A class of adaptive robust controllers for uncertain dynamical systems with unknown virtual control coefficients
by Yuchao Wang; Hansheng Wu
International Journal of Advanced Mechatronic Systems (IJAMECHS), Vol. 6, No. 2/3, 2015

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.

Online publication date: Mon, 20-Jul-2015

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