An H∞-norm-based approach for operating point selection and LPV model identification from local experiments

Abstract

When the identification of linear parameter-varying (LPV) models from local experiments is considered, the question of the necessary number of local operating points as well as the problem of the efficient interpolation of the locally-estimated linear time-invariant models arise. These challenging problems are tackled herein by using the H∞-norm. First, thanks to the nu-gap metric, an heuristic technique is introduced to optimize the number as well as the position of the local operating points (along a given trajectory of the scheduling variables) with respect to the information brought by the local models. Having access to a reliable set of local models, the second step of the procedure, i.e., the parameter estimation step, consists of the optimization a second H∞-norm-based cost function measuring the fit between the local information (represented by the locally-estimated LTI models) and the local behavior of a parameterized global LPV model. A special attention is given to parameterized LPV models satisfying a fully-parametrized or a physically-structured linear fractional representation.