Related papers: Model order reduction for discrete time-delay syst…

Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the…

In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…

In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

This paper develops a closed-form spectral decomposition framework for the Gramian matrices of discrete-time linear dynamical systems. The main results provide explicit decompositions of the discrete-time controllability Gramian and its…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various…

This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point…

In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…

In this paper, we focus on model reduction of biomolecular systems with multiple time-scales, modeled using the Linear Noise Approximation. Considering systems where the Linear Noise Approximation can be written in singular perturbation…

Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…

Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

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…

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction…

When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…