Redesign of backstepping for robustness against unmodelled dynamics (Q2730990)

In the recent literature there have been several approaches designed to make backstepping control laws robust against linear unmodelled dynamics at the input of a plant. Adaptive backstepping achieves global stabilization in the presence of unknown parameters. Robust backstepping is designed for systems with disturbances. A dynamic normalization method uses a special signal to counteract the destabilizing effect of the unmodelled dynamics. Other approaches to robust re-designs of backstepping make assumptions of small gain or strict passivity.NEWLINENEWLINENEWLINEThis paper offers a re-design of backstepping which requires the unmodelled dynamics subsystem to be relative degree zero and minimum phase. The authors prove that the closed-loop solution converges to a ball around the origin whose radius can be made arbitrarily small by increasing the controller gain. They provide a numerical example that shows that the relative degree zero and minimum phase conditions cannot be relaxed.