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Robust H∞ control for discrete-time fuzzy systems with infinite-distributed delays
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust H∞ control problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays and uncertain parameters. The time delay is assumed to be infinitely distributed in the discrete-time domain, and the uncertain parameters are norm-bounded. By using the linear matrix inequality (LMI) technique, sufficient conditions are derived for ensuring the exponential stability as well as the H infin performance for the closed-loop fuzzy control system. It is also shown that the controller gain can be characterized in terms of the solution to a set of LMIs, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out
This paper investigates the evolution of strategic play where players drawn
from a finite well-mixed population are offered the opportunity to play in a
public goods game. All players accept the offer. However, due to the
possibility of unforeseen circumstances, each player has a fixed probability of
being unable to participate in the game, unlike similar models which assume
voluntary participation. We first study how prescribed stochastic opting-out
affects cooperation in finite populations. Moreover, in the model, cooperation
is favored by natural selection over both neutral drift and defection if return
on investment exceeds a threshold value defined solely by the population size,
game size, and a player's probability of opting-out. Ultimately, increasing the
probability that each player is unable to fulfill her promise of participating
in the public goods game facilitates natural selection of cooperators. We also
use adaptive dynamics to study the coevolution of cooperation and opting-out
behavior. However, given rare mutations minutely different from the original
population, an analysis based on adaptive dynamics suggests that the over time
the population will tend towards complete defection and non-participation, and
subsequently, from there, participating cooperators will stand a chance to
emerge by neutral drift. Nevertheless, increasing the probability of
non-participation decreases the rate at which the population tends towards
defection when participating. Our work sheds light on understanding how
stochastic opting-out emerges in the first place and its role in the evolution
of cooperation.Comment: 30 pages, 4 figures. This is one of the student project papers arsing
from the Mathematics REU program at Dartmouth 2017 Summer. See
https://math.dartmouth.edu/~reu/ for more info. Comments are always welcom
The Beylkin-Cramer Summation Rule and A New Fast Algorithm of Cosmic Statistics for Large Data Sets
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm
that enable us to explore the high order statistics efficiently in large data
sets. Central to this technique is to make decomposition both of fields and
operators within the framework of multi-resolution analysis (MRA), and realize
theirs discrete representations. Accordingly, a homogenous point process could
be equivalently described by a operation of a Toeplitz matrix on a vector,
which is accomplished by making use of fast Fourier transformation. The
algorithm could be applied widely in the cosmic statistics to tackle large data
sets. Especially, we demonstrate this novel technique using the spherical,
cubic and cylinder counts in cells respectively. The numerical test shows that
the algorithm produces an excellent agreement with the expected results.
Moreover, the algorithm introduces naturally a sharp-filter, which is capable
of suppressing shot noise in weak signals. In the numerical procedures, the
algorithm is somewhat similar to particle-mesh (PM) methods in N-body
simulations. As scaled with , it is significantly faster than the
current particle-based methods, and its computational cost does not relies on
shape or size of sampling cells. In addition, based on this technique, we
propose further a simple fast scheme to compute the second statistics for
cosmic density fields and justify it using simulation samples. Hopefully, the
technique developed here allows us to make a comprehensive study of
non-Guassianity of the cosmic fields in high precision cosmology. A specific
implementation of the algorithm is publicly available upon request to the
author.Comment: 27 pages, 9 figures included. revised version, changes include (a)
adding a new fast algorithm for 2nd statistics (b) more numerical tests
including counts in asymmetric cells, the two-point correlation functions and
2nd variances (c) more discussions on technic
Baryon electric dipole moments from strong CP violation
The electric dipole form factors and moments of the ground state baryons are
calculated in chiral perturbation theory at next-to-leading order. We show that
the baryon electric dipole form factors at this order depend only on two
combinations of low-energy constants. We also derive various relations that are
free of unknown low-energy constants. We use recent lattice QCD data to
calculate all baryon EDMs. In particular, we find d_n = -2.9\pm 0.9 and d_p =
1.1\pm 1.1 in units of 10^{-16} e \theta_0 cm. Finite volume corrections to the
moments are also worked out. We show that for a precision extraction from
lattice QCD data, the next-to-leading order terms have to be accounted for.Comment: 30 pages, 8 figures, to appear in JHE
Corrugated structure insertion for extending the SASE bandwidth up to 3% at the European XFEL
The usage of x-ray free electron laser (XFEL) in femtosecond
nanocrystallography involves sequential illumination of many small crystals of
arbitrary orientation. Hence a wide radiation bandwidth will be useful in order
to obtain and to index a larger number of Bragg peaks used for determination of
the crystal orientation. Considering the baseline configuration of the European
XFEL in Hamburg, and based on beam dynamics simulations, we demonstrate here
that the usage of corrugated structures allows for a considerable increase in
radiation bandwidth. Data collection with a 3% bandwidth, a few microjoule
radiation pulse energy, a few femtosecond pulse duration, and a photon energy
of 5.4 keV is possible. For this study we have developed an analytical modal
representation of the short-range wake function of the flat corrugated
structures for arbitrary offsets of the source and the witness particles.Comment: 29 pages, 17 figure
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