Robust adaptive nonlinear regulation with dynamic uncertainties

Abstract

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 non-linearities and unmeasured input-to-state stable dynamics. In contrast to [4, 5, 6], the adaptive control laws proposed in this paper do not require any dynamic dominating signal to guarantee Lagrange stability. The numerical example of a simple pendulum with unknown parameters and without velocity measurement illustrates our theoretical results.