Abstract
We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivalent model using these functions is derived. This allows constructing reduced order models achieving interpolation in the Loewner sense.
Highlights
The goal of model order reduction is to determine a simplified model of a dynamical system while preserving some desired properties of the system itself, for example stability or steady state behaviour for selected signals
The Loewner matrix, see [23], is an important object that has been used in the development of reduced order models for linear time-invariant (LTI) systems, and in the solution of the so-called generalized realization problem for LTI systems, see [24]
These new objects are the left- and the right-Loewner matrices, and they can be interpreted as the input and output gains of a transformed experimental setup. This experimental setup involves encoding the interpolation points into two generators which are interconnected with the plant. This interpretation allows for a more sophisticated usage of the tools associated to the Loewner matrices, for example the authors have used this new interpretation to develop a model order reduction procedure for linear time-varying systems in [35]
Summary
The goal of model order reduction is to determine a simplified model of a dynamical system while preserving some desired properties of the system itself, for example stability or steady state behaviour for selected signals. This experimental setup involves encoding the interpolation points into two generators which are interconnected with the plant This interpretation allows for a more sophisticated usage of the tools associated to the Loewner matrices, for example the authors have used this new interpretation to develop a model order reduction procedure for linear time-varying systems in [35]. In this paper we utilize the state-space interpretation of the Loewner matrices to generalize the Loewner method for model reduction to nonlinear input-affine systems. We conclude this introduction by noting that this paper has been written in the same spirit as papers such as [24], [7], [8], [29], [36], [3]; it is a theoretical paper introducing ideas and tools for general nonlinear affine systems, and while comparison to other methods and large-scale numerical validation of this work is important this is the subject of further work relying on the methods built
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