1,179 research outputs found
Finite dimensional quantizations of the (q,p) plane : new space and momentum inequalities
We present a N-dimensional quantization a la Berezin-Klauder or frame
quantization of the complex plane based on overcomplete families of states
(coherent states) generated by the N first harmonic oscillator eigenstates. The
spectra of position and momentum operators are finite and eigenvalues are
equal, up to a factor, to the zeros of Hermite polynomials. From numerical and
theoretical studies of the large behavior of the product of non null smallest positive and largest eigenvalues, we infer
the inequality (resp. ) involving, in suitable
units, the minimal () and maximal () sizes of
regions of space (resp. momentum) which are accessible to exploration within
this finite-dimensional quantum framework. Interesting issues on the
measurement process and connections with the finite Chern-Simons matrix model
for the Quantum Hall effect are discussed
Chaotic multi-objective optimization based design of fractional order PI{\lambda}D{\mu} controller in AVR system
In this paper, a fractional order (FO) PI{\lambda}D\mu controller is designed
to take care of various contradictory objective functions for an Automatic
Voltage Regulator (AVR) system. An improved evolutionary Non-dominated Sorting
Genetic Algorithm II (NSGA II), which is augmented with a chaotic map for
greater effectiveness, is used for the multi-objective optimization problem.
The Pareto fronts showing the trade-off between different design criteria are
obtained for the PI{\lambda}D\mu and PID controller. A comparative analysis is
done with respect to the standard PID controller to demonstrate the merits and
demerits of the fractional order PI{\lambda}D\mu controller.Comment: 30 pages, 14 figure
Polytopic invariant and contractive sets for closed-loop discrete fuzzy systems
In this work a procedure for obtaining polytopic lambda-contractive sets for Takagi Sugeno fuzzy systems is
presented, adapting well-known algorithms from literature on discrete-time linear difference inclusions
(LDI) to multi-dimensional summations. As a complexity parameter increases, these sets tend to the
maximal invariant set of the system when no information on the shape of the membership functions is
available. lambda-contractive sets are naturally associated to level sets of polyhedral Lyapunov functions proving a decay-rate of lambda. The paper proves that the proposed algorithm obtains better results than a class of Lyapunov methods for the same complexity degree: if such a Lyapunov function exists, the proposed
algorithm converges in a finite number of steps and proves a larger lambda-contractive set.This work has been supported by Projects DPI2011-27845-C02-01 and DPI2011-27845-C02-02, both from Spanish Government.Arino, C.; Perez, E.; Sala Piqueras, A.; Bedate, F. (2014). Polytopic invariant and contractive sets for closed-loop discrete fuzzy systems. Journal of The Franklin Institute. 351(7):3559-3576. https://doi.org/10.1016/j.jfranklin.2014.03.014S35593576351
Tree Regular Model Checking for Lattice-Based Automata
Tree Regular Model Checking (TRMC) is the name of a family of techniques for
analyzing infinite-state systems in which states are represented by terms, and
sets of states by Tree Automata (TA). The central problem in TRMC is to decide
whether a set of bad states is reachable. The problem of computing a TA
representing (an over- approximation of) the set of reachable states is
undecidable, but efficient solutions based on completion or iteration of tree
transducers exist. Unfortunately, the TRMC framework is unable to efficiently
capture both the complex structure of a system and of some of its features. As
an example, for JAVA programs, the structure of a term is mainly exploited to
capture the structure of a state of the system. On the counter part, integers
of the java programs have to be encoded with Peano numbers, which means that
any algebraic operation is potentially represented by thousands of applications
of rewriting rules. In this paper, we propose Lattice Tree Automata (LTAs), an
extended version of tree automata whose leaves are equipped with lattices. LTAs
allow us to represent possibly infinite sets of interpreted terms. Such terms
are capable to represent complex domains and related operations in an efficient
manner. We also extend classical Boolean operations to LTAs. Finally, as a
major contribution, we introduce a new completion-based algorithm for computing
the possibly infinite set of reachable interpreted terms in a finite amount of
time.Comment: Technical repor
Takagi-Sugeno Fuzzy Model Based Discrete Time Model Predictive Control for a Hypersonic Re-Entry Vehicle
In this thesis, we present a control algorithm for a hypersonic re-entry vehicle during a Martian aerocapture maneuver. The proposed algorithm utilizes a discrete-time model predictive control technique with a Takagi-Sugeno fuzzy model of the vehicle to control the re-entry vehicle along an arbitrary trajectory using bank angle modulation. Simulations using model parameters and initial conditions from a Martian aerocapture mission demonstrate the stability, performance, and robustness of the proposed controller
Hyperspectral images segmentation: a proposal
Hyper-Spectral Imaging (HIS) also known as chemical or spectroscopic imaging is an emerging technique that combines
imaging and spectroscopy to capture both spectral and spatial information from an object. Hyperspectral images are
made up of contiguous wavebands in a given spectral band. These images provide information on the chemical
make-up profile of objects, thus allowing the differentiation of objects of the same colour but which possess make-up
profile. Yet, whatever the application field, most of the methods devoted to HIS processing conduct data analysis without
taking into account spatial information.Pixels are processed individually, as an array of spectral data without any spatial
structure. Standard classification approaches are thus widely used (k-means, fuzzy-c-means hierarchical
classification...). Linear modelling methods such as Partial Least Square analysis (PLS) or non linear approaches like
support vector machine (SVM) are also used at different scales (remote sensing or laboratory applications). However,
with the development of high resolution sensors, coupled exploitation of spectral and spatial information to process
complex images, would appear to be a very relevant approach. However, few methods are proposed in the litterature.
The most recent approaches can be broadly classified in two main categories. The first ones are related to a direct
extension of individual pixel classification methods using just the spectral dimension (k-means, fuzzy-c-means or FCM,
Support Vector Machine or SVM). Spatial dimension is integrated as an additionnal classification parameter (Markov
fields with local homogeneity constrainst [5], Support Vector Machine or SVM with spectral and spatial kernels
combination [2], geometrically guided fuzzy C-means [3]...). The second ones combine the two fields related to each
dimension (spectral and spatial), namely chemometric and image analysis. Various strategies have been attempted. The
first one is to rely on chemometrics methods (Principal Component Analysis or PCA, Independant Component Analysis or
ICA, Curvilinear Component Analysis...) to reduce the spectral dimension and then to apply standard images processing technics on the resulting score images i.e. data projection on a subspace. Another approach is to extend the definition
of basic image processing operators to this new dimensionality (morphological operators for example [1, 4]).
However, the approaches mentioned above tend to favour only one description either directly or indirectly (spectral or
spatial). The purpose of this paper is to propose a hyperspectral processing approach that strikes a better balance in the
treatment of both kinds of information....Cet article présente une stratégie de segmentation d’images hyperspectrales liant de façon symétrique et
conjointe les aspects spectraux et spatiaux. Pour cela, nous proposons de construire des variables latentes
permettant de définir un sous-espace représentant au mieux la topologie de l’image. Dans cet article, nous
limiterons cette notion de topologie à la seule appartenance aux régions. Pour ce faire, nous utilisons d’une
part les notions de l’analyse discriminante (variance intra, inter) et les propriétés des algorithmes de
segmentation en région liées à celles-ci. Le principe générique théorique est exposé puis décliné sous la
forme d’un exemple d’implémentation optimisé utilisant un algorithme de segmentation en région type split
and merge. Les résultats obtenus sur une image de synthèse puis réelle sont exposés et commentés
- …