Adaptive tracking for a class of feedback linearizable systems

A state feedback control is presented which achieves asymptotic tracking of signals generated by a known exosystem for single-input single-output nonlinear systems with unknown parameters entering linearly. The following assumptions are required: the nominal system is feedback linearizable; the tracking dynamics are not affected by unknown parameters; the linear approximation of the zero dynamics has no eigenvalue with zero real part; pure feedback conditions are satisfied on the vector fields multiplying unknown parameters. This extends to a class of nonlinear uncertain systems the regulator theory of Isidori and Byrnes (1990) and provides adaptive tracking for systems with unbounded tracking dynamics which were excluded in Kanallakopoulos, Kokotovic and Morse (1991)