Gaussian radial basis functions and the approximation of input–output maps

Radial basis functions are of interest in connection with a variety of approximation problems in the neural networks area, and in other areas as well. Here we show that the members of some interesting families of shift‐varying input–output maps, that take a function space into a function space, can be uniformly approximated, over an infinite time or space domain, in a certain special way using Gaussian radial basis functions. Copyright © 2003 John Wiley & Sons, Ltd.     

Z+ fading memory and extensions of input–output maps

An Erratum for this article has been published in the International Journal of Circuit Theory and Applications 30(4) 2002, 179. Much is known about time‐invariant non‐linear systems with inputs and outputs defined on Z₊ that possess approximately‐finite memory. For example, under mild additional conditions, they can be approximated arbitrarily well by the maps of certain interesting simple structures. An important fact that gives meaning to results concerning such systems is that the approximately‐finite‐memory condition is known to be often met. Here we consider the known proposition that if a causal time‐invariant discrete‐time input–output map H has fading memory on a set of bounded functions defined on all of the integers Z, then H can be approximated arbitrarily well by a finite Volterra series operator. We show that in a certain sense, involving the existence of extensions of system maps, this result too has wide applicability. Copyright © 2001 John Wiley & Sons, Ltd.     

Time‐varying linear systems and input–output stability

One useful strategy for establishing input–output stability is to seek conditions on the system map so that a certain lower‐bound condition is met. We show here that, for a large class of time‐varying linear systems, the lower‐bound condition for stability is in fact necessary. Copyright © 2000 John Wiley & Sons, Ltd.     

An input–output linearization algorithm‐based control for optimization of DFIG

This paper proposes an input–output linearization‐based active power control strategy to maximize the energy production of a doubly fed induction generator (DFIG)‐based wind energy conversion system (WECS). The DFIG‐based wind turbine is a nonlinear system, and the nonlinear behavior will result in tracking errors. The proposed control strategy utilizing state feedback successfully deals with the nonlinear behavior existing in the WECS. Such a control will linearize the system input and output first. Then, the control loop and parameters can be designed by the linear system control algorithm. The simulations carried in MATLAB/Simulink demonstrate that the proposed control strategy is effective and promising. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

下限分析中屈服面的最佳线性逼近问题

目前下限分析中往往采用内接正多边形来逼近屈服面以保证解的下限性质.从数值分析角度来看,采用其它拟合方式也能够从下方逼近极限荷载.本文研究了以下几种屈服面的多边形逼近方式:外切逼近、等面积逼近、最佳平方逼近、最优一致逼近、等周长逼近和内接逼近.计算分析表明:最优一致逼近在保证下限性质和求解精度的同时收敛更快,提高了求解效率,便于工程应用.     

Uniform approximation of time‐invariant non‐linear systems

An Erratum has been published for this article in International Journal of Circuit Theory and Applications 2004; 32(6):633. It is shown that the elements of a large class of time‐invariant non‐linear input–output maps can be uniformly approximated arbitrarily well, over infinite time intervals, using a certain structure that can be implemented in many ways using, for example, radial basis functions, polynomial functions, piecewise linear functions, sigmoids, or combinations of these functions. For the special case in which these functions are taken to be certain polynomial functions, the input–output map of our structure is a generalized finite Volterra series. Results are given for the case in which inputs and outputs are defined on ?. The case in which inputs and outputs are defined on the half‐line ?₊ is also addressed, and in both cases inputs need not be functions that are continuous. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis and design of a ZVS converter for high voltage input–low voltage output application

This paper proposes a full‐bridge (d = 50%) cascaded buck topology which is a very suitable circuit for high voltage input–low voltage output applications with high output current. Benefiting from working under a large duty cycle, the proposed converter can easily achieve zero voltage switching turn‐on and turn‐off of active switches in a full bridge. Small‐signal model of this topology is analyzed through its corresponding peak current mode control. Its small‐signal transfer function is given, and the control loop design is discussed. Advantages of this topology and operation principles are analyzed. Design guidelines, drawn from this analysis, are applied on a low‐voltage (3.3 V) output voltage prototype to validate the proposed concept. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Polynomial chaos‐based macromodeling of multiport systems using an input–output approach

An innovative technique to build stochastic frequency‐domain macromodels of generic linear multiport systems is presented. The proposed method calculates a macromodel of the system transfer function including its statistical properties, making it tailored for variability analysis. The combination of the modeling power of the Vector Fitting algorithm with the Polynomial Chaos expansion applied at an input–output level allows to accurately and efficiently describe the system variability features. Thanks to its versatility and automated order selection, the proposed technique is suitable to be applied to a large range of complex modern electrical systems (e.g., filters and interconnections) and can tackle the case of correlated random variables. The performance in terms of accuracy and computational efficiency of the proposed method is compared with respect to the standard Monte Carlo analysis for two pertinent numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

