Approximate models for adaptive feedback linearization

A result obtained by Sastry and Isidori in 1989 on the adaptive stabilization and tracking of affine systems with a well defined global relative degree and linear parametric uncertainty is reviewed, and a generalization is developed to include bounded output disturbances. From this, we develop neurocontrol results, for linear weight approximants with compactly supported basis functions, where the disturbance term is used to handle the approximation error. In contrast with many results in the neurocontrol literature the control is a state feedback law, taking measurements from the original coordinates and not from the normal form. A local-weights result is given, and under some nonlinearity constraints from Sastry and Isidori a global result is proved, where the dimension of the controller varies according to the size of the initial conditions and tracking signal.