In this paper, we introduce the incremental welfare consensus algorithm for solving the energy management problem in a smart grid environment populated with distributed generators and responsive demands. The proposed algorithm is distributed and cooperative such that it eliminates the need for a central energy-management unit, central price coordinator, or leader. The optimum energy solution is found through local peer-to-peer communications among smart devices. Each distributed generation unit is connected to a local price regulator, as is each consumer unit. In response to the price of energy proposed by the local price regulators, the power regulator on each generation/consumer unit determines the level of generation/consumption power needed to optimize the benefit of the device. The consensus-based coordination among price regulators drives the behavior of the overall system toward the global optimum, despite the greedy behavior of each unit. The primary advantages of the proposed approach are: 1) convergence to the global optimum without requiring a central controller/coordinator or leader, despite the greedy behavior at the individual level and limited communications; and 2) scalability in terms of per-node computation and communications burden.

Incremental Welfare Consensus Algorithm for Cooperative Distributed Generation/Demand Response in Smart Grid

Magnetic susceptibility is an important physical property of tissues, and can be used as a contrast mechanism in magnetic resonance imaging (MRI). Recently, targeting contrast agents by conjugation with signaling molecules and labeling stem cells with contrast agents have become feasible. These contrast agents are strongly paramagnetic, and the ability to quantify magnetic susceptibility could allow accurate measurement of signaling and cell localization. Presented here is a technique to estimate arbitrary magnetic susceptibility distributions by solving an ill-posed inversion problem from field maps obtained in an MRI scanner. Two regularization strategies are considered: conventional Tikhonov regularization and a sparsity promoting nonlinear regularization using the norm. Proof of concept is demonstrated using numerical simulations, phantoms, and in a stroke model in a rat. Initial experience indicates that the nonlinear regularization better suppresses noise and streaking artifacts common in susceptibility estimation.

http://ieeexplore.ieee.org/iel5/42/5405633/05067387.pdf

Nonlinear Regularization for Per Voxel Estimation of Magnetic Susceptibility Distributions From

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis

PCA-based groupwise image registration for quantitative MRI.

This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science

/pdf/fourier-and-laplace-transforms-32a31jtv0v.pdf

Fourier and Laplace transforms

In many engineering applications, the physical quantities that have to be computed are obtained by solving a related eigenvalue problem. The matrix under consideration and thus its eigenvalues usually depend on some parameters. A natural question then is how sensitive the physical quantity is with respect to (some of) these parameters, i.e., how it behaves for small changes in the parameters. To find this sensitivity, eigenvalue and/or eigenvector derivatives with respect to those parameters need to be found. A method is provided to compute first order derivatives of the eigenvalues and eigenvectors for a general complex-valued, non-defective matrix.

/pdf/computation-of-eigenvalue-and-eigenvector-derivatives-for-a-53o2q0sq3k.pdf

Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem

Fourier and Laplace Transforms: Laplace transforms

INTRODUCTION From parts 2 and 3 it is obvious that Fourier series and Fourier integrals play an important role in the analysis of continuous-time signals. In many cases we are forced to calculate the Fourier coefficients or the Fourier integral on the basis of a given sampling of the signal. We are therefore interested in a transformation that will transform a discrete-time signal, in this case a sampling, directly into the frequency domain. In general, such transformations are called discrete transforms. A particularly important discrete transform is the so-called discrete Fourier transform , abbreviated as DFT, and it will be the central theme of the present chapter. It arises naturally if one approximates the Fourier coefficients of a periodic continuous-time signal numerically using the trapezoidal rule. This is the subject of the first section of this chapter, which also introduces the DFT as a transform defined for periodic discrete-time signals. In the next section we introduce the inverse DFT in the so-called fundamental theorem of the discrete Fourier transform, which very much resembles the fundamental theorem of Fourier series. In the remaining sections, all kinds of properties of the DFT are treated, and again we will encounter many similarities with Fourier series and Fourier integrals. For example, one can formulate a Parseval theorem for periodic discrete-time signals. Following the introduction of the so-called cyclical convolution we can derive convolution theorems, which look very similar to the ones derived for continuous-time signals.

The discrete Fourier transform

In this paper, we present two DRM formulations. For a pseudo-Poisson equation, if the right-hand side is a linear operation on the dependent variable, we can derive a new DRM formulation. In comparison with the traditional DRM formulation for the same equation, the proposed approach is much easier and more efficient. For the axisymmetric Poisson equation, we construct a DRM formulation by using the linear axisymmetric radial basis function. The particular solution involved is obtained in a closed form, and thus speeds up the evaluation of the particular solution. Three numerical examples demonstrate the accuracy and efficiency of these formulations.

https://pure.tue.nl/ws/files/2069063/553615.pdf

H. G. ter Morsche

Papers

Fourier and Laplace transforms

Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem

Fourier and Laplace Transforms: Laplace transforms

The discrete Fourier transform

Alternative DRM formulations