Robust identification/invalidation in an LPV framework

Abstract

SUMMARYA robust linear parameter varying (LPV) identification/invalidation method is presented. Starting from a given initial model, the proposed method modifies it and produces an LPV model consistent with the assumed uncertainty/noise bounds and the experimental information. This procedure may complement existing nominal LPV identification algorithms, by adding the uncertainty and noise bounds which produces a set of models consistent with the experimental evidence. Unlike standard invalidation results, the proposed method allows the computation of the necessary changes to the initial model in order to place it within the consistency set. Similar to previous LPV identification procedures, the initial parameter dependency is fixed in advance, but here a methodology to modify this dependency is presented. In addition, all calculations are made on state-space matrices which simplifies further controller design computations. The application of the proposed method to the identification of nonlinear systems is also discussed.

A convex optimization approach to model (in)validation of switched ARX systems with unknown switches

“…Thus, a key step before using the resulting models, is to (in)validate them using additional experimental data. In the case where the mode variable can be directly measured, the problem is closely related to that of validating Linear Parameter Varying (LPV) models and can be solved using techniques similar to those proposed in [19], [3]. However, in many practical situations, the mode variable is not directly available.…”

Set-membership LPV model identification of vehicle lateral dynamics

“…Only few contributions can be found in the literature addressing the identification of LPV models when the measurement errors are supposed to be bounded. In (Sznaier and Mazzarro, 2003;Bianchi and Sanchez-Pena, 2010) identification and model invalidation of LPV systems in presence of bounded noise and a possible nonparametric part is considered. Belforte and Gay (Belforte and Gay, 2004) consider the identification of discrete-time LPV models with finite impulse response structure and output measurements affected by bounded noise.…”

Incremental closed-loop identification of linear parameter varying systems

“…[7] presents a simple ARX method; [8] proposes a control-oriented identification framework that relies on solution of a set of Linear Matrix Inequalities. [9] considers robust invalidation of candidate LPV models. [10] discusses an approach where linear local models in a number of operating points are found by applying standard identifications procedures for linear systems in time domain.…”