French, M. and Rogers, E.
Approximate Models for Adaptive Feedback Linearisation.
International Journal of Control, 68, (6), .
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A result in Sastry & Isidori (1989) on the adaptive stabilisation/tracking of affine systems with a well defined global relative degree and linear parametric uncertainty is reviewed, and a generalisation 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 a 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. Finally an analysis of the dimension of the controllers is given. Sastry, S. & Isidori, A. (1989), `Adaptive control of linearizable systems', IEEE Trans. on Automatic Control 34 (11) p1123--1131.
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