Adaptive inverse control of weakly nonlinear systems

A weak nonlinear plant can be linearized and will track an input signal if the plant is preceded by a nonlinear controller which approximates the inverse of the plant’s transfer function. Present techniques for adjusting the controller adaptively to the plant require an additional nonlinear adaptive filter to perform a separate system identification. Straightforward update algorithms can not directly update the filter parameter in the controller because the transfer function of the plant might cause instabilities in the adaptive process. This problem is overcome by performing additional linear filtering to the nonlinear state vector and/or error signal. Novel filtered-A and filtered-E modifications of the stochastic gradient based methods are presented which are capable to update generic as well as special block-oriented nonlinear filter architectures.