687 research outputs found
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
Model reduction of networked passive systems through clustering
In this paper, a model reduction procedure for a network of interconnected
identical passive subsystems is presented. Here, rather than performing model
reduction on the subsystems, adjacent subsystems are clustered, leading to a
reduced-order networked system that allows for a convenient physical
interpretation. The identification of the subsystems to be clustered is
performed through controllability and observability analysis of an associated
edge system and it is shown that the property of synchronization (i.e., the
convergence of trajectories of the subsystems to each other) is preserved
during reduction. The results are illustrated by means of an example.Comment: 7 pages, 2 figures; minor changes in the final version, as accepted
for publication at the 13th European Control Conference, Strasbourg, Franc
Reduced order models for control of fluids using the Eigensystem Realization Algorithm
In feedback flow control, one of the challenges is to develop mathematical
models that describe the fluid physics relevant to the task at hand, while
neglecting irrelevant details of the flow in order to remain computationally
tractable. A number of techniques are presently used to develop such
reduced-order models, such as proper orthogonal decomposition (POD), and
approximate snapshot-based balanced truncation, also known as balanced POD.
Each method has its strengths and weaknesses: for instance, POD models can
behave unpredictably and perform poorly, but they can be computed directly from
experimental data; approximate balanced truncation often produces vastly
superior models to POD, but requires data from adjoint simulations, and thus
cannot be applied to experimental data.
In this paper, we show that using the Eigensystem Realization Algorithm (ERA)
\citep{JuPa-85}, one can theoretically obtain exactly the same reduced order
models as by balanced POD. Moreover, the models can be obtained directly from
experimental data, without the use of adjoint information. The algorithm can
also substantially improve computational efficiency when forming reduced-order
models from simulation data. If adjoint information is available, then balanced
POD has some advantages over ERA: for instance, it produces modes that are
useful for multiple purposes, and the method has been generalized to unstable
systems. We also present a modified ERA procedure that produces modes without
adjoint information, but for this procedure, the resulting models are not
balanced, and do not perform as well in examples. We present a detailed
comparison of the methods, and illustrate them on an example of the flow past
an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure
Balanced Truncation of Networked Linear Passive Systems
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 specifically selected generalized Gramians is implemented on the
asymptotically stable part of the full-order network model, which leads to a
reduced-order system preserving the passivity of each subsystem. Moreover, it
is proven that there exists a coordinate transformation to convert the
resulting reduced-order model to a state-space model of Laplacian dynamics.
Thus, the proposed method simultaneously reduces the complexity of the network
structure and individual agent dynamics, and it preserves the passivity of the
subsystems and the synchronization of the network. Moreover, it allows for the
a priori computation of a bound on the approximation error. Finally, the
feasibility of the method is demonstrated by an example
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