1,231 research outputs found
Maximum Hands-Off Control: A Paradigm of Control Effort Minimization
In this paper, we propose a new paradigm of control, called a maximum
hands-off control. A hands-off control is defined as a control that has a short
support per unit time. The maximum hands-off control is the minimum support (or
sparsest) per unit time among all controls that achieve control objectives. For
finite horizon control, we show the equivalence between the maximum hands-off
control and L1-optimal control under a uniqueness assumption called normality.
This result rationalizes the use of L1 optimality in computing a maximum
hands-off control. We also propose an L1/L2-optimal control to obtain a smooth
hands-off control. Furthermore, we give a self-triggered feedback control
algorithm for linear time-invariant systems, which achieves a given sparsity
rate and practical stability in the case of plant disturbances. An example is
included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear
Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization
We introduce normal coordinates on the infinite dimensional group
introduced by Connes and Kreimer in their analysis of the Hopf algebra of
rooted trees. We study the primitive elements of the algebra and show that they
are generated by a simple application of the inverse Poincar\'e lemma, given a
closed left invariant 1-form on . For the special case of the ladder
primitives, we find a second description that relates them to the Hopf algebra
of functionals on power series with the usual product. Either approach shows
that the ladder primitives are given by the Schur polynomials. The relevance of
the lower central series of the dual Lie algebra in the process of
renormalization is also discussed, leading to a natural concept of
-primitiveness, which is shown to be equivalent to the one already in the
literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy
Geometric Thermodynamics of Schwarzschild-AdS black hole with a Cosmological Constant as State Variable
The thermodynamics of the Schwarzschild-AdS black hole is reformulated within
the context of the recently developed formalism of geometrothermodynamics
(GTD). Different choices of the metric in the equilibrium states manifold are
used in order to reproduce the Hawking-Page phase transition as a divergence of
the thermodynamical curvature scalar. We show that the enthalpy and total
energy representations of GTD does not reproduce the transition while the
entropy rep- resentation gives the expected behavior.Comment: 14 page
Quantum bounds for gravitational de Sitter entropy and the Cardy-Verlinde formula
We analyze different types of quantum corrections to the Cardy-Verlinde
entropy formula in a Friedmann-Robertson-Walker universe and in an (anti)-de
Sitter space. In all cases we show that quantum corrections can be represented
by an effective cosmological constant which is then used to redefine the
parameters entering the Cardy-Verlinde formula so that it becomes valid also
with quantum corrections, a fact that we interpret as a further indication of
its universality. A proposed relation between Cardy-Verlinde formula and the
ADM Hamiltonian constraint is given.Comment: LaTeX file, 15 pages, reference is adde
Time and "angular" dependent backgrounds from stationary axisymmetric solutions
Backgrounds depending on time and on "angular" variable, namely polarized and
unpolarized Gowdy models, are generated as the sector inside
the horizons of the manifold corresponding to axisymmetric solutions. As is
known, an analytical continuation of ordinary -branes, -branes allows
one to find -brane solutions. Simple models have been constructed by means
of analytic continuation of the Schwarzchild and the Kerr metrics. The
possibility of studying the -Gowdy models obtained here is outlined with an
eye toward seeing if they could represent some kind of generalized -branes
depending not only on time but also on an ``angular'' variable.Comment: 24 pages, 5 figures, corrected typos, references adde
Towards the entropy of gravity time-dependent models via the Cardy-Verlinde formula
For models with several time-dependent components generalized entropies can
be defined. This is shown for the Bianchi type IX model. We first derive the
Cardy-Verlinde formula under the assumption that the first law of
thermodynamics is valid. This leads to an explicit expression of the total
entropy associated with this type of universes. Assuming the validity of the
Cardy entropy formula, we obtain expressions for the corresponding Bekenstein,
Bekenstein-Hawking and Hubble entropies. We discuss the validity of the
Cardy-Verlinde formula and possible extensions of the outlined procedure to
other time-dependent models.Comment: 13 page
Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
We study the thermodynamics and the thermodynamic geometries of charged
rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the
thermodynamics of these systems within the context of the Weinhold and
Ruppeiner thermodynamic geometries and the recently developed formalism of
geometrothermodynamics (GTD). Considering the behavior of the heat capacity and
the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot
describe completely the thermodynamics of these black holes and of their
limiting case of vanishing electric charge. In contrast, the Legendre
invariance imposed on the metric in GTD allows one to describe the CR-BTZ black
holes and their limiting cases in a consistent and invariant manner
The Abelian Topological Mass Mechanism From Dimensional Reduction
We show that the abelian topological mass mechanism in four dimensions,
described by the Cremmer-Sherk action, can be obtained from dimensional
reduction in five dimensions. Starting from a gauge invariant action in five
dimensions, where the dual equivalence between a massless vector field and a
massless second-rank antisymmetric field in five dimensions is established, the
dimensional reduction is performed keeping only one massive mode. Furthermore,
the Kalb-Ramond action and the Stuckelberger formulation for massive spin-1 are
recovered.Comment: Three references added, 6 pages, late
TeV-Scale Z' Bosons from D-branes
Generic D-brane string models of particle physics predict the existence of
extra U(1) gauge symmetries beyond hypercharge. These symmetries are not of the
E_6 class but rather include the gauging of Baryon and Lepton numbers as well
as certain Peccei-Quinn-like symmetries. Some of the U(1)'s have triangle
anomalies, but they are cancelled by a Green-Schwarz mechanism. The
corresponding gauge bosons typically acquire a mass of order the string scale
M_S by combining with two-index antisymmetric fields coming from the closed
string sector of the theory. We argue that in string models with a low string
scale M_S proportional to 1-10 TeV, the presence of these generic U(1)'s may be
amenable to experimental test. Present constraints from electroweak precision
data already set important bounds on the mass of these extra gauge bosons. In
particular, for large classes of models, rho-parameter constraints imply M_S >=
1.5 TeV. In the present scheme some fraction of the experimentally measured Z^0
mass would be due not to the Higgs mechanism, but rather to the mixing with
these closed string fields. We give explicit formulae for recently constructed
classes of intersecting D6- and D5-brane models yielding the Standard Model
(SM) fermion spectrum.Comment: 46 pages, LaTeX, JHEP.cls, 21 Figures. minor correction
Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory
We investigate the thermodynamic properties of 5D static and spherically
symmetric black holes in (i) Einstein-Maxwell-Gauss-Bonnet theory, (ii)
Einstein-Maxwell-Gauss-Bonnet theory with negative cosmological constant, and
in (iii) Einstein-Yang-Mills-Gauss-Bonnet theory. To formulate the
thermodynamics of these black holes we use the Bekenstein-Hawking entropy
relation and, alternatively, a modified entropy formula which follows from the
first law of thermodynamics of black holes. The results of both approaches are
not equivalent. Using the formalism of geometrothermodynamics, we introduce in
the manifold of equilibrium states a Legendre invariant metric for each black
hole and for each thermodynamic approach, and show that the thermodynamic
curvature diverges at those points where the temperature vanishes and the heat
capacity diverges.Comment: New sections added, references adde
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