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Perturb and observe (P&O) maximum power point tracking (MPPT) algorithms are commonly used in photovoltaic (PV) generation system (PGS) due to its ease of implementation. However, conventional fixed step-size P&O exhibits a trade-off between tracking speed and tracking accuracy. By contrast, variable step-size MPPT can achieve satisfactory tracking accuracy and speed while maintains advantage of simple calculation. This paper aimed to study the performance of different variable step-size P&O MPPT techniques. Initially, a MATLAB based PGS model is developed and validated. Then, variable step-size MPPT methods are compared in terms of energy captured, rise time, settling time and steady-state tracking accuracy under various operating conditions. Performance indices are also proposed in this paper to improve the reliability of the comparison. Finally, the response of these MPPT techniques is evaluated in rapidly changing weather conditions using international standard EN50530 to study the dynamic MPPT efficiency of each method. The pros and cons of each method are then summarized and relevant design suggestions are proposed. [ABSTRACT FROM AUTHOR]

This paper presents a variable step-size updating algorithm for wavelet neural network (WNN) in setting the enhanced PID controller parameters. Compared to the iterative method with constant step-size, the most innovative character of the algorithm proposed is its capability of shortening tracking time and improving the convergence in weights updating process for complex systems or large-scale networks. By combining the relationship among WNN, the Kalman filter and the normalized least mean square (NLMS), we introduce the T–S fuzzy inference mechanism for activation derived functions. Furthermore, a once-through steam generator (OTSG) model is established for validating the practicability and reliability in a real complicated system. Finally, simulation results are presented to exhibit the effectiveness of the proposed variable step-size algorithm. [ABSTRACT FROM AUTHOR]

To improve the computing efficiency of the ordinarily used variable stepsize RKF algorithm, an adaptive variable stepsize RKF method based on norm control is presented. The quantitative functional relationship between the local truncation error, tolerance and stepsize is given, and then the stepsizes are automatically adjusted, and the conditions under which the local error norm equals to zero or minimum are discussed. The description of the satellite orbit dynamic system can be attributed to the solution to the initial value problems of first-order vector ordinary differential equations. The proposed method is used to solve this problem to achieve the satellite orbit integral under the consideration of earth non-spherical and a third body perturbation. Simulation results indicate that the proposed method can satisfy the requirements of high precision orbit prediction, improve computing speed, and is worthy of use in the orbit prediction. [ABSTRACT FROM AUTHOR]

• To analyze the performance of three proportionate algorithms in impulsive noises. • To reveal the ranges and relations of the step-sizes in three proportionate algorithms. • To develop a decorrelation technique based variable step-size scheme to deal with the trade-off between convergence rate and steady-state error. In the literature, the proportionate least mean M-estimate (PLMM) algorithm exhibits good performance when dealing with sparse systems in the presence of impulsive noises. In this paper, the mean and mean-square behaviors of three recursion types of the PLMM algorithm are studied in depth. We derive analytically the stability, transient and steady-state results of these PLMM recursions, and find that they can achieve the same performance when properly choosing the step-size and the proportionate matrix. To improve the filter performance in both convergence rate and steady-state error, we derive a variable step-size (VSS) scheme and then present the VSS-based PLMM algorithms. In addition, based on the adaptive decorrelation strategy aiming at the colored input signals, the VSS adaptive decorrelation PLMM algorithms are developed to further speed up the convergence. Computer simulations have verified our theoretical analyses and the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

We construct a family of embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods of order 2 ≤ p ≤ 4 to be used to obtain numerical solution of spatially discretized hyperbolic PDEs. In this construction, the goals include non-defective property, large stability region, and small error values as defined in Dekker and Verwer (1984) and Kennedy et al. (2000). The new family of embedded pairs offer the ability for strong stability preserving (SSP) methods to adapt by varying the step-size. Through several numerical experiments, we assess the overall effectiveness in terms of work versus precision while also taking into consideration accuracy and stability. [ABSTRACT FROM AUTHOR]

As one of the most promising linearization techniques, adaptive Digital Predistortion (PD) has been widely utilized in modern wireless communication systems for improving the efficiency of Power Amplifier (PA). In view of the non-stationary signal environment for the wideband PAs, an efficient indirect learning adaptive PD is proposed in the paper based on the Memory Polynomial Model (MPM). The coefficients of the proposed PD can be effectively identified by the Modified Least Mean Square (MLMS) learning algorithm. In addition, more stable convergence and lower steady-state error can be achieved simultaneously for the PAs with deep memory effects by adopting the variable step-size parameter. Theoretical analysis results regarding the learning stability, convergence behavior, and selection criteria of initial settings are derived. Simulations demonstrate that MLMS outperforms traditional LMS, Normalized LMS (NLMS), and Generalized Normalized Gradient Descent (GNGD) algorithms in terms of the Normalized Mean Square Error (NMSE) and out-of-band Power Spectral Density (PSD) under the noisy feedback condition for the wideband PAs1. [ABSTRACT FROM AUTHOR]

