Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems

In this paper, we propose a new algorithm for adaptive backstepping control of non-linear uncertain systems. Current backstepping algorithms require repeated differentiations of the modelled non-linearities. The addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non-linearities. The uncertainties are assumed to be linear in the unknown constant parameters. The combined adaptive backstepping/first order filter system is proven to be semi-globally stable for sufficiently fast filters by a singular perturbation approach.