A fast approximation algorithm for Set-Membership system identification

The Set Membership nonlinear identification method is a flexible technique, suitable for the identification of non-linear systems where no information on the system structure is available. This method generates a non-parametric model, embedded on the identification data set, with optimality properties and bounds on the possible values the variable can assume. However, the complexity of the model grows with the product of the input dimension and the size of the data set. This is problematic when a big data set is employed. In this paper, the nearest point approximation to the exact Set Membership model, found in literature, is analyzed and a novel approximation is proposed, whose complexity does not depend on the size of the data set. Guaranteed bounds on the worst-case approximation error are given. Two examples, considering simulated and experimental data, illustrate the validity and applicability of the obtained results. © 2011 IFAC.