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

Stability analysis of event-triggered anytime control with multiple control laws

To deal with time-varying processor availability and lossy communication channels in embedded and networked control systems, one can employ an event-triggered sequence-based anytime control (E-SAC) algorithm. The main idea of E-SAC is, when computing resources and measurements are available, to compute a sequence of tentative control inputs and store them in a buffer for potential future use. State-dependent Random-time Drift (SRD) approach is often used to analyse and establish stability properties of such E-SAC algorithms. However, using SRD, the analysis quickly becomes combinatoric and hence difficult to extend to more sophisticated E-SAC. In this technical note, we develop a general model and a new stability analysis for E-SAC based on Markov jump systems. Using the new stability analysis, stochastic stability conditions of existing E-SAC are also recovered. In addition, the proposed technique systematically extends to a more sophisticated E-SAC scheme for which, until now, no analytical expression had been obtained.Comment: Accepted for publication in IEEE Transactions on Automatic Contro

Towards a microscopic construction of flavour vacua from a space-time foam model

The effect on flavour oscillations of simple expanding background space-times, motivated by some D-particle foam models, is calculated for a toy-model of bosons with flavour degrees of freedom. The presence of D-particle defects in the space-time, which can interact non trivially (via particle capture) with flavoured particles in a flavour non-preserving way, generates mixing in the effective field theory of low-energy string excitations. Moreover, the recoil of the D-particle defect during the capture/scattering process implies Lorentz violation, which however may be averaged to zero in isotropic D-particle populations, but implies non-trivial effects in correlators. Both features imply that the flavoured mixed state sees a non-trivial flavour (Fock-space) vacuum of a type introduced earlier by Blasone and Vitiello in a generic context of theories with mixing. We discuss the orthogonality of the flavour vacua to the usual Fock vacua and the effect on flavour oscillations in these backgrounds. Furthermore we analyse the equation of state of the Flavour vacuum, and find that, for slow expansion rates induced by D particle recoil, it is equivalent to that of a cosmological constant. Some estimates of these novel non-perturbative contribution to the vacuum energy are made. The contribution vanishes if the mass difference and the mixing angle of the flavoured states vanish.Comment: 27 pages RevTex, 2 eps figures incorporate

Dynamical Evolution of the Extra Dimension in Brane Cosmology

The evolution of the extra dimension is investigated in the context of brane world cosmology. New cosmological solutions are found. In particular, solutions in the form of waves travelling along the extra dimension are identified.Comment: Latex file, 10 page

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

Geometric description of BTZ black holes thermodynamics

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction

Time and "angular" dependent backgrounds from stationary axisymmetric solutions

Backgrounds depending on time and on "angular" variable, namely polarized and unpolarized $S^1 \times S^2$ 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 $D$-branes, $iD$-branes allows one to find $S$-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzchild and the Kerr metrics. The possibility of studying the $i$-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized $S$-branes depending not only on time but also on an ``angular'' variable.Comment: 24 pages, 5 figures, corrected typos, references adde

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