Function approximation, “neural” networks, and adaptive nonlinear control

The resurgence of interest in flexible computational methods loosely inspired by biological signal processing mechanisms has produced a variety of possible new algorithms for adaptively controlling partially known nonlinear systems. However, for such methods to be useful in practice, the exact factors which govern successful applications must be identified and quantified; ad hoc, trial and error approaches must be supplanted by rigorous theoretical foundations and practical, constructive algorithms. Recent developments in this direction have provided just such a framework, by combining into a single methodology elements of constructive approximation theory, nonlinear stability theory, and robust nonlinear adaptation and control techniques. This paper presents an overview of this methodology and illustrates it by reviewing the structure of “neural” adaptive robot controllers with guaranteed stability and convergence properties