Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks Zhao Lu a , Leang-San Shieh a, * , Guanrong Chen b , Norman P. Coleman c a Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4005, USA b Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, PR China c US Army Armament Center, Dover, NJ 07801, USA Received 16 April 2004; received in revised form 8 July 2005; accepted 9 August 2005 Abstract In the realm of nonlinear control, feedback linearization via differential geometric techniques has been a concept of paramount importance. However, the applicability of this approach is quite limited, in the sense that a detailed knowledge of the system nonlinearities is required. In practice, most physical chaotic systems have inherent unknown nonlinearities, making real-time control of such chaotic systems still a very challenging area of research. In this paper, we propose using the recurrent high-order neural network for both identifying and controlling unknown chaotic systems, in which the feedback linearization technique is used in an adaptive manner. The global uniform boundedness of parameter estimation errors and the asymptotic stability of tracking errors are proved by the Lyapunov stability theory and the LaSalle–Yoshizawa theo- rem. In a systematic way, this method enables stabilization of chaotic motion to either 0020-0255/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2005.08.002 * Corresponding author. Tel.: +1 713 743 4439; fax: +1 713 743 4444. E-mail address: lshieh@uh.edu (L.-S. Shieh). Information Sciences 176 (2006) 2337–2354 www.elsevier.com/locate/ins