Set-membership nonlinear regression approach to parameter estimation. (October 2018) - Perić, Nikola D.; Paulen, Radoslav; Villanueva, Mario E.; Chachuat, Benoît
Highlights: The paper contributes set-membership regression (SMR), a new approach to nonlinear parameter estimation under measurement uncertainty. Links between SMR and both guaranteed parameter estimation and classical statistical inference are investigated. Several approaches to describing tight enclosures of the SMR regions using complete- search methods are developed. Case studies are presented to illustrate various theoretical and computational aspects of SMR. Abstract: This paper introduces set-membership nonlinear regression (SMR), a new approach to nonlinear regression under uncertainty. The problem is to determine the subregion in parameter space enclosing all (global) solutions to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigate the connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within bounded measurement errors. We also develop a computational framework to describe tight enclosures of the SMR regions using semi-infinite programming and complete-search methods, in the form of likelihood contour and polyhedral enclosures. The case study of a parameter estimation problem in microbial growth is presented to illustrate various theoretical and computational aspects of the SMR approach.