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The Last decade saw significant growth in the digital terrestrial television (DTT) subscribers. The High peak-to-average power ratio (PAPR) of the transmitted signal is implied by the large fluctuations in its amplitude, which is a serious issue in the contemporary and next generation DTT broadcasting systems. These large fluctuations prevent feeding the high power amplifier (HPA) at an operating point near its non-linear (NL) saturation region, thereby lowering its power efficiency. For a better future, energy-efficient green communications is the need of hour. This paper focuses on digital predistortion (DPD), which is among the widely used techniques for HPA linearization in order to minimize the NL effects. DPD technique requires a feedback signal. This paper proposes a novel adding signal-based digital predistortion, where the output of the HPA is gradually linearized by adding a signal at the input in an iterative manner. By Taylor series approximation, the DPD problem can be posed as a convex one. We prove that a tighter upper bound exists for the convergence factor and instead of directly solving the convex problem, we pick a convergence factor value within its bounds that offers a good trade-off between convergence speed and residual error value. The simulation results show that the proposed technique can quickly linearize the HPA with good convergence. [ABSTRACT FROM AUTHOR]

Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks, where one task is nested inside the other. In machine learning and computer vision fields, despite the different motivations and mechanisms, a lot of complex problems, such as hyper-parameter optimization, multi-task and meta learning, neural architecture search, adversarial learning and deep reinforcement learning, actually all contain a series of closely related subproblms. In this paper, we first uniformly express these complex learning and vision problems from the perspective of BLO. Then we construct a best-response-based single-level reformulation and establish a unified algorithmic framework to understand and formulate mainstream gradient-based BLO methodologies, covering aspects ranging from fundamental automatic differentiation schemes to various accelerations, simplifications, extensions and their convergence and complexity properties. Last but not least, we discuss the potentials of our unified BLO framework for designing new algorithms and point out some promising directions for future research. A list of important papers discussed in this survey, corresponding codes, and additional resources on BLOs are publicly available at: https://github.com/vis-opt-group/BLO. [ABSTRