There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

http://ieeexplore.ieee.org/iel5/5610941/5624686/05624745.pdf

Power electronics

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

An algebraic approach is presented for the fast feed-forward adaptation of the angular velocity trajectory tracking task in a Boost-converter driven dc-motor system. For the adaptation, the load torque perturbations are assumed piecewise constant and are, nonasymptotically, online estimated using the available noisy measurements of the state variables. The controller is a linear controller based on the exact tracking error dynamics passive output feedback (ETEDPOF) controller design methodology including suitable adaptive feed-forward precompensation depending explicitly on the precisely estimated torque. The performance of the adaptation, which is achieved by means of the algebraic online-estimation of the current unknown load torque, is successfully validated in an experimental laboratory setup.

Load Torque Estimation and Passivity-Based Control of a Boost-Converter/DC-Motor Combination

This paper discusses the use of techniques related to the modulating function method for performing joint parameter and state estimation. After a short review of other methods related to modulating functions, we look at observability issues and the so-called Least-Squares observers to extend currently existing results on joint parameter and state estimation using modulating functions. An example is given as illustration.

Finite-time simultaneous parameter and state estimation using modulating functions

Flatness based control of a buck-converter driven dc motor

In this contribution, we use the so-called algebraic derivative method for a non-asymptotic state observation of nonlinear SISO systems. We derive a general formula of a time-varying filter that allows a non-model-based, quasiinstantaneous estimation of time derivatives of arbitrary analog time signals. The estimates are based on integrals of measured signals alone. For preserving accuracy, the estimation process has to be re-initialized after some period of time. Besides resetting the estimation time-interval equidistantly, estimated absolute error bounds and integral error bounds are also used for improving the efficiency of the estimation process. As an example, we use Chen’s chaotic oscillator to illustrate the velocity and the robustness of our observation method with respect to uncertainty of initial values and uniformly distributed measurement noise.

/pdf/on-non-asymptotic-observation-of-nonlinear-systems-1yuvva709u.pdf

On non-asymptotic observation of nonlinear systems

This paper studies the position estimation of an underwater vehicle using a single acoustic transponder. The chosen estimation approach is based on nonlinear differential algebraic methods which allow to express very simply conditions for observability. These are then used in combination with an integrator-based time-derivative estimation technique to design an algebraic estimator, which, contrary to asymptotic observers, does not require sometimes tedious convergence verification. Simple simulation results are presented to illustrate the approach.

Johann Reger

Papers

Load Torque Estimation and Passivity-Based Control of a Boost-Converter/DC-Motor Combination

Finite-time simultaneous parameter and state estimation using modulating functions

Flatness based control of a buck-converter driven dc motor

On non-asymptotic observation of nonlinear systems

An algebraic perspective to single-transponder underwater navigation