Adaptive robust stabilization of a class of nonlinear systems with partially known uncertainties

The problem of robust stabilization of nonlinear systems with partially known uncertainties is considered. A class of continuous adaptive robust state feedback controllers with simpler structure is proposed. It is shown that the resulting closed-loop nonlinear systems with uncertainties are stable in the sense of uniform ultimate boundedness. In contrast with some results presented in the control literature, the proposed adaptive law for updating the estimate values of the unknown parameters is continuous, and the existence of the solutions to the resulting closed-loop systems in the usual sense can well be guaranteed. Moreover, due to the continuity of state feedback controller and adaptive law, the proposed adaptive robust state feedback controllers is easily implemented in practical robust control problems. Finally, an illustrative example is given to demonstrate the utilization of the results