A class of adaptive robust controllers for uncertain dynamical systems with unknown virtual control coefficients. (2015)

• Record Type: Journal Article
• Authors: Wang, Yuchao; Wu, Hansheng
• Is Part Of: International journal of advanced mechatronic systems. Volume 6:Number 2/3(2015)
• Page Start: 65
• Page End: 74
• Publication Date: 2015
• Subjects: adaptive control -- robust control -- backstepping -- uncertain dynamical systems -- asymptotic stability -- virtual control coefficients -- uncertainty -- controller design -- state feedback control; Mechatronics -- Periodicals; 629.89
• Languages: English
• ISSNs: 1756-8412

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.