Related papers: Least Squares Model Reduction: A Two-Stage System-…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
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…
Two moment-matching methods for model reduction of linear switched systems (LSSs) are presented. The methods are similar to the Krylov subspace methods used for moment matching for linear systems. The more general one of the two methods, is…
In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full…
This work proposes a windowed least-squares (WLS) approach for model-reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space-time trial…
This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Two approaches to moment matching based model reduction of aperiodically sampled data systems are given. The term "aperiodic sampling" is used in the paper to indicate that the time between two consecutive sampling instants can take its…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
We propose a recursive least-squares method with multiple forgetting schemes to track time-varying model parameters which change with different rates. Our approach hinges on the reformulation of the classic recursive least-squares with…
We propose a two-stage penalized least squares method to build large systems of structural equations based on the instrumental variables view of the classical two-stage least squares method. We show that, with large numbers of endogenous…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in the constrained discrete-time state-space estimation, the state…