Abstract: This article is aimed to study the modeling problems of combinational signals or periodic signals. To overcome the computation complexity of modeling the signals with plenty of characteristic parameters, a parameter separation scheme is developed based on the different characteristic of the signals to be modeled. For the purpose of achieving high-accuracy performance and reducing complexity, two multi-innovation gradient-based iterative (MIGI) subalgorithms are presented by means of gradient search. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous (SS) interactive estimation method is proposed to eliminate the coupling parameters and perform the signal modeling algorithm in accordance with the hierarchical principle. By means of simulation experiments, the proposed SS iterative signal modeling algorithm based on the moving batch data is used for estimating a power signal with three sine waves and a periodic square wave signal. The results demonstrate the effectiveness of the proposed method for modeling the combinational signals with multiple frequencies and other periodic signals. Since the proposed method combines real-time data sampling and iterative estimation, it can be used for on-line identification.

Abstract: This article focuses on the parameter estimation issues for a fractional‐order nonlinear system with autoregressive noise. In the process, the challenge and difficulty are to identify the parameters of the system as well as the order. To reduce the complexity of the structure, we split the system into two subsystems by utilizing the hierarchical identification principle and derive a two‐stage gradient‐based iterative (2S‐GI) algorithm by minimizing two criterion functions. Compared with the calculation amount of the gradient‐based iterative algorithm, the computation of the 2S‐GI algorithm is significantly reduced. Moreover, in order to improve the identification accuracy, we propose a two‐stage moving‐data‐window gradient‐based iterative algorithm. Finally, the simulation examples test the effectiveness of the proposed algorithms.

Abstract: For interpolated discrete Fourier transform (IpDFT)-based phasor estimators, the out-of-band interference (OOBI) test is among the most challenging ones. The typical iterative-interpolated DFT (i-IpDFT) phasor estimator utilizes a two-step iterative framework to eliminate the effects of the negative frequency and OOBI. However, the speed of estimation is limited by the adopted frequency estimator and the redundant iterations. To this end, this article proposes a fast i-IpDFT (FiIpDFT) method for the phasor estimation of an OOBI contaminated signal, which utilizes the three-point IpDFT (I3pDFT) technique. The proposed method first applies a noniterative frequency, amplitude, and phase estimator to eliminate the negative frequency interference. Then, a straightforward formula and two-stop criterion are introduced to reduce the computational burden of the OOBI elimination process. The accuracy and effectiveness of the proposed FiIpDFT method are validated by simulations. These are designed, under steady and dynamic conditions, according to the requirements of the Standard IEC/IEEE 60255-118-1.

Abstract: Poisson surface reconstruction (PSR) remains a popular technique for reconstructing watertight surfaces from 3D point samples thanks to its efficiency, simplicity, and robustness. Yet, the existing PSR method and subsequent variants work only for oriented points. This paper intends to validate that an improved PSR, called iPSR, can completely eliminate the requirement of point normals and proceed in an iterative manner. In each iteration, iPSR takes as input point samples with normals directly computed from the surface obtained in the preceding iteration, and then generates a new surface with better quality. Extensive quantitative evaluation confirms that the new iPSR algorithm converges in 5--30 iterations even with randomly initialized normals. If initialized with a simple visibility based heuristic, iPSR can further reduce the number of iterations. We conduct comprehensive comparisons with PSR and other powerful implicit-function based methods. Finally, we confirm iPSR's effectiveness and scalability on the AIM@SHAPE dataset and challenging (indoor and outdoor) scenes. Code and data for this paper are at https://github.com/houfei0801/ipsr.

Abstract: This article presents a new scheme to extract the rotor position angle of interior permanent magnet synchronous motors using a high-frequency signal injection method with an iterative strategy. An iterative strategy based on the binary principle is proposed to reduce the computational burden using discrete rotor position angles. These discrete rotor position angles are obtained from the angle space, which is divided into several separate sectors and employed to calculate the defined cost function that generates the optimal rotor position angle. With the number of iterations increasing, the accuracy of the iterative search strategy will increase geometrically. Finally, a series of experimental tests have been carried out to compare the performances of the proposed and the conventional low-speed sensorless methods. Experimental results have verified the effectiveness of the proposed low-speed sensorless scheme.

