Approximate Parameterisations for Adaptive Feedback Linearisation

Description/Abstract

A generalisation of a result in 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 neuro-control 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 neuro-control literature the control is state feedback law, taking measurements from the original coordinates not from the normal form. A local in the weights result is given, and under some nonlinearity constraints inherited from Sastry & Isidori (1989) a global result is proved, where the dimension of the controller varies according to the size of the initial conditions and tracking signal. A final global result is obtained where an `external' controller is used to return the state vector to within a region over which the neuro controller can operate. Sastry, S. & Isidori, A. (1989), `Adaptive control of linearizable systems', IEEE Trans. on Automatic Control 34 (11) p1123--1131.