A local identification method for linear parameter-varying systems based on interpolation of state-space matrices and least-squares approximation. (1st January 2017) - Ferranti, Francesco; Rolain, Yves
Abstract: This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results. Abstract : Highlights: We present a novel local approach to model linear parameter-varying (LPV) systems. Linear state coordinate transformations extracted for a set of local LTI models. Similarity transformation matrices computed by linear least-squares approximations. Least-squares-based algorithms with fixed and dynamic reference state trajectories. This LPV modeling method is easy-to-implement and relies on robust numerical tools.