On least‐squares identification of stochastic linear systems with noisy input–output data

In a recent paper, two least‐squares (LS) based methods, which do not involve prefiltering of noisy measurements or parameter extraction, are established for unbiased identification of linear noisy input–output systems. This paper introduces more computationally efficient estimation schemes for the measurement noise variances and develops a new version of two LS based algorithms in combination with the bias correction technique. The proposed two algorithms work directly with the underlying noisy system, thereby being substantially different from the previous methods that need to actually identify an augmented system. It is shown that a significant saving in the computational cost can be achieved by this better way of implementation of the two LS‐based algorithms while at almost no sacrifice of the parameter estimation accuracy. The performance of the proposed two identification algorithms and comparisons with their predecessors are substantiated using simulation data. Copyright © 1999 John Wiley & Sons, Ltd.     

Use of WKB approximation for analytical boundary conditions in numerical solution of Schrödinger equation: application to semiconductor–high‐k dielectric interfaces

Numerical methods used to solve 1D Schrödinger's equation in quantum structures, such as Numerov's integration of wavefunction or the shooting method iterative solution of energy levels, require knowledge of two‐point boundary conditions at interfaces. This is especially true when the interfaces are not symmetrical or where exponential decay of wavefunction at asymptotically large distances does not hold. A closed‐form expression for boundary conditions, which is not sensitive to intermediate solutions at interfaces, can minimize possible divergence during iterations and relax simulation grid size and simulation time. In this work, the Wentzel‐Kramers‐Brillouin (WKB) approximation within potential barriers is proposed to analytically calculate the boundary conditions for abrupt interfaces, such as dielectric–semiconductor interface. An analytical expression for the slope at the interface is derived, and the errors are estimated with respect to numerical methods. An application is shown for self‐consistent solution of coupled Poisson–Schrödinger's equations at multi‐layer HfO₂‐SiO₂ dielectric gate stack corresponding to International Technology Roadmap for Semiconductors‐projected 10 nm bulk single‐gate Complementary Metal‐Oxide‐Semiconductor (CMOS) technology node, where wavefunction penetration into the dielectric is of critical importance. Application to dual gate structures with 5 nm fin width and high‐k dielectric with 0.5 nm equivalent oxide thickness is also shown. A quantum mechanical simulator ‘hksim’ based on this principle is posted for public domain usage. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct voltage regulation of DC–DC buck converter in a wide range of operation using adaptive input–output linearization

In this paper, an adaptive nonlinear controller is designed for voltage control of the DC–DC buck converter in both continuous and discontinuous conduction modes. The proposed controller is developed based on input–output linearization, which is robust and stable against converter load changes, input voltage variations, and parameter uncertainties. In the proposed approach, all the converter parameters, namely input voltage, load resistance, and other parasitic elements of the power circuit, are assumed to be uncertain and estimated using a suitable Lyapunov function. Using a stand‐alone TMS320F2810 digital signal processor from Texas Instruments, some simulations and experimental results are obtained to verify the proposed control approach. The results are in good agreement and prove the effectiveness and capability of the controller over a wide range of operations. Also, advantages of the designed nonlinear regulator are indicated in comparison with a pulse width modulation (PWM)‐based sliding mode controller. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Multiple input–multiple output adaptive feedback control strategies for the active headrest system: design and real‐time implementation

In this article, multiple input–multiple output adaptive feedback control techniques for acoustic noise control in a headrest system are developed. The main goal underlying their design is to provide acoustic comfort to the user, i.e. high noise attenuation level over possibly large areas at the ears. Classical Internal Model Control system does not yield acceptable performance. An approach based on estimates of the residual noise at the ears is then proposed. It is shown that increase in the number of secondary sources to operate for one channel improves the performance. The experiments of tonal noise control are performed on an originally set‐up prototype of the active headrest system. The results obtained are illustrated in the promoted form of distribution of zones of quiet. Copyright © 2003 John Wiley & Sons, Ltd.     

I. W. Sandberg, ‘Linear shift‐invariant input–output maps do not necessarily commute’. International Journal of Circuit Theory and Applications, 2000; 28:513–518.

The original article to which this Erratum refers was published in the International Journal of Circuit Theory and Applications, 2000; 28 :513–518.     

Risk‐sensitive filtering for nonlinear Markov jump systems on the basis of particle approximation

In this paper, the risk‐sensitive filtering method that relaxes the dependence on model accuracy is extended to nonlinear Markov jump systems (MJSs). In the method, the so‐called reference probability technique together with particle approximation is utilized to derive the risk‐sensitive filter in nonlinear non‐Gaussian framework. The novelty of the proposed approach is that a ‘risky’ interacting resampling step is performed to both moderate the modeling uncertainties and to solve the problem of particle explosion. A designer‐chosen parameter named risk‐sensitive parameter allows us to make a trade‐off between the filtering accuracy for the nominal model and the robustness to uncertainties. With a meaningful example, it shows that the developed method can outperform the widely used method‐particle filter and interacting multiple model‐particle filter in nonlinear MJSs with uncertainties. Copyright © 2011 John Wiley & Sons, Ltd.     

Real‐time identification of nonlinear multiple‐input–multiple‐output systems with unknown input time delay using Wiener model with Neuro‐Laguerre structure

In this article, a real‐time block‐oriented identification method for nonlinear multiple‐input–multiple‐output systems with input time delay is proposed. The proposed method uses the Wiener structure, which consists of a linear dynamic block (LDB) followed by a nonlinear static block (NSB). The LDB is described by the Laguerre filter lattice, whereas the NSB is characterized using the neural networks. Due to the online adaptation of the parameters, the proposed method can cope with the changes in the system parameters. Moreover, the convergence and bounded modeling error are shown using the Lyapunov direct method. Four practical case studies show the effectiveness of the proposed algorithm in the open‐loop and closed‐loop identification scenarios. The proposed method is compared with the recently published methods in the literature in terms of the modeling accuracy, parameter initialization, and required information from the system.     

Novel stability criteria of Cohen–Grossberg neural networks with time‐varying delays

In this paper, a class of Cohen–Grossberg neural networks with time‐varying delays is investigated. Based on several new Lyapunov–Krasovskii functionals, by employing the homeomorphism mapping principle, the Halanay inequality, a nonlinear measure approach and linear matrix inequality techniques, several delay‐independent sufficient criteria are obtained for the existence, uniqueness and globally exponential stability of considered neural networks. Without assuming the boundedness and monotonicity of activation functions, the obtained conditions generalize some previous results in the literature. Two examples are also given to show the less conservativeness of the obtained conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Differential equation description and Chebyshev approximation of linear time‐invariant circuits

The approximation technology of analogue circuit functions is crucial to the computer‐aided simulation, analysis, and design automation of electronic circuits. Chebyshev polynomials and various differential equations are proposed in this paper to approximate the functions of linear time‐invariant circuits. The coefficient calculation methods of the Chebyshev expansion and the differential equation matrices are thoroughly deduced, and the construction methods employed in the functions and the actual time mapping of the linear time‐invariant circuits are presented in this paper. An example of an analogue filter verifies the effectiveness and accuracy of the proposed approximation algorithm and elaborates on the selection process of the order number and the time step length of the Chebyshev expansion according to the demanded truncation error.     

Robust output tracking of uncertain nonlinear systems with completely unknown dead‐zone input: A self‐tuning design approach

The main purpose of this paper is to propose a direct and simple approach, called a self‐tuning design approach, to dealing with any nonsymmetric dead‐zone input nonlinearity where its information is completely unknown. In order to describe the approach, the output tracking problem is considered for a class of uncertain nonlinear systems with any nonsymmetric dead‐zone input. First, a dead‐zone input is represented as a time‐varying input‐dependent function such that the considered dynamical system with dead‐zone input can be transfered into an uncertain nonlinear dynamical system subject to a linear input with time‐varying input coefficient. Then, by making use of the self‐tuning design approach, a class of adaptive robust output tracking control schemes with a rather simple structure is synthesized. Thus, the proposed direct and simple self‐tuning design approach can be easily understood by the engineering designers, and the resulting simple adaptive robust control schemes can be well implemented in most practical engineering control problems. By combining the proposed self‐tuning design approach with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain nonlinear dynamical systems with dead‐zone in the actuators. Finally,the simulations of some numerical examples are provided to demonstrate the validity of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Gaussian pulse approximation using standard CMOS and its application for sub‐GHz UWB impulse radio

Gaussian pulse is widely used in communication systems. The true Gaussian function is not physically realizable, but it can be approximated through linear functions. This paper presents a Gaussian pulse approximation approach to generate a quasi‐Gaussian pulse by using the transient response of a CMOS inverter. The basic structure of the proposed design includes a digital variable square pulse generator, a Gaussian pulse generator and a small antenna model. The digital variable square pulse generator makes the amplitude and width of the generated quasi‐Gaussian pulse tunable. The proposed pulse generator works well for three different electrical small antenna models. The simulation results show that the generated pulse approximates the Gaussian shape very well and the radiated signal at the antennas is compliant with the Federal Communication Commission's spectral mask for the 0–960 MHz band. The simple structure of this Gaussian pulse generator lends itself to a low‐power, single‐chip UWB transceiver solution. Copyright © 2008 John Wiley & Sons, Ltd.