Adaptive learning control of nonlinear systems by output error feedback

This paper addresses the problem of designing an output error feedback control for single-input, single-output nonlinear systems with uncertain, smooth, output-dependent nonlinearities whose local Lipschitz constants are known. The considered systems are required to be observable, minimum phase with known relative degree and known high frequency gain sign: linear systems are included. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which "learns" the input reference signal by identifying its Fourier coefficients: bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the Fourier series expansion is finite, while arbitrary small tracking errors are exponentially achieved otherwise. The resulting control is not model based, is independent of the system order and depends only on the relative degree, the reference signal period and the high frequency gain sign.