M‐matrices and global convergence of discontinuous neural networks

The paper considers a general class of neural networks possessing discontinuous neuron activations and neuron interconnection matrices belonging to the class of M‐matrices or H‐matrices. A number of results are established on global exponential convergence of the state and output solutions towards a unique equilibrium point. Moreover, by exploiting the presence of sliding modes, conditions are given under which convergence in finite time is guaranteed. In all cases, the exponential convergence rate, or the finite convergence time, can be quantitatively estimated on the basis of the parameters defining the neural network. As a by‐product, it is proved that the considered neural networks, although they are described by a system of differential equations with discontinuous right‐hand side, enjoy the property of uniqueness of the solution starting at a given initial condition. The results are proved by a generalized Lyapunov‐like approach and by using tools from the theory of differential equations with discontinuous right‐hand side. At the core of the approach is a basic lemma, which holds under the assumption of M‐matrices or H‐matrices, and enables to study the limiting behaviour of a suitably defined distance between any pair of solutions to the neural network. Copyright © 2006 John Wiley & Sons, Ltd.     

The inverse laplace transform of a function of the m-derived filters

The inverse Laplace transformation of a transfer function of the m-derived wave filters is presented. Using this result, the transient responses of a composite wave filter and a distributed amplifier using m-derived filter sections are derived. They are shown to be expressible as sums of integrals involving generalized hypergeometric functions in the same way that the solutions for other wave filters involve Bessel functions.     

A globally convergent direct adaptive pole‐placement controller for nonminimum phase systems with relaxed excitation assumptions

In this paper, we propose the first solution to the long‐standing problem of designing a globally convergent direct adaptive pole‐placement controller for linear, time‐invariant discrete‐time systems with arbitrary zeros that does not rely on persistency of excitation assumptions. As is well known, the main difficulty of this design is that it involves the estimation of parameters that enter nonlinearly in the regression model. This problem can be overcome introducing an overparameterized representation of the system, which imposes very strict persistency of excitation conditions to prove the parameter convergence. The latter is avoided here using a new version of the dynamic regressor extension and mixing parameter estimator recently proposed in the literature. The main feature of this estimator is that it generates, out of an m‐dimensional vector regression, m scalar regression models. This property allows us to estimate only the controller parameters of interest for the adaptive implementation, whose convergence is ensured under assumptions that are strictly weaker than the classical persistency of excitation requirement. Simulation results that illustrate the performance of the proposed scheme are also presented.     

Atomic Mixing Behavior of Co/Al(001) vs. Al/fcc-Co(001): Molecular Dynamics Simulation

Using molecular dynamics simulations, we investigated the interface structures and the growth behaviors of nano-scale Al/Co/Al multilayers. For Co on Al(001), interface mixing occurred irrespective of the incident energy (K_i). Interestingly, increasing the incident energy increased the thickness of the mixing layers and decreased the roughness of the Co surface. In the case of Al on Co(001), in contrast to the case of Co/Al, interface mixing could not be found, especially for low incident energy. From these investigations, an optimized deposition technique is proposed that improves the quality of the interface/surface of the deposited thin film by controlling the incident adatom energies.     

Electrical circuits RC,LC, and RL described by Atangana–Baleanu fractional derivatives

In this paper, the analytical solutions for the electrical series circuits RC, LC, and RL using novel fractional derivatives of type Atangana–Baleanu with non‐singular and nonlocal kernel in Liouville–Caputo and Riemann–Liouville sense were obtained. The fractional equations in the time domain are considered derivatives in the range α ∈(0;1]; analytical solutions are presented considering different source terms introduced in the fractional equation. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. On the basis of the Mittag–Leffler function, new behaviors for the voltage and current were obtained; the classical cases are recovered when α =1. Copyright © 2017 John Wiley & Sons, Ltd.     

On the application of degree theory to the analysis of resistive nonlinear networks

This paper presents an application of the theory of the degree of a map to the study of the existence of solutions and some related problems for resistive nonlinear networks. Many well-known results in this area have been generalized to allow coupling among the nonlinear resistors. The usual hypothesis requiring the nonlinear resistors to be eventually increasing has been weakened considerably by only requiring the resistors to be eventually passive. Instead of investigating special cases by special techniques, we study the network equations from a geometrical point of view. The concept of homotopy of odd fields provides a unified yet simple approach for analyzing a large class of practical nonlinear networks. Many known results belong to this category and are derived as special cases of our generalized theorems. This approach leads to a much better understanding of the geometric structure of the vector fields associated with the network equations. As a result, in so far as the existence of solutions is concerned, the concept of eventual passivity is shown to be far more basic than that of eventual increasingness. The emphasis of the concept of eventual passivity also leads naturally to the inclusion of coupling among the nonlinear resistors. The homotopy of odd fields also provides some useful techniques for locating the solutions. Along this line, we also study the bounding region of solutions and discuss the operating range of nonlinear resistors.     

