Stable Adaptive Control of a General Class of Non-linear Systems

The properties of an adaptive control system based on a general class of non-linear models are analyzed. The class of models contains NARX models represented by feedforward neural networks with sigmoidal non-linearity, some radial basis-function expansions, local model networks, and some fuzzy systems. We apply a simple adaptive feedback linearizing controller. The analysis takes into account modeling error and slowly time-varying nominal model parameters. We discuss stability of the closed loop, as well as robustness, and derive performance bounds on the tracking error. Due to the general setup, the results are mainly of a qualitative nature. Finally, we discuss the relevance of the results, and outline some practical modiications and possible extensions.