INVERTIBLE NONLINEAR PARAMETRIC FUNCTIONS FOR SYSTEMS IDENTIFICATION AND CONTROL

In the field of data-based control system design, nonlinear parametric functions play a key role, in fitting sets of measured data. In many cases, one of the constraints one may wish to impose on the estimated function is the invertibility with respect to one input, a constraint typically hard to handle rigorously with the currently available unive rsal approximators. In this paper, a new class of parametric nonlinear functions, named piecewise multi-parabolic (PMP) functions, is presen ted. PMP functions can be considered a special class of quadratic spli nes (or - to some extent - a class of Takagi-Sugeno models with triang ular membership functions), the main feature of which is the way they are parametrized. Thanks to such a parametrization, imposing distribut ed constraints on their first land second) derivatives, and, in partic ular, an invertibility constraint, is shown to be easy and computation ally efficient. (C) 1998 John Wiley & Sons, Ltd.