Adaptive learning control for feedback linearizable systems

This paper addresses the problem of designing a state feedback tracking control for single-input, single-output uncertain feedback linearizable systems with maximal relative degree and matching unstructured uncertainties (no parametrization is available for uncertain nonlinearities). Under the assumption that the reference signal is periodic with known period, by developing in Fourier series expansion the unknown periodic reference input signal, an adaptive learning control is designed which 'learns' the reference control signal starting from zero, by identifying the Fourier-coefficients of any truncated approximation. This result holds for every initial condition and for every reference signal in a given compact set of the state space: L-2 and L-infinity transient performance for the output tracking error are guaranteed in the 'learning phase'.