Adaptive robust stabilization for a class of uncertain nonlinear systems with external disturbances

The problem of adaptive robust stabilization is considered for a class of nonlinear systems with uncertainties which consist of uncertain system parameters and multiple external disturbances. It is supposed that the upper bounds of these uncertainties are unknown. In particular, different from the results reported in the control literature, in this paper the multiple external disturbances are assumed only to be any continuous and bounded functions, and the boundedness of their time derivatives is not required. Some improved adaptation laws with σ-modification are employed to estimate such unknown bounds. Then, by making use of the updated values of these unknown bounds, a class of continuous adaptive robust state feedback controllers is synthesized for such uncertain nonlinear systems. The standard adaptive backstepping design approach is properly modified to allow the use of our adaptive robust control technique. It is also shown that the resulting adaptive closed-loop control systems are uniformly bounded, and the states converge uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.