Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values

This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE.

Equações com impasse e problemas de perturbação singular

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On singularly perturbed Filippov systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Piecewise Bounded Quadratic Systems in the Plane

In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z=(X,Y). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.

Singular value analyses of voltage stability on power system considering wind generation variability

Pós-graduação em Engenharia Elétrica - FEIS

Sliding vector fields for non-smooth dynamical systems having intersecting switching manifolds

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770066]

Modulation-mode Assignment for SVD-assisted Multiuser MIMO Systems with Correlation.

Multiuser multiple-input multiple-output (MIMO) downlink (DL) transmission schemes experience both multiuser interference as well as inter-antenna interference. The singular value decomposition provides an appropriate mean to process channel information and allows us to take the individual user’s channel characteristics into account rather than treating all users channels jointly as in zero-forcing (ZF) multiuser transmission techniques. However, uncorrelated MIMO channels has attracted a lot of attention and reached a state of maturity. By contrast, the performance analysis in the presence of antenna fading correlation, which decreases the channel capacity, requires substantial further research. The joint optimization of the number of activated MIMO layers and the number of bits per symbol along with the appropriate allocation of the transmit power shows that not necessarily all user-specific MIMO layers has to be activated in order to minimize the overall BER under the constraint of a given fixed data throughput.

Diseño de un sistema de climatización para un edificio singular mediante el uso de fuentes de energía renovable

El proyecto consiste en el diseño del sistema de climatización de un edificio ubicado en la ciudad de Madrid que utilice la energía solar como fuente de calor y electricidad. El objetivo es que el edificio tenga un consumo energético lo más bajo posible y que utilice energías de origen renovable para su explotación. Se incluye el cálculo de cargas térmicas, el dimensionamiento del sistema de climatización y de los sistemas de captación de energía solar (térmica y fotovoltaica). Adicionalmente, se definen las principales características de un sistema de control centralizado que permita optimizar el rendimiento y monitorizar el funcionamiento de la instalación de forma continua. Se incluye el diseño de las instalaciones auxiliares con un grado de detalle suficiente que permita su valoración, tanto desde el punto de vista energético como económico. Como parte fundamental del proyecto, se extraen conclusiones acerca del ahorro energético de las instalaciones y se analiza la viabilidad económica de las inversiones. ABSTRACT The project covers the design of a Heating and Climatization System for a building located in the city of Madrid (Spain). The facilities will use solar energy as the main source for both heat and electricity. The main goals are to achieve the lowest possible energy consumption and to use renewable sources of energy to cover it. Calculation of thermal charges is included, together with the sizing of both the Climatization System and the Solar Energy (Thermal and PV) facilities. In addition, the main characteristics of a Centralized Control System are defined. This will help both to optimize the performance of the different systems involved and to monitor the operation. Design of all auxiliary systems is included with enough level of detail as to be able to evaluate them from both energetic and economic points of view. Paramount in this project is to be able to draw conclusions about the energy savings and the profitability (or not) of the main investments to be carried out

Transmitter-side antennas correlation in SVD-assisted MIMO systems

MIMO techniques allow increasing wireless channel performance by decreasing the BER and increasing the channel throughput and in consequence are included in current mobile communication standards. MIMO techniques are based on benefiting the existence of multipath in wireless communications and the application of appropriate signal processing techniques. The singular value decomposition (SVD) is a popular signal processing technique which, based on the perfect channel state information (PCSI) knowledge at both the transmitter and receiver sides, removes inter-antenna interferences and improves channel performance. Nevertheless, the proximity of the multiple antennas at each front-end produces the so called antennas correlation effect due to the similarity of the various physical paths. In consequence, antennas correlation drops the MIMO channel performance. This investigation focuses on the analysis of a MIMO channel under transmitter-side antennas correlation conditions. First, antennas correlation is analyzed and characterized by the correlation coefficients. The analysis describes the relation between antennas correlation and the appearance of predominant layers which significantly affect the channel performance. Then, based on the SVD, pre- and post-processing is applied to remove inter-antenna interferences. Finally, bit- and power allocation strategies are applied to reach the best performance. The resulting BER reveals that antennas correlation effect diminishes the channel performance and that not necessarily all MIMO layers must be activated to obtain the best performance.

On the Difference of 4-Gonal Linear Systems on some Curves

Let C = (C, g^1/4 ) be a tetragonal curve. We consider the scrollar invariants e1 , e2 , e3 of g^1/4 . We prove that if W^1/4 (C) is a non-singular variety, then every g^1/4 ∈ W^1/4 (C) has the same scrollar invariants.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.