Title: A class of adaptive robust controllers for uncertain dynamical systems with unknown virtual control coefficients

Authors: Yuchao Wang; Hansheng Wu

Addresses: Graduate School of Comprehensive Scientific Research, Prefectural University of Hiroshima, Hiroshima City, Hiroshima 734-8558, Japan ' Department of Information Science, Prefectural University of Hiroshima, Hiroshima City, Hiroshima 734-8558, Japan

Abstract: The problem of backstepping approach-based adaptive robust controller design is considered for a class of nonlinear systems in the presence of uncertain system parameters, external disturbances, and unknown time-varying virtual control coefficients. It is supposed that the upper bounds of external disturbances and unknown time-varying virtual control coefficients are unknown. In particular, it is also supposed that the lower bounds of time-varying virtual control coefficients are unknown. Then, the improved adaptation laws with σ-modification are employed to estimate the unknown values containing all the unknown bounds of such uncertainties. With the help of the adaptation laws, a class of backstepping approach-based continuous adaptive robust state feedback controllers is developed. Furthermore, by employing the improved Lyapunov-Krasovskii functional method, it is also shown that the proposed adaptive robust backstepping controller can guarantee the uniform asymptotic stability of such uncertain dynamical systems. Finally, a numerical example is given to demonstrate the validity of the results.

Keywords: adaptive control; robust control; backstepping; uncertain dynamical systems; asymptotic stability; virtual control coefficients; uncertainty; controller design; state feedback control.

DOI: 10.1504/IJAMECHS.2015.070707

International Journal of Advanced Mechatronic Systems, 2015 Vol.6 No.2/3, pp.65 - 74

Received: 25 Nov 2014
Accepted: 06 Feb 2015
Published online: 21 Jul 2015 *

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