Abstract: Hyperspectral image super-resolution (HSI-SR) can be achieved by fusing a paired multispectral image (MSI) and hyperspectral image (HSI), which is a prevalent strategy. But, how to precisely reconstruct the high spatial resolution hyperspectral image (HR-HSI) by fusion technology is a challenging issue. In this paper, we propose an iterative regularization method based on tensor subspace representation (IR-TenSR) for MSI-HSI fusion, thus HSI-SR. First, we propose a tensor subspace representation (TenSR)-based regularization model that integrates the global spectral-spatial low-rank and the nonlocal self-similarity priors of HR-HSI. These two priors have been proven effective, but previous HSI-SR works cannot simultaneously exploit them. Subsequently, we design an iterative regularization procedure to utilize the residual information of acquired low-resolution images, which are ignored in other works that produce suboptimal results. Finally, we develop an effective algorithm based on the proximal alternating minimization method to solve the TenSR-regularization model. With that, we obtain the iterative regularization algorithm. Experiments implemented on the simulated and real datasets illustrate the advantages of the proposed IR-TenSR compared with state-of-the-art fusion approaches. The code is available at https://github.com/liangjiandeng/IR-TenSR.

Abstract: This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs.

Abstract: In this article, a data-driven distributed leader–follower iterative learning consensus tracking control approach is proposed for unknown repetitive nonlinear nonaffine discrete-time multi-agent systems. The leader’s command is only communicated to a subset of the following agents and each following agent exchanges information only with its neighbors under a directed graph. A local iterative learning consensus control protocol is designed using only local measurements communicated among neighboring agents without the availability of physical and structural information of each agent by virtue of the dynamic linearization method both on the agent and the ideal distributed learning controller along the iteration axis. The convergent consensus properties of the tracking errors along the iteration axis are rigorously established under the strongly connected iteration-independent and iteration-varying communication topologies. One example is provided to validate the effectiveness of the proposed iterative learning consensus control protocol.

Abstract: Deformable image registration is a crucial step in medical image analysis for finding a non-linear spatial transformation between a pair of fixed and moving images. Deep registration methods based on Convolutional Neural Networks (CNNs) have been widely used as they can perform image registration in a fast and end-to-end manner. However, these methods usually have limited performance for image pairs with large deformations. Recently, iterative deep registration methods have been used to alleviate this limitation, where the transformations are iteratively learned in a coarse-to-fine manner. However, iterative methods inevitably prolong the registration runtime, and tend to learn separate image features for each iteration, which hinders the features from being leveraged to facilitate the registration at later iterations. In this study, we propose a Non-Iterative Coarse-to-finE registration Network (NICE-Net) for deformable image registration. In the NICE-Net, we propose: (i) a Single-pass Deep Cumulative Learning (SDCL) decoder that can cumulatively learn coarse-to-fine transformations within a single pass (iteration) of the network, and (ii) a Selectively-propagated Feature Learning (SFL) encoder that can learn common image features for the whole coarse-to-fine registration process and selectively propagate the features as needed. Extensive experiments on six public datasets of 3D brain Magnetic Resonance Imaging (MRI) show that our proposed NICE-Net can outperform state-of-the-art iterative deep registration methods while only requiring similar runtime to non-iterative methods.

Abstract: In this article, a multidirection-based gradient iterative (GI) algorithm for Hammerstein systems with irregular sampling data is proposed. The algorithm updates the parameter estimates using several orthogonal directions at each iteration. The convergence rate is significantly improved with an increasing number of directions. The convergence property and two simulation examples are provided to demonstrate the effectiveness of the proposed algorithm. In addition, the multidirection-based GI algorithm establishes a relationship between the traditional GI and least squares (LS) algorithms. Thus, our algorithm that combines the LS and GI algorithms constructs an identification framework for a significantly wider class of systems.

Abstract: As the basis of contouring motion control, the estimation of contouring error is one of the most important research topic in the field of multiaxis coordination control. In extreme contour cases with high speed, large curvature and sharp corner, inaccurate contouring error estimation and poor real-time performance are two key problems for existing estimation methods. In order to guarantee the real-time performance of the iterative based contouring error estimation methods, a novel iterative calculation method based on Atiken acceleration is proposed in this article. By means of local linearization of the iteration points, the proposed method can not only accelerate the solution of contouring error points, but also effectively prevent the divergence problem caused by improper selection of initial value points, thus guaranteeing the accuracy of contouring error estimation. The proposed accelerated iterative algorithm is verified on a three-axis motion system and compared with the existing numerical iteration method and noniterative method for contouring error estimation. The experimental results show that the proposed method is significantly improved in both calculation speed and solution accuracy, especially in the case of extreme contour.

