Related papers: H2 model reduction of linear network systems by mo…
In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…
H2-conic controller design seeks to minimize the closed-loop H2-norm for a nominal linear system while satisfying the Conic Sector Theorem for nonlinear stability. This problem has only been posed with limited design freedom, as opposed to…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…
In this paper, we bring together the worlds of model order reduction for stochastic linear systems and $\mathcal H_2$-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
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…
This paper investigates the optimal $H_2$ model order reduction for linear systems with quadratic outputs. In the framework of Galerkin projection, we first formulate the optimal $H_2$ MOR as an unconstrained Riemannian optimization problem…
We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013], which is…
We consider the problem of locating a nearest descriptor system of prescribed reduced order to a descriptor system with large order with respect to the ${\mathcal L}_\infty$ norm. Widely employed approaches such as the balanced truncation…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
In this paper, we compute a low order approximation of a system of large order $n$ that matches $\nu$ moments of order $j_i$ of the transfer function, at $\nu$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches…
The paper addresses the model reduction problem by least squares moment matching for continuous-time, linear, time-invariant systems. The basic idea behind least squares moment matching is to approximate a transfer function by ensuring that…
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 paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and…
This paper studies stability and symmetry preserving $H^2$ optimal model reduction problems of linear systems which include linear gradient systems as a special case. The problem is formulated as a nonlinear optimization problem on the…
We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…