Non‐unique solutions in drift diffusion modelling of phototransistors

We report non‐unique solutions for the potential in a Drift Diffusion (DD) model of a two terminal phototransistor. These solutions are present under bias without illumination, and persist until high illumination levels. It is well known that the DD equations can yield non‐unique solutions for pn structures which contain three or more junctions and two terminals with applied biases greater than k_BT log 2 where k_BT is the thermal energy at a temperature T, but DD models of phototransistors under illumination have been less well studied. The implicit belief is that one needs to artificially impose a potential in the base of the phototransistor in order to obtain a unique solution. We show here that this is only necessary because of a weakness in the numerical methods used to solve the equations, and describe two methods which circumvent this for which we show that this problem does not occur. These methods are used to investigate the operation of GaAs and In_0·53Ga_0·47As homojunction phototransistors, including the influence of the position of the illumination region and base doping. Copyright © 2000 John Wiley & Sons, Ltd.     

High proton relaxivity for gadolinium oxide nanoparticles

Objective: Nanosized materials of gadolinium oxide can provide high-contrast enhancement in magnetic resonance imaging (MRI). The objective of the present study was to investigate proton relaxation enhancement by ultrasmall (5 to 10 nm) Gd₂O₃ nanocrystals. Materials and methods: Gd₂O₃ nanocrystals were synthesized by a colloidal method and capped with diethylene glycol (DEG). The oxidation state of Gd₂O₃ was confirmed by X-ray photoelectron spectroscopy. Proton relaxation times were measured with a 1.5-T MRI scanner. The measurements were performed in aqueous solutions and cell culture medium (RPMI). Results: Results showed a considerable relaxivity increase for the Gd₂O₃–DEG particles compared to Gd-DTPA. Both T ₁ and T ₂ relaxivities in the presence of Gd₂O₃–DEG particles were approximately twice the corresponding values for Gd–DTPA in aqueous solution and even larger in RPMI. Higher signal intensity at low concentrations was predicted for the nanoparticle solutions, using experimental data to simulate a T₁-weighted spin echo sequence. Conclusion: The study indicates the possibility of obtaining at least doubled relaxivity compared to Gd–DTPA using Gd₂O₃–DEG nanocrystals as contrast agent. The high T ₁ relaxation rate at low concentrations of Gd₂O₃ nanoparticles is very promising for future studies of contrast agents based on gadolinium-containing nanocrystals.     

Improving time integration scheme for FEM analysis of MTL problems

This paper presents improved algorithm for electromagnetic transient calculations on multiconductor transmission line (MTL) achieved by improvement of the time integration when forming a local system of equations for a finite element. Improvement of accuracy was obtained by using Heun's method. Previously developed local system of equations of MTL has been obtained using the generalized trapezoidal rule (ϑ -method). The use of the generalized trapezoidal rule for the time integration sometimes causes numerical oscillations or numerical diffusion of numerical solutions. Numerical solutions obtained using Heun's method and using the generalized trapezoidal rule for different values of a time integration parameter are compared with analytical solution. It has been shown that Heun's method yields the results with much higher accuracy comparing to results obtained by generalized trapezoidal rule.     

Computational aspects of the DC analysis of transistor networks

For a general transistor-resistor network a method is proposed to obtain, in some normed linear vector space Rⁿ, the numerical solution of the dc equation G(U) = C for a given constant vector C = C*. At each step k, k = 0, 1,…, a vector C^k is chosen from a certain set Γ_k and the equation solved for C = C^k by a Newtonian iteration yielding the locally unique solution U^k. Convergence in a finite number of steps is proved for a sequence {C^k} on the straight line through C° and C*, provided this line does not contain a point C? between C° and C*, such that at the solution C? of G(U) = C?, the derivative G'(ū) is singular. Otherwise another initial point C° must be chosen, or the path of {C^k be altered to reach C*. The method is restricted to a closed and bounded subset of Rⁿ, in which all the solutions of the dc equation have to lie. To find all the solutions, this bounded subset can be covered with balls. The method proposed in this paper is also useful in the analysis of a transistor-resistor circuit, where often the important problem arises of whether the circuit will admit its correct dc bias, since this problem can be best understood by investigating the uniqueness of solutions of the dc equation.     

