Abstract
The problem of adaptive robust stabilization for a class of uncertain single-input and single-output (SISO) nonlinear systems is considered. It is assumed for the uncertainty to be bounded. The bound, however, may be unknown. Based on Lyapunov method and input/output linearization approach, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we desgin a class of continuous state feedback controllers. It is shown that under the proposed controller with adaptive laws the states of the controlled system converge to zero as time approaches infinity. Because of its continuity, our continuous controller can guarantee the existence of the solution to the dynamical system in usual sense. Finally, a numerical example is presented to demonstrate the effectiveness of the approach developed in this paper.
