L2-stability of feedback systems in general integral form

2006 ◽  
pp. 145-168
Keyword(s):  
Integral Form ◽  
Feedback Systems ◽  
General Integral ◽  
L2 Stability

scholarly journals Relation between weather radar equation and first-order backscattering theory

2003 ◽  
Vol 3 (1) ◽  
pp. 301-322
Author(s):  
F. S. Marzano ◽  
G. Ferrauto
Keyword(s):  
Weather Radar ◽  
Integral Form ◽  
Radar Reflectivity ◽  
Range Resolution ◽  
First Order ◽  
General Integral ◽  
Extinction Factor ◽  
Statistical Relationships ◽  
The Impact ◽  
Radar Equation

Abstract. Aim of this work is to provide a new insight into the physical basis of the meteorological-radar theory in attenuating media. Starting form the general integral form of the weather radar equation, a modified form of the classical weather radar equation at attenuating wavelength is derived. This modified radar equation includes a new parameter, called the range-bin extinction factor, taking into account the rainfall path attenuation within each range bin. It is shown that, only in the case of low-to-moderate attenuating media, the classical radar equation at attenuating wavelength can be used. These theoretical results are corroborated by using the radiative transfer theory where multiple scattering phenomena can be quantified. From a new definition of the radar reflectivity, in terms of backscattered specific intensity, a generalised radar equation is deduced. Within the assumption of first-order backscattering, the generalised radar equation is reduced to the modified radar equation, previously obtained. This analysis supports the conclusion that the description of radar observations at attenuating wavelength should include, in principle, first-order scattering effects. Numerical simulations are performed by using statistical relationships among the radar reflectivity, rain rate and specific attenuation, derived from literature. Results confirm that the effect of the range-bin extinction factor, depending on the considered frequency and range resolution, can be significant at X band for intense rain, while at Ka band and above it can become appreciable even for moderate rain. A discussion on the impact of these theoretical and numerical results is finally included.

scholarly journals X-ray fluorescence at nanoscale resolution for multicomponent layered structures: a solar cell case study

2017 ◽  
Vol 24 (1) ◽  
pp. 288-295 ◽  
Author(s):  
Bradley M. West ◽  
Michael Stuckelberger ◽  
April Jeffries ◽  
Srikanth Gangam ◽  
Barry Lai ◽  
...  
Keyword(s):  
Solar Cell ◽  
Multicomponent System ◽  
Incident Beam ◽  
Integral Form ◽  
Fluorescence Signal ◽  
Elemental Distribution ◽  
X Ray ◽  
Spatially Resolved ◽  
General Integral ◽  
Thickness Variations

The study of a multilayered and multicomponent system by spatially resolved X-ray fluorescence microscopy poses unique challenges in achieving accurate quantification of elemental distributions. This is particularly true for the quantification of materials with high X-ray attenuation coefficients, depth-dependent composition variations and thickness variations. A widely applicable procedure for use after spectrum fitting and quantification is described. This procedure corrects the elemental distribution from the measured fluorescence signal, taking into account attenuation of the incident beam and generated fluorescence from multiple layers, and accounts for sample thickness variations. Deriving from Beer–Lambert's law, formulae are presented in a general integral form and numerically applicable framework. The procedure is applied using experimental data from a solar cell with a Cu(In,Ga)Se2 absorber layer, measured at two separate synchrotron beamlines with varied measurement geometries. This example shows the importance of these corrections in real material systems, which can change the interpretation of the measured distributions dramatically.

scholarly journals Relation between weather radar equation and first-order backscattering theory

2003 ◽  
Vol 3 (3) ◽  
pp. 813-821 ◽  
Author(s):  
F. S. Marzano ◽  
G. Ferrauto
Keyword(s):  
Weather Radar ◽  
Integral Form ◽  
Radar Reflectivity ◽  
Range Resolution ◽  
First Order ◽  
General Integral ◽  
Extinction Factor ◽  
Statistical Relationships ◽  
The Impact ◽  
Radar Equation

