Non-linear set-membership identification approach based on the Bayesian framework

This study deals with the problem of set-membership identification of non-linear-in-the-parameters models. To solve this problem, this study illustrates how the Bayesian approach can be used to determine the feasible parameter set (FPS) by assuming uniform distributed estimation error and flat model prior probability distributions. The key point of the methodology is the interval evaluation of the likelihood function and the result is a set of boxes with associated credibility indices. For each box, the credibility index is in the interval (0, 1] and gives information about the amount of consistent models inside the box. The union of the boxes with credibility value equal to one provides an inner approximation of the FPS, whereas the union of all boxes provides an outer estimation. The boxes with credibility value smaller than one are located around the boundary of the FPS and their credibility index can be used to iteratively refine the inner and outer approximations up to a desired precision. The main issues and performance of the developed algorithms are discussed and illustrated by means of examples.