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In this paper, a new affine projection sign algorithm with a variable step-size, robust in impulsive noise environments, is proposed. For that purpose, ℓ1-norm of the a posteriori error vector is minimized under a box constraint on the step-size. Since the proposed ℓ1-norm minimization problem is non-differentiable convex one, an efficient numerical procedure is developed for the affine projection structure algorithm. Finally, it is demonstrated that the proposed algorithm, not requiring any a priori knowledge, yields more robust convergence in various impulsive noise environments than conventional algorithms with robustness to outliers and recent variable step-size algorithms with a priori information. [ABSTRACT FROM AUTHOR]

Abstract: This letter proposes a band-dependent variable step-size sign subband adaptive filter using the concept of mean-square deviation (MSD) minimization. Since it is difficult to obtain the value of the MSD accurately, the proposed step size is derived by minimizing the upper bound of the conditional MSD with given input. By assigning the different step size in each band, the filter performance can be improved. Moreover, we suggest the estimation method of the measurement-noise variance in an impulsive-noise environment, because the proposed algorithm needs the measurement-noise variance to calculate the step size. The reset algorithm is also applied for maintaining the filter performance when a system change occurs suddenly. Simulation results demonstrate that the proposed algorithm performs better than the existing algorithms in aspects of the convergence rate and the steady-state estimation error. [Copyright &y& Elsevier]

For the contradition of existing variable step-size adaptive algorithms between convergence speed and steady-state error, a new variable step-size least mean square(LMS) adaptive filtering algorithm is proposed. Based on a function of the class S, this new algorithm introduces a reference of adjustment factor P to perform real-time adjustments of the shape of step function, and adjusts the step according to errors autocorrelation mean value so that the convergence is faster innitially and the step changes more smoothly at steady state. The introduction of maximum likelihood weighted algorithm further suppresses the spurious peaks of adaptive filter weights. The new algorithm with maximum likelihood weighted is applied in adaptive time delay estimation experiment, and the result shows under the condition of the existing fixed parameters, the newly-proposed algorithm has faster convergence and smaller steady-state error. Meanwhile, accurate delay estimation when SNR is above -3 dB can be achieved effectively. [ABSTRACT FROM AUTHOR]

Since the disadvantage of traditional MPPT algorithms of variable step-size, proposed power tracking based on variable step-size with the advantage method of the constant-voltage and the perturb-observe (P&O)[1-3]. The control strategy modify the problem of voltage fluctuation caused by perturb-observe method, at the same time, introducing the advantage of constant-voltage method and simplify the circuit topology. With the theoretical derivation, control the output power of photovoltaic modules to change the duty cycle of main switch. Achieve the maximum power stabilization output, reduce the volatility of energy loss effectively, and improve the inversion efficiency[3,4]. Given the result of experimental test based theoretical derivation and the curve of MPPT when the prototype work.

The article discusses the proposal of variable step-size adaptive filter, which has been determined to have a better tracking performance than the original variable step-size convex combination of least mean squares (VSCLMS) algorithm.

Abstract: Fractional step Runge–Kutta methods are a class of additive Runge–Kutta schemes that provide efficient time discretizations for evolutionary partial differential equations. This efficiency is due to appropriate decompositions of the elliptic operator involving the spatial derivatives. In this work, we tackle the design and analysis of embedded pairs of fractional step Runge–Kutta methods. Such methods suitably estimate the local error at each time step, thus providing efficient variable step-size time integrations. Finally, some numerical experiments illustrate the behaviour of the proposed algorithms. [Copyright &y& Elsevier]

Abstract: By building the generalized Sigmoid function relationship between normalized step-size and the power of error signal, a novel variable step-size NLMS algorithm is proposed. It is proved that the step-size of NPVSS-NLMS changes as the new algorithm does when A=σv -m and B=2. The physical meanings of the parameters in this algorithm are explored. The theoretical analysis illustrate that this algorithm combine the virtues of NPVSS-NLMS and Sigmoid function, and it leads to faster convergence rate and lower final misalignment. The computer simulation results support the theoretical analysis. [Copyright &y& Elsevier]