Abstract. Aim of this work is to provide a new insight into the physical basis of the meteorological-radar theory in attenuating media. Starting form the general integral form of the weather radar equation, a modified form of the classical weather radar equation at attenuating wavelength is derived. This modified radar equation includes a new parameter, called the range-bin extinction factor, taking into account the rainfall path attenuation within each range bin. It is shown that, only in the case of low-to-moderate attenuating media, the classical radar equation at attenuating wavelength can be used. These theoretical results are corroborated by using the radiative transfer theory where multiple scattering phenomena can be quantified. From a new definition of the radar reflectivity, in terms of backscattered specific intensity, a generalised radar equation is deduced. Within the assumption of first-order backscattering, the generalised radar equation is reduced to the modified radar equation, previously obtained. This analysis supports the conclusion that the description of radar observations at attenuating wavelength should include, in principle, first-order scattering effects. Numerical simulations are performed by using statistical relationships among the radar reflectivity, rain rate and specific attenuation, derived from literature. Results confirm that the effect of the range-bin extinction factor, depending on the considered frequency and range resolution, can be significant at X band for intense rain, while at Ka band and above it can become appreciable even for moderate rain. A discussion on the impact of these theoretical and numerical results is finally included.

scholarly journals New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution

2020 ◽  
Vol 76 (3) ◽  
pp. 421-428
Author(s):  
V. G. Kohn ◽  
I. A. Smirnova
Keyword(s):  
Analytical Solution ◽  
Single Crystal ◽  
Wave Amplitude ◽  
Spherical Wave ◽  
Integral Form ◽  
Linear Change ◽  
Laue Diffraction ◽  
X Ray ◽  
General Integral ◽  
Exit Surface

The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.

On the ESO Based Reinforcement Learning for Pure Feedback Systems

2017 ◽  
Author(s):  
Dazi Li ◽  
Wei Wang ◽  
Zhiqiang Gao
Keyword(s):  
Reinforcement Learning ◽  
Learning Algorithm ◽  
Integral Form ◽  
Feedback System ◽  
State Observer ◽  
Extended State Observer ◽  
Reference Trajectory ◽  
Extended State ◽  
Feedback Systems ◽  
Detailed Model

The control of pure feedback system, which is widely used but has non-affine property, has always been an important and challenging problem. In order to achieve precise tracking control of pure feedback system through improving the disturbance rejection ability of existing reinforcement learning algorithm, a reinforcement learning (RL) control strategy based on extended state observer (ESO) is proposed in this paper. In the proposed method, the extended state observer can reject the total disturbances and transform the pure feedback system which is in an input-output predictor from to overcome the non-causal problem into a cascade integral form. This allows the continuous reinforcement learning strategy of the actor-critic (AC) structure not to depend on the detailed model information, which makes it practically data-driven. It is worth noting that, in order to further improve the ability to track the changing reference trajectory, a novel curvature acceleration factor is proposed, which can adjust the learning speed of the reinforcement learning controller according to the curvature of the reference trajectory. The validity of the proposed algorithm is verified by the simulation results.

scholarly journals Neural networks with memory

1991 ◽  
Vol 4 (4) ◽  
pp. 313-332 ◽  
Author(s):  
T. A. Burton
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Equilibrium Points ◽  
Integral Form ◽  
The Third ◽  
General Integral ◽  
The Neural Networks ◽  
The Stability ◽  
With Memory ◽  
Stability Results

This paper is divided into four parts. Part 1 contains a survey of three neural networks found in the literature and which motivate this work. In Part 2 we model a neural network with a very general integral form of memory, prove a boundedness result, and obtain a first result on asymptotic stability of equilibrium points. The system is very general and we do not solve the stability problem. In the third section we show that the neural networks are very robust. The fourth section concerns simplification of the systems from the second part. Several asymptotic stability results are obtained for the simplified systems.

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