10,575 research outputs found
Frequency-Weighted Model Reduction with Applications to Structured Models
In this paper, a frequency-weighted extension of a
recently proposed model reduction method for linear systems
is presented. The method uses convex optimization and can be
used both with sample data and exact models. We also obtain
bounds on the frequency-weighted error. The method is combined
with a rank-minimization heuristic to approximate multiinput–
multi-output systems.We also present two applications—
environment compensation and simplification of interconnected
models — where we argue the proposed methods are useful
Order Reduction of the Chemical Master Equation via Balanced Realisation
We consider a Markov process in continuous time with a finite number of
discrete states. The time-dependent probabilities of being in any state of the
Markov chain are governed by a set of ordinary differential equations, whose
dimension might be large even for trivial systems. Here, we derive a reduced
ODE set that accurately approximates the probabilities of subspaces of interest
with a known error bound. Our methodology is based on model reduction by
balanced truncation and can be considerably more computationally efficient than
the Finite State Projection Algorithm (FSP) when used for obtaining transient
responses. We show the applicability of our method by analysing stochastic
chemical reactions. First, we obtain a reduced order model for the
infinitesimal generator of a Markov chain that models a reversible,
monomolecular reaction. In such an example, we obtain an approximation of the
output of a model with 301 states by a reduced model with 10 states. Later, we
obtain a reduced order model for a catalytic conversion of substrate to a
product; and compare its dynamics with a stochastic Michaelis-Menten
representation. For this example, we highlight the savings on the computational
load obtained by means of the reduced-order model. Finally, we revisit the
substrate catalytic conversion by obtaining a lower-order model that
approximates the probability of having predefined ranges of product molecules.Comment: 12 pages, 6 figure
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
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
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