estimation for an Euler–Bernoulli beam equation with uncertain harmonic disturbance under boundary output feedback control  Bao-Zhu Guo a, b, ∗ , Wei Guo a a Institute of Systems Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P.R. China b School of Computational and Applied Mathematics, University of the Witwatersrand, Wits-2050, Johannesburg, South Africa Received 2 January 2004; accepted 23 November 2004 Abstract This paper is concerned with the boundary stabilization and parameter estimation of an Euler– Bernoulli beam equation with one end fixed, and control and uncertain amplitude of harmonic dis- turbance at another end. A high-gain adaptive regulator is designed in terms of measured collocated end velocity. The existence and uniqueness of the classical solution as well as smooth solution of the closed-loop system are justified. It is shown that the state of the system approaches the standstill as time goes to infinity and meanwhile the estimated parameter converges to the unknown parameter.  2004 Elsevier Ltd. All rights reserved. MSC: 93C20; 93D15; 35B35; 35P10 Keywords: Beam equation; Harmonic disturbance rejection; Existence and uniqueness of solution  Supported by the National Natural Science Foundation of China. ∗ Corresponding author. Tel.: +86 1062651443; fax: +86 10 61587343. E-mail addresses: bzguo@iss03.iss.ac.cn, bzguo@cam.wits.ac.za (B.Z. Guo). 0362-546X/$ - see front matter  2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2004.11.007