Abstract: A novel adaptive variable step-size constant module medical CT image blind equalization algorithm was proposed. The proposed algorithm overcomes the shortcoming of conventional constant module blind equalization algorithm with the fixed iteration step-size. The processing of image restoration transformed by a linear operation is equivalent to one dimensional blind equalization. The constant modulus blind equalization cost function applied to medical CT image was founded. The mean square error was utilized as step-size control factor to speed up the convergence and improve the performance of the algorithm. Computer simulations show that new algorithm improves peak signal to noise ratio, restoration effects and efficiency of operations, and decrease state residual error. [Copyright &y& Elsevier]

In this paper, we propose an optimal adaptive FIR filter, in which the step-size and error nonlinearity are simultaneously optimized to maximize the decrease of the mean square deviation (MSD) of the weight error vector at each iteration. The optimal step-size and error nonlinearity are derived, and a variable step-size stochastic information gradient (VS-SIG) algorithm is developed to approximately implement the optimal adaptation. Simulation results indicate that this new algorithm achieves faster convergence rate and lower misadjustment error in comparison with other adaptive algorithms. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the issue of the acoustic feedback during online operation of active noise control (ANC) systems. In the existing approach, two FIR filters are used for this task: adaptive for feedback path modeling (FBPM) and fixed for feedback neutralization (FBN). Previously, a simplified method is proposed where these two tasks of modeling and neutralization have been combined into one feedback path modeling and neutralization (FBPMN) adaptive filter. Here we introduce an intuition based variable step size (VSS) parameter, for LMS equation of FBPMN filter. This VSS is motivated from the fact that the error signal of FBPMN filter contains a disturbance-component that is decreasing in nature. The computer simulations are carried out for single-channel and multichannel ANC systems. It is demonstrated that the proposed method achieves better performance than the existing methods. [Copyright &y& Elsevier]

Abstract: In this letter, we propose a variable step-size normalized least mean square (NLMS) algorithm. We study the relationship among the NLMS, recursive least square and Kalman filter algorithms. Based on the relationship, we derive an equation to determine the step-size of NLMS algorithm at each time instant. In steady state, the convergence of the proposed algorithm is verified by using the equation, which describes the relationship among the mean-square error, excess mean-square error, and measurement noise variance. Through computer simulation results, we verify the performance of the proposed algorithm and the change in the variable step-size over iterations. [Copyright &y& Elsevier]

Abstract: A frequency estimator based on the linear prediction property of sinusoidal signals has recently been proposed for the direct estimation of real tone frequency in white noise. We propose a variable step-size direct frequency estimator (VS-DFE), which shows improved performance on account of the use of a dynamically updated step-size instead of a fixed step-size. A comparison of the simulation results of the proposed estimator with those of conventional estimators clearly indicates its superior performance. [Copyright &y& Elsevier]

The normalized subband adaptive filter (NSAF) presented by Lee and Gan can obtain faster convergence rate than the normalized least-mean-square (NLMS) algorithm with colored input signals. However, similar to other fixed step-size adaptive filtering algorithms, the NSAF requires a tradeoff between fast convergence rate and low misadjustment. Recently, a set-membership NSAF (SM-NSAF) has been developed to address this problem. Nevertheless, in order to determine the error bound of the SM-NSAF, the power of the system noise should be known. In this paper, we propose a variable step-size matrix NSAF (VSSM-NSAF) from another point of view, i.e., recovering the powers of the subband system noises from those of the subband error signals of the adaptive filter, to further improve the performance of the NSAF. The VSSM-NSAF uses an effective system noise power estimate method, which can also be applied to the under-modeling scenario, and therefore need not know the powers of the subband system noises in advance. Besides, the steady-state mean-square behavior of the proposed algorithm is analyzed, which theoretically proves that the VSSM-NSAF can obtain a low misadjustment. Simulation results show good performance of the new algorithm as compared to other members of the NSAF family. [ABSTRACT FROM PUBLISHER]

The Constant Modulus Algorithm (CMA), although it is the most commonly used blind equalization technique, converges very slowly. The convergence rate of the CMA is quite sensitive to the adjustment of the step size parameter used in the update equation as in the Least Mean Squares (LMS) algorithm. A novel approach in adjusting the step size of the CMA using the fuzzy logic based outer loop controller is presented in this paper. Inspired by successful works on the variable step size LMS algorithms, this work considers designing a training trajectory that it overcomes hurdles of an adaptive blind training via controlling the level of error power (LOEP) and trend of error power (TOEP) and then obtains a more robust training process for the simple CMA algorithm. The controller design involves with optimization of training speed and convergence rate using experience based linguistic rules that are generated as a part of FLC. The obtained results are compared with well-known versions of CMA; Conventional CMA, Normalized-CMA [Jones, IEEE conference record of the twenty-ninth asilomar conference on signals, systems and computers (Vol. 1, pp. 694–697), 1996], Modified-CMA [Chahed, et al., Canadian conference on electrical and computer engineering (Vol. 4, pp. 2111–2114), 2004], Soft Decision Directed-CMA (Chen, IEE Proceedings of Visual Image Signal Processing, 150, 312–320, 2003) for performance measure and validation. [ABSTRACT FROM AUTHOR]

This paper presents a family variable step-size (VSS) affine projection (AP) adaptive filtering algorithms with selective regressors (SR). The presented algorithms have good convergence speed, low steady state mean square error, and low computational complexity features. The stability bounds of the family of SR-APA algorithms are analyzed based on the energy conservation arguments. This analysis does not need to assume a Gaussian or white distribution for the regressors. We demonstrate the good performance of the proposed algorithms through simulations in system identification and acoustic echo cancellation scenarios. [ABSTRACT FROM AUTHOR]

This paper proposes a new variable step-size least-mean-square (VSLMS) algorithm with an approach in which a gradient-based weighted average is used to improve the weakness of previous VSLMS for application to unknown channel estimation or system identification in Iow-SNR or colored input environments. The proposed scheme leads to a faster convergence rate and a lower misadjustment error. [ABSTRACT FROM AUTHOR]

Abstract: An improved robust variable step-size least mean square (LMS) algorithm is developed in this paper. Unlike many existing approaches, we adjust the variable step-size using a quotient form of filtered versions of the quadratic error. The filtered estimates of the error are based on exponential windows, applying different decaying factors for the estimations in the numerator and denominator. The new algorithm, called more robust variable step-size (MRVSS), is able to reduce the sensitivity to the power of the measurement noise, and improve the steady-state performance for comparable transient behavior, with negligible increase in the computational cost. The mean convergence, the steady-state performance and the mean step-size behavior of the MRVSS algorithm are studied under a slow time-varying system model, which can be served as guidelines for the design of MRVSS algorithm in practical applications. Simulation results are demonstrated to corroborate the analytic results, and to compare MRVSS with the existing representative approaches. Superior properties of the MRVSS algorithm are indicated. [Copyright &y& Elsevier]

Based on a known observation that symplecticity is preserved under certain Sundman time transformations, adaptive symplectic integrators of an arbitrary order are constructed for separable Hamiltonian systems, for two classes of scaling functions. Due to symplecticity, these adaptive integrators have excellent long-time energy behaviour, which is theoretically explained using standard results on the existence of a modified Hamiltonian function. In Contrast to reversible adaptive integration, the constructed methods have good long-time behaviour also for non-reversible systems. Numerical examples of this are given. [ABSTRACT FROM AUTHOR]

Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed time-step versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit (VSIMEX) linear multistep methods for time-dependent PDEs. Families of order-p, p-step VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers' equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior. [ABSTRACT FROM AUTHOR]

Abstract: Employing a recently introduced framework within which a large number of classical and modern adaptive filter algorithms can be viewed as special cases, we extend this framework to cover block normalized LMS (BNLMS) and normalized data reusing LMS (NDRLMS) adaptive filter algorithms. Accordingly, we develop a generic variable step-size adaptive filter. Variable step-size normalized LMS (VSSNLMS) and VSS affine projection algorithms (VSSAPA) are particular examples of adaptive algorithms covered by this generic variable step-size adaptive filter. In this paper we introduce two new VSS adaptive filter algorithms named the variable step-size BNLMS (VSSBNLMS) and the variable step-size NDRLMS (VSSNDRLMS) based on the generic VSS adaptive filter. The proposed algorithms show the higher convergence rate and lower steady-state mean square error compared to the ordinary BNLMS and NDRLMS algorithms. [Copyright &y& Elsevier]

Abstract: We consider stability properties of a class of adaptive time-stepping schemes based upon the Milstein method for stochastic differential equations with a single scalar forcing. In particular, we focus upon mean-square stability for a class of linear test problems with multiplicative noise. We demonstrate that desirable stability properties can be induced in the numerical solution by the use of two realistic local error controls, one for the drift term and one for the diffusion. [Copyright &y& Elsevier]

This letter proposes two new variable step-size algorithms for normalized least mean square and affine projection. The proposed schemes lead to faster convergence rate and lower mis-adjustment error. [ABSTRACT FROM AUTHOR]

To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound. [ABSTRACT FROM AUTHOR]

The numerical integration of differential equations with oscillatory solutions is a very common problem in many fields of the applied sciences. Some methods have been specially devised for this kind of problem. In most of them, the calculation of the coefficients needs more computational effort than the classical codes because such coefficients depend on the step-size in a not simple manner. On the contrary, in this work we present new algorithms specially designed for perturbed oscillators whose coefficients have a simple dependence on the step-size. The methods obtained are competitive when comparing with classical and special codes. [Copyright &y& Elsevier]