Loewner Framework Research Articles

Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model

Computing responses to discrete gusts are sizing steps when designing and optimizing a new aircraft structure and geometry. Indeed, this is part of the imposed clearance certifications requested by the flight authorities. During the aircraft preliminary design phase, this clearance is done by intensive simulations, however, due to the involved models complexity, these latter are time consuming and imply an important computational burden. Especially as these simulations are involved at different steps of the aircraft optimisation process e.g. by aeroelastic, flight and control engineers. In this paper we propose a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework. The proposed approach gathers recent advances in aeroelastic modelling and model approximation techniques. As illustrated on a high fidelity long range aircraft model, the drastic reduction of the simulation time does not induce any significant loss of accuracy.

Frequency-domain data-driven control design in the Loewner framework

In this article, a direct data-driven design method, based on frequency-domain data, is proposed. The identification of the plant is skipped and the controller is designed directly from the measurements. The identification task is reported on a fixed-order controller using for the first time the Loewner approach, known for model approximation and reduction. The method is validated on two numerical examples including the control of an industrial hydroelectric generation plant, modelled by irrational equations.

Data-driven interpolation of dynamical systems with delay

We present a data-driven realization for systems with delay, which generalizes the Loewner framework. The realization is obtained with low computational cost directly from measured data of the transfer function. The internal delay is estimated by solving a least-square optimization over some sample data. Our approach is validated by several examples, which indicate the need for preserving the delay structure in the reduced model.

Reprint of “A bilinear differential forms approach to parametric structured state-space modelling”

We use one-variable Loewner techniques to compute polynomial-parametric models for MIMO systems from vector-exponential data gathered at various points in the parameter space. Instrumental in our approach are the connections between vector-exponential modelling via bilinear differential forms and the Loewner framework.

A bilinear differential forms approach to parametric structured state-space modelling

We use one-variable Loewner techniques to compute polynomial-parametric models for MIMO systems from vector-exponential data gathered at various points in the parameter space. Instrumental in our approach are the connections between vector-exponential modelling via bilinear differential forms and the Loewner framework.

Model Reduction of Bilinear Systems in the Loewner Framework

The Loewner framework for model reduction is extended to the class of bilinear systems. The main advantage of this framework over existing ones is that the Loewner pencil introduces a trade-off between accuracy and complexity. Furthermore, through this framework, one can derive state-space models directly from input-output data without requiring initial system matrices. The recently introduced methodology of Volterra series interpolation is also addressed. Several numerical experiments illustrate the main features of this approach.

The Loewner framework and transfer functions of singular/rectangular systems

A connection is established between the Loewner framework for model reduction and the generalized inverses of singular and rectangular matrices. In this context both the Moore–Penrose and the Drazin inverses are involved. As a consequence this approach yields transfer functions for singular and rectangular systems. Thus the Loewner framework constitutes a natural and direct way for constructing models from measured input/output data.

Data-driven model reduction for weakly nonlinear systems: A summary

Model reduction seeks to replace complex dynamical systems with simpler ones, having similar characteristics. One approach is data-driven reduction based on system data which are either measured or computed. In this regard the Loewner framework is a powerful tool for dealing with the reduction of both linear and nonlinear systems.