Related papers: Model order reduction for bilinear systems with no…
In this paper, we consider the problem of finding surrogate models for large-scale second-order linear time-invariant systems with inhomogeneous initial conditions. For this class of systems, the superposition principle allows us to…
In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once…
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…
We propose two kinds of model order reduction methods for discrete time-delay systems with inhomogeneous initial conditions. The peculiar properties of discrete Walsh functions are directly utilized to compute the Walsh coefficients of the…
The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…
In this paper, we prove several new results that give new insights into bilinear systems. We discuss conditions for asymptotic stability using probabilistic arguments. Moreover, we provide a global characterization of reachability in…
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…
We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…
This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstra{\ss} canonical form and, thus, be decoupled into differential…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…
This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…
In this paper, we establish new strategies to reduce the dimension of large-scale controlled stochastic differential equations with non-zero initial states. The first approach transforms the original setting into a stochastic system with…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…