Approximate parametrisations for adaptive feedback linearisation

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