DeepAI AI Chat
Log In Sign Up

A framework for fitting quadratic-bilinear systems with applications to models of electrical circuits

12/02/2021
by   Dimitrios S. Karachalios, et al.
0

In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the original model into a quadratic-bilinear format. Here, data represent generalized transfer function values. This method is an extension of methods that do bilinear, or quadratic inference, separately. It is based on first fitting a linear model with the classical Loewner framework, and then on inferring the best supplementing nonlinear operators, in a least-squares sense. The application scope of this method is given by electrical circuits with nonlinear components (such as diodes). We propose various test cases to illustrate the performance of the method.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/13/2020

Toward fitting structured nonlinear systems by means of dynamic mode decomposition

The dynamic mode decomposition (DMD) is a data-driven method used for id...
11/25/2020

Learning reduced-order models of quadratic control systems from input-output data

In this paper, we address an extension of the Loewner framework for lear...
05/05/2023

A technical note on bilinear layers for interpretability

The ability of neural networks to represent more features than neurons m...
04/27/2023

Structured interpolation for multivariate transfer functions of quadratic-bilinear systems

High-dimensional/high-fidelity nonlinear dynamical systems appear natura...
01/13/2022

Neural Koopman Lyapunov Control

Learning and synthesizing stabilizing controllers for unknown nonlinear ...
07/08/2021

Existence of The Solution to The Quadratic Bilinear Equation Arising from A Class of Quadratic Dynamical Systems

A quadratic dynamical system with practical applications is taken into c...
10/23/2019

A Unifying Framework of Bilinear LSTMs

This paper presents a novel unifying framework of bilinear LSTMs that ca...