648 research outputs found
Type II balanced truncation for deterministic bilinear control systems
When solving partial differential equations numerically, usually a high order
spatial discretisation is needed. Model order reduction (MOR) techniques are
often used to reduce the order of spatially-discretised systems and hence
reduce computational complexity. A particular MOR technique to obtain a reduced
order model (ROM) is balanced truncation (BT), a method which has been
extensively studied for deterministic linear systems. As so-called type I BT it
has already been extended to bilinear equations, an important subclass of
nonlinear systems. We provide an alternative generalisation of the linear
setting to bilinear systems which is called type II BT. The Gramians that we
propose in this context contain information about the control. It turns out
that the new approach delivers energy bounds which are not just valid in a
small neighbourhood of zero. Furthermore, we provide an -error bound
which so far is not known when applying type I BT to bilinear systems
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
Dynamic programming for optimal stopping via pseudo-regression
We introduce new variants of classical regression-based algorithms for
optimal stopping problems based on computation of regression coefficients by
Monte Carlo approximation of the corresponding inner products instead of
the least-squares error functional. Coupled with new proposals for simulation
of the underlying samples, we call the approach "pseudo regression". A detailed
convergence analysis is provided and it is shown that the approach
asymptotically leads to less computational cost for a pre-specified error
tolerance, hence to lower complexity. The method is justified by numerical
examples
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Type II singular perturbation approximation for linear systems with Lévy noise
When solving linear stochastic partial differential equations
numerically, usually a high order spatial discretisation is needed. Model
order reduction (MOR) techniques are often used to reduce the order of
spatially-discretised systems and hence reduce computational complexity. A
particular MOR technique to obtain a reduced order model (ROM) is singular
perturbation approximation (SPA), a method which has been extensively studied
for deterministic systems. As so-called type I SPA it has already been
extended to stochastic equations. We provide an alternative generalisation of
the deterministic setting to linear systems with Lévy noise which is called
type II SPA. It turns out that the ROM from applying type II SPA has better
properties than the one of using type I SPA. In this paper, we provide new
energy interpretations for stochastic reachability Gramians, show the
preservation of mean square stability in the ROM by type II SPA and prove two
different error bounds for type II SPA when applied to Lévy driven systems
Information Management System for the California State Water Resources Control Board (SWRCB)
A study was made to establish the requirements for an integrated state-wide information management system for water quality control and water quality rights for the State of California. The data sources and end requirements were analyzed for the data collected and used by the numerous agencies, both State and Federal, as well as the nine Regional Boards under the jurisdiction of the State Board. The report details the data interfaces and outlines the system design. A program plan and statement of work for implementation of the project is included
Beyond Nationalism? Blank Spaces at the documenta 1955 – The Legacy of an Exhibition Between Old Europe and New World Order
Was the first documenta really beyond nationalism? documenta 1955 has been widely regarded as conciliation for the fascist legacy of the exhibition “Degenerate Art” (1937), and as an attempt to reintegrate Germany into the international arts community. This article employs published and archival sources in order to understand if and how documenta was impacted by the legacy of nationalism in post-fascist Germany. A biographic sketch of Antonio Corpora (1909-2004) shows how the purportedly “universalist” selection criteria employed by documenta erased cultural specificity and solidified nationalist conceptions of center and periphery
Biological Monitoring of the Capsule Mechanical Training Model During Assembly in the Sterilization Assembly Development Laboratory
Microbial burden sterilization assembly procedure development using rigorous monitoring progra
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