7,582 research outputs found
H-infinity optimal control for infinite-dimensional systems with strictly negative generator
A simple form for the optimal H-infinity state feedback of linear time-invariant infinite-dimensional systems is derived. It is applicable to systems with bounded input and output operators and a closed, densely defined, self-adjoint and strictly negative state operator. However, unlike other state-space algorithms, the optimal control is calculated in one step. Furthermore, a closed-form expression for the L2-gain of the closed-loop system is obtained. The result is an extension of the finite-dimensional case, derived by the first two authors. Examples demonstrate the simplicity of synthesis as well as the performance of the control law
General computational approach for optimal fault detection
We propose a new computational approach to solve the optimal fault detection
problem in the most general setting. The proposed procedure is free of any technical assumptions
and is applicable to both proper and non-proper systems. This procedure forms the basis of
an integrated numerically reliable state-space algorithm, which relies on powerful descriptor
systems techniques to solve the underlying computational subproblems. The new algorithm has
been implemented into a Fault Detection Toolbox for Matlab
Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio
In this paper we consider the design of spectrally efficient time-limited
pulses for ultrawideband (UWB) systems using an overlapping pulse position
modulation scheme. For this we investigate an orthogonalization method, which
was developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set of
N orthogonal (L\"owdin) pulses, which remain time-limited and spectrally
efficient for UWB systems, from a set of N equidistant translates of a
time-limited optimal spectral designed UWB pulse. We derive an approximate
L\"owdin orthogonalization (ALO) by using circulant approximations for the Gram
matrix to obtain a practical filter implementation. We show that the centered
ALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tends
to infinity. The set of translates of the Nyquist pulse forms an orthonormal
basis or the shift-invariant space generated by the initial spectral optimal
pulse. The ALO transform provides a closed-form approximation of the L\"owdin
transform, which can be implemented in an analog fashion without the need of
analog to digital conversions. Furthermore, we investigate the interplay
between the optimization and the orthogonalization procedure by using methods
from the theory of shift-invariant spaces. Finally we develop a connection
between our results and wavelet and frame theory.Comment: 33 pages, 11 figures. Accepted for publication 9 Sep 201
Optimal rates of decay for operator semigroups on Hilbert spaces
We investigate rates of decay for -semigroups on Hilbert spaces under
assumptions on the resolvent growth of the semigroup generator. Our main
results show that one obtains the best possible estimate on the rate of decay,
that is to say an upper bound which is also known to be a lower bound, under a
comparatively mild assumption on the growth behaviour. This extends several
statements obtained by Batty, Chill and Tomilov (J. Eur. Math. Soc., vol.
18(4), pp. 853-929, 2016). In fact, for a large class of semigroups our
condition is not only sufficient but also necessary for this optimal estimate
to hold. Even without this assumption we obtain a new quantified asymptotic
result which in many cases of interest gives a sharper estimate for the rate of
decay than was previously available, and for semigroups of normal operators we
are able to describe the asymptotic behaviour exactly. We illustrate the
strength of our theoretical results by using them to obtain sharp estimates on
the rate of energy decay for a wave equation subject to viscoelastic damping at
the boundary.Comment: 25 pages. To appear in Advances in Mathematic
Transition from ergodic to explosive behavior in a family of stochastic differential equations
We study a family of quadratic stochastic differential equations in the
plane, motivated by applications to turbulent transport of heavy particles.
Using Lyapunov functions, we find a critical parameter value
such that when the system is
ergodic and when solutions are not defined for all
times. H\"{o}rmander's hypoellipticity theorem and geometric control theory are
also utilized.Comment: 35 pages, 6 figure
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