Journal
NONLINEAR DYNAMICS
Volume 81, Issue 4, Pages 1597-1610Publisher
SPRINGER
DOI: 10.1007/s11071-015-2093-2
Keywords
Adaptive robust control; Backstepping; Uncertain dynamical systems; Neural networks; Asymptotic stability
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The problem of robust stabilization is considered for a class of nonlinear systems in the presence of structure uncertainties, external disturbances, and unknown time-varying virtual control coefficients. It is supposed that the upper bounds of the external disturbances and the virtual control coefficients are unknown. The unknown structural uncertainties are approximated by using neural networks (NNs). In particular, the prior knowledge about the weights and approximation errors of NNs is not required. The improved adaptation laws with -modification are employed to estimate the unknown parameters, which contain the upper bounds of the external disturbances and the virtual control coefficients, and the norm forms of weights and approximate errors of the NNs. Then, by making use of the updated values of these unknown parameters, a class of backstepping approach-based continuous adaptive robust state feedback controllers is synthesized. It is also shown that the proposed adaptive robust backstepping controller can guarantee the uniform asymptotic stability of such uncertain dynamical systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed controller.
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