Continuous adaptive robust controllers guaranteeing uniformultimate boundedness for uncertain nonlinear systems

The problem of robust stabilization of non-linear systems with partially known uncertainties is considered. A class of continuous adaptive robust state feedback controllers which can guarantee uniform ultimate boundedness of the resulting closed-loop systems in the presence of the uncertainties is proposed. In contrast with some results presented in the control literature, the 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 be guaranteed. Moreover, due to the continuity of the state feedback controller and adaptive law, the proposed adaptive robust state feedback controller is easily implemented in practical robust control problems, and no chattering will appear in implementation for control. Finally, an illustrative example is given to demonstrate the utilization of the results.