Abstract: In this paper, we investigate unmanned aerial vehicle (UAV) assisted physical layer security in multi-beam satellite enabled vehicle communications. Particularly, the UAV is exploited as a relay to improve the secure satellite-to-vehicle link, and simultaneously serves as a jammer by deliberately generating artificial noise (AN) to confuse Eve. The satellite beamforming (BF) and UAV power allocation (PA) are jointly optimized to maximize the secrecy rate of the legitimate user within a target beam while guaranteeing the quality of service (QoS) of users within other beams. Since the problem is nonconvex, we first convert it into an equivalent two-stage problem. Then, the outer-stage problem is solved by using one-dimensional search, and the inner-stage problem is transformed to a bi-convex problem by using the semi-definite relaxation (SDR) and Charnes Cooper transformation. To solve the inner-stage bi-convex problem, we propose an iterative alternating optimization algorithm, where the optimal BF is obtained by semi-definite programming (SDP), and the optimal UAV PA is subsequently obtained by solving the reformulated fractional programming problem with an iterative Dinkelbach method. The tightness of SDR and the complexity of our proposed approach are analyzed, and extensive simulations are carried out to evaluate the effectiveness of our proposed approach.

Abstract: The current–voltage characteristics of the double diode and triple diode models of solar cells are highly nonlinear functions, for which there is no analytical solution. Hence, an iterative approach for calculating the current as a function of voltage is required to estimate the parameters of these models, regardless of the approach (metaheuristic, hybrid, etc.) used. In this regard, this paper investigates the performance of four standard iterative methods (Newton, modified Newton, Secant, and Regula Falsi) and one advanced iterative method based on the Lambert W function. The comparison was performed in terms of the required number of iterations for calculating the current as a function of voltage with reasonable accuracy. Impact of the initial conditions on these methods’ performance and the time consumed was also investigated. Tests were performed for different parameters of the well-known RTC France solar cell and Photowatt-PWP module used in many research works for the triple and double diode models. The advanced iterative method based on the Lambert W function is almost independent of the initial conditions and more efficient and precise than the other iterative methods investigated in this work.

Abstract: In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution.

Abstract: In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, automatically tuned , parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes and halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate steering procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality feasible solutions in computation times at least two orders of magnitude faster than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the real electricity and gas transmission networks of the state of Victoria with actual linepack and demand profiles.

Abstract: With the falling cost of Distributed Energy Resources (DERs) and the shift from fossil fuel to renewable energy in many countries, the integration of DERs is expected to grow. This can lead to a wide range of problems in the power system, such as voltage violations, overloading of distribution lines, reverse power flow, etc. Therefore, it is imperative to account for these adverse effects of the integration of DERs on the distribution network and minimize their impact when calculating the Hosting Capacity (HC). Two algorithms are presented in this study derived from a novel modified iterative method and a novel Repeated Particle Swarm Optimization (RPSO) method for determining the HC for multiple DER units simultaneously or a single DER unit integrating into radial or mesh networks. These algorithms calculate the optimal HC based on six scenarios of annual load and DER generation profiles. The developed algorithms were tested on the IEEE 123 bus network, and their results were compared. For a large-scale DER case, the modified iterative method significantly outperforms both the PSO and the normal iterative method in terms of computation time (30 minutes versus 3 hours versus 6 hours, respectively). In the case of multiple DERs, the RPSO method is the only option, as the other two methods cannot simultaneously optimize multiple DERs. As a result, it has been concluded that it is necessary to select HC calculation methods carefully and in accordance with the application, as each method has its own strengths and weaknesses.

Abstract: In this paper, we consider the iterative properties of positive solutions for a general Hadamard-type singular fractional turbulent flow model involving a nonlinear operator. By developing a double monotone iterative technique we firstly establish the uniqueness of positive solutions for the corresponding model. Then we carry out the iterative analysis for the unique solution including the iterative schemes converging to the unique solution, error estimates, convergence rate and entire asymptotic behavior. In addition, we also give an example to illuminate our results.

Abstract: In this article, we study the trajectory control, subchannel assignment, and user association design for unmanned aerial vehicles (UAVs)-based wireless networks. We propose a method to optimize the max-min average rate subject to data demand constraints of ground users (GUs) where spectrum reuse and co-channel interference management are considered. The mathematical model is a mixed-integer nonlinear optimization problem which we solve by using the alternating optimization approach where we iteratively optimize the user association, subchannel assignment, and UAV trajectory control until convergence. For the subchannel assignment subproblem, we propose an iterative subchannel assignment (ISA) algorithm to obtain an efficient solution. Moreover, the successive convex approximation (SCA) is used to convexify and solve the nonconvex UAV trajectory control subproblem. Via extensive numerical studies, we illustrate the effectiveness of our proposed design considering different UAV flight periods and number of subchannels and GUs as compared with a simple heuristic.