Multi-objective Phasor Measurement Unit Placement in Electric Power Networks: Integer Linear Programming Formulation

A multi-objective optimal phasor measurement unit placement model using integer linear programming is presented in this article. The proposed model simultaneously optimizes two objectives, i.e., minimization of phasor measurement unit numbers and maximization of measurement redundancy. To calculate the redundancy criteria, the single-line outage and the phasor measurement unit loss are considered simultaneously. A linear formulation is presented for both objective functions. Also herein, to address conflicting attributes and identify Pareto optimal solutions of the multi-objective optimal phasor measurement unit placement problem, a new multi-objective mathematical programming method is proposed. Finally, a new index, i.e., minimum distance to utopia point, is implemented to select the most preferred solution among the available Pareto front based options on the goal to achieve judicious decision makers. Two test systems, i.e., a modified 9-bus and an IEEE 118-bus test systems, are used to illustrate the effectiveness of the proposed framework.     

On the Well-posedness of the PWM Control System

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of Carathéodory solutions in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Furthermore, it is clear that when carrier signal h(t)=0, closed-loop pulse-width modulation (PWM) DC-DC converters are not well posed, and when some condition is satisfied, the closed-loop PWM DC-DC converters with a P controller are well posed. Translated from Acta Automatica Sinica, 2004, 30(1): 37–44 (in Chinese)     

Reduction of dimensionality in choosing optimal control

Given that x(t) = (x₁(t),…,x_n(t)) represents a trajectory of the considered dynamical system, we demonstrate that reduction of dimensionality of x(t) by using its principal components in choosing the optimal control u(t) is necessary to overcome the computational difficulties that might arise in obtaining a solution of the optimal control problem. We obtain explicit solutions for linear time‐varying systems with quadratic cost functional and show how to overcome difficulties appearing in non‐linear matrix differential equations of Riccati type. A gradient method of searching for the close‐to‐optimal trajectory and control in non‐linear optimal control problems is also considered. Copyright © 2002 John Wiley & Sons, Ltd.     

Exact solutions of cyclically symmetric oscillator equations with non-linear coupling

Kaplan and Yardeni have found very simple exact limit cycle solutions in cyclically symmetric systems of N oscillator equations with linear coupling in zero order of a perturbation parameter and non-linear coupling in first order. In contrast with such solutions in other non-linear systems, each of these limit cycles is a normal mode of the unperturbed equations, with no change in frequency. the sources of this simple behaviour are studied here with the equations expressed in terms of the normal mode co-ordinates of the unperturbed system rather than in the original co-ordinates. It is found that the simplicity of the Kaplan-Yardeni solutions arises partly from an additional symmetry of the perturbation terms beyond the cyclic symmetry and partly from the specific choices of the perturbations. Extension of their systems to arbitrary N leads to the result that all such sets of equations have similar simple limit cycles. More general cyclically symmetric sets of equations are also discussed, with limit cycle solutions whose frequencies are shifted from the zero-order values by easily calculated amounts or with solutions which are linear combinations of zero-order normal modes.     

Electrical circuits described by fractional conformable derivative

In the last 3 years, the fractional conformable derivative and its properties have been introduced. Unlike other definitions, this new fractional derivative is based on the basic limit definition of the derivative and satisfies the same formulas of derivation, such as product and quotient of 2 functions and the chain rule. Using this new derivative, we obtain a new class of linear ordinary differential equations with noninteger power variable coefficients for the Resistance Capacitance (RC), Inductance Capacitance (LC), and Resistance, Inductance Capacitance (RLC) electric circuits. The numerical solutions are solved through the Matlab software. Solutions depend on time and on the fractional order parameter 0 < γ ≤ 1. The computing using this new derivative is much easier than using other definitions of fractional derivative. It has been shown that in the particular case γ = 1, these solutions become the ordinary ones. Also, a comparison has been made with the Caputo fractional derivative for the case of the RC circuit with constant source.     

Preparation of PZN-Based Ceramics Using a Sequential Mixing Columbite Method

In this experiment Pb(Zn_1/3Nb_2/3)O₃(PZN)-BaTiO₃ (BT)-Pb(Zr_0.52Ti_0.48)O₃ (PZT) ceramics were prepared using solid state reactions via columbite method by mixing the relevant oxides and were processed employing conventional sintering techniques. Dielectric, ferroelectric and piezoelectric properties were evaluated and the corresponding microstructures were examined using transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS). The experimental results imply that it is difficult to prepare PZN-PZT-BT ceramics with a full perovskite structure using a conventional columbite method, i.e., PZN was prepared using the columbite method and then mixed, calcined and sintered with PT, PZ and BT. A modified approach (MC) of mixing and calcining all B-site elements first, then mixing and sintering with all A site elements was adopted. Electrical properties were enhanced but a small amount of pyrochlore phase still exists. Finally, a mixing and calcining sequence (sequential mixing columbite, SMC) of well calcined B-site elements, firstly with BaO then with PbO was utilized. A full perovskite structure of the specimen with excellent electrical properties can be obtained. Microstructural investigations showed Ba segregation at triple junctions for IC and MC processes, implying that stabilization of the perovskite structure of the specimens was not completely achieved due to element segregation.     

Admissible Model Matching using 𝒟R‐regions: Fault accommodation and robustness against FDD inaccuracies

This paper proposes a reformulation of the Admissible Model Matching (AMM) method for Fault‐Tolerant Control (FTC) using Linear Matrix Inequality (LMI) regional pole placement. The essential feature of the AMM approach is that the FTC design is based on the specification of a set of admissible closed‐loop behaviors whose limits represent the acceptable control performance degradation in the presence of faults. In the original formulation, this set is characterized by inequalities relating the coefficients of the closed‐loop system matrix, derived ‘ad hoc’ for the particular system and the provided control specification, and the FTC design problem is formulated as a non‐linear constrained optimization problem. In this paper, the set of admissible behaviors is specified by restricting the closed‐loop spectrum in a union of particular convex regions called ??_R‐regions. On one hand, this allows a straightforward representation for a wide variety of practical control specifications while preserving the convexity of the problem. On the other hand, ??_R‐regions are characterized by LMIs and the fault accommodation can be formulated in terms of several LMI (feasibility) problems. Moreover, the robustness of the solutions against errors in the fault estimations provided by the Fault Detection and Diagnosis module is characterized as well as a LMI‐constrained optimization problem. The versatility and the effectiveness of the proposed method are illustrated using an example. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical formula of induced electric fields in a spherical conductor by an ELF dipole magnetic field source

An analytical formula of induced electric field E in a spherical conductor by an ELF dipole magnetic field source is mathematically derived in vector form based on the equivalent mutlipole moment method with reexpansion technique (RE‐EMMM), where M _‖ and are parallel and perpendicular components of M , respectively. The validity of the formula is confirmed in the following three ways: (i) the derivation of the formula from the Sarvas equation with the reciprocity theorem derived by Eaton; (ii) the convergence of the formula to that of homogeneous magnetic field when M _‖ is located at the infinite distance; (iii) comparison of the analytical solutions with numerical solutions by RE‐EMMM. Furthermore, a formula for the trajectory, which satisfies E = 0 , is derived for the field by M _‖. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(3): 8– 17, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20739     

Novel combination schemes of individual weighting factors sign subband adaptive filter algorithm

To improve the performance of the recently presented individual weighting factors sign subband adaptive filter (IWF‐SSAF) algorithm, its 2 combination algorithms using different step sizes are proposed. The first algorithm is to convexly combine the weight vectors of a large step‐size IWF‐SSAF filter and a small step‐size one; and the second algorithm is to obtain a time‐varying step size for the IWF‐SSAF by combining a large step size and a small one. The minimization of the sum of the l₁‐norm of subband errors is used to indirectly update the mixing parameters in these 2 algorithms through a modified sigmoidal function. Moreover, in the first algorithm, to implement a smooth transition from the large step‐size IWF‐SSAF filter to the small step‐size one, the component filters receive a cyclic feedback of the combined weight vector. Both proposed algorithms have almost the same convergence performance, but the second algorithm saves computational cost. Simulation results in impulsive noise scenarios demonstrate the superiority of our proposed algorithms.     

High-frequency propagation on nonuniform multiconductor transmission lines in uniform media

The asymptotic form, for high frequencies, of the equations of propagation on a nonuniform N-conductor transmission line is considered. Under the assumption of perfect conditions in uniform, isotropic media, all N propagation velocities are the same, but the characteristic impedance matrix is allowed to vary with position along the line. Closed-form solutions are obtained for some cases of interest.