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 output regulator theory given in Isidori-Byrnes (1990) and provides adaptive tracking for systems which may have unbounded tracking dynamics.