7,499 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
Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
We study reduced-order models of three-dimensional perturbations in
linearized channel flow using balanced proper orthogonal decomposition (BPOD).
The models are obtained from three-dimensional simulations in physical space as
opposed to the traditional single-wavenumber approach, and are therefore better
able to capture the effects of localized disturbances or localized actuators.
In order to assess the performance of the models, we consider the impulse
response and frequency response, and variation of the Reynolds number as a
model parameter. We show that the BPOD procedure yields models that capture the
transient growth well at a low order, whereas standard POD does not capture the
growth unless a considerably larger number of modes is included, and even then
can be inaccurate. In the case of a localized actuator, we show that POD modes
which are not energetically significant can be very important for capturing the
energy growth. In addition, a comparison of the subspaces resulting from the
two methods suggests that the use of a non-orthogonal projection with adjoint
modes is most likely the main reason for the superior performance of BPOD. We
also demonstrate that for single-wavenumber perturbations, low-order BPOD
models reproduce the dominant eigenvalues of the full system better than POD
models of the same order. These features indicate that the simple, yet accurate
BPOD models are a good candidate for developing model-based controllers for
channel flow.Comment: 35 pages, 20 figure
Dynamics of aerospace vehicles
The focus of this research was to address the modeling, including model reduction, of flexible aerospace vehicles, with special emphasis on models used in dynamic analysis and/or guidance and control system design. In the modeling, it is critical that the key aspects of the system being modeled be captured in the model. In this work, therefore, aspects of the vehicle dynamics critical to control design were important. In this regard, fundamental contributions were made in the areas of stability robustness analysis techniques, model reduction techniques, and literal approximations for key dynamic characteristics of flexible vehicles. All these areas are related. In the development of a model, approximations are always involved, so control systems designed using these models must be robust against uncertainties in these models
Motif Statistics and Spike Correlations in Neuronal Networks
Motifs are patterns of subgraphs of complex networks. We studied the impact
of such patterns of connectivity on the level of correlated, or synchronized,
spiking activity among pairs of cells in a recurrent network model of integrate
and fire neurons. For a range of network architectures, we find that the
pairwise correlation coefficients, averaged across the network, can be closely
approximated using only three statistics of network connectivity. These are the
overall network connection probability and the frequencies of two second-order
motifs: diverging motifs, in which one cell provides input to two others, and
chain motifs, in which two cells are connected via a third intermediary cell.
Specifically, the prevalence of diverging and chain motifs tends to increase
correlation. Our method is based on linear response theory, which enables us to
express spiking statistics using linear algebra, and a resumming technique,
which extrapolates from second order motifs to predict the overall effect of
coupling on network correlation. Our motif-based results seek to isolate the
effect of network architecture perturbatively from a known network state
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