Robust stabilization of nonlinear uncertain systems in the presence of input unmodeled dynamics

In this paper, motivated by the recent results on control of nonlinear systems with input uncertainties and converse Lyapunov results with respect to an invariant set, we address the robust adaptive control issue in the presence of uncertainties including input unmodeled nonlinear dynamics. Nonlinear damping terms are introduced via backstepping to counteract the uncertainties and observer design is also employed to cancel the affects of the nonlinear unmodeled dynamics. To this end, nonlinear systems transformable to the Extended Strict Feedback Form with Input Uncertainties are considered. A robust adaptive controller is designed to achieve semiglobal stability with respect to an invariant set in the presence of uncertainties utilizing partial state feedback. The results are also extended to a class of decentralized systems.