A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics

This paper presents a constructive robust adaptive nonlinear control scheme which can be regarded as a robustification of the now popular adaptive backstepping algorithm. The allowed class of uncertainties includes nonlinearly appearing parametric uncertainty, uncertain nonlinearities, and unmeasured input-to-state stable dynamics. The adaptive control laws proposed in this paper do not require any dynamic dominating signal to guarantee the robustness property of Lagrange stability. The numerical example of a simple pendulum with unknown parameters and without velocity measurement illustrates our theoretical results.