Invertible nonlinear parametric functions for systems identification and control

✍ Scribed by Sergio M. Savaresi; Guido O. Guardabassi

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 463 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(19980730)8:9<741::aid-rnc342>3.0.co;2-5

✦ Synopsis

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 universal approximators. In this paper, a new class of parametric nonlinear functions, named piecewise multi-parabolic (PMP) functions, is presented. PMP functions can be considered a special class of quadratic splines (orto some extent -a class of Takagi-Sugeno models with triangular membership functions), the main feature of which is the way they are parametrized. Thanks to such a parametrization, imposing distributed constraints on their first (and second) derivatives, and, in particular, an invertibility constraint, is shown to be easy and computationally efficient.