Nonlinear time-varying system control using the adaptive backstepping technique

This paper focuses on the problem of adaptively controlling nonlinear systems with time-varying and unknown parameters. Both state feedback and output feedback systems are considered. We seek plant stabilization and output reference tracking. The control problem is dealt with using a back-stepping adaptive controller including a switching a modification. In the case of state feedback systems, all the closed loop signals are shown to remain globally bounded. Such a result becomes regional when output feedback systems are considered, then the attraction region is a K_∞ function of the (time-varying) parameters rate. In both cases, the asymptotic (tracking) quality is shown to be proportional to the parameters rate.