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The quadrature-based balanced truncation (QuadBT) framework of arXiv:2104.01006 is a non-intrusive reformulation of balanced truncation (BT), a classical projection-based model-order reduction technique for linear systems. QuadBT is…
We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for…
Quadrature-based approximation of Gramians in standard balanced truncation yields a non-intrusive, data-driven implementation that requires only transfer function samples on the imaginary axis, which can be measured experimentally. This…
This paper presents data-driven implementations of balanced truncation and several of its generalizations that rely exclusively on transfer function samples on the imaginary axis. Rather than implicitly approximating the Gramians via…
Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…
We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear~(QB) form via a process called…
This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
To implement deep learning models on edge devices, model compression methods have been widely recognized as useful. However, it remains unclear which model compression methods are effective for Structured State Space Sequence (S4) models…
This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The…
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…
This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject…
Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…