290 research outputs found
Model Reduction using a Frequency-Limited H2-Cost
We propose a method for model reduction on a given frequency range, without
the use of input and output filter weights. The method uses a nonlinear
optimization approach to minimize a frequency limited H2 like cost function.
An important contribution in the paper is the derivation of the gradient of
the proposed cost function. The fact that we have a closed form expression for
the gradient and that considerations have been taken to make the gradient
computationally efficient to compute enables us to efficiently use
off-the-shelf optimization software to solve the optimization problem.Comment: Submitted to Systems and Control Letter
Towards Time-Limited -Optimal Model Order Reduction
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 and hence reduce computational complexity. A particular class of MOR
techniques are -optimal methods such as the iterative rational
Krylov subspace algorithm (IRKA) and related schemes. However, these methods
are used to obtain good approximations on a infinite time-horizon. Thus, in
this work, our main goal is to discuss MOR schemes for time-limited linear
systems. For this, we propose an alternative time-limited -norm
and show its connection with the time-limited Gramians. We then provide
first-order optimality conditions for an optimal reduced order model (ROM) with
respect to the time-limited -norm. Based on these optimality
conditions, we propose an iterative scheme, which, upon convergence, aims at
satisfying these conditions approximately. Then, we analyze how far away the
obtained ROM due to the proposed algorithm is from satisfying the optimality
conditions. We test the efficiency of the proposed iterative scheme using
various numerical examples and illustrate that the newly proposed iterative
method can lead to a better reduced-order compared to the unrestricted IRKA in
the finite time interval of interest
Empirical balanced truncation of nonlinear systems
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 fundamental solution for a Linear Time-Varying system. Relationships
between the given gramians for nonlinear systems and the standard gramians for
both Linear Time-Invariant and Linear Time-Varying systems are established as
well as relationships to prior constructions proposed for empirical gramians.
Application of the new gramians is illustrated through a sample test-system.Comment: LaTeX, 11 pages, 2 figure
emgr - The Empirical Gramian Framework
System Gramian matrices are a well-known encoding for properties of
input-output systems such as controllability, observability or minimality.
These so-called system Gramians were developed in linear system theory for
applications such as model order reduction of control systems. Empirical
Gramian are an extension to the system Gramians for parametric and nonlinear
systems as well as a data-driven method of computation. The empirical Gramian
framework - emgr - implements the empirical Gramians in a uniform and
configurable manner, with applications such as Gramian-based (nonlinear) model
reduction, decentralized control, sensitivity analysis, parameter
identification and combined state and parameter reduction
A Frequency-Limited H2 Model Approximation Method with Application to a Medium-Scale Flexible Aircraft
In this paper, the problem of approximating a medium-scale MIMO LTI dynamical system over a bounded frequency range is addressed. A new method based on the SVD-Tangential model order reduction framework is proposed. Grounded on the frequency-limited gramians defined in [5], the contribution of this paper is to propose a frequency-limited iterative SVD-Tangential interpolation algorithm (FL-ISTIA) to achieve frequency-limited model approximation without involving weighting filters. The efficiency of the approach is addressed both on standard benchmark and on an industrial flexible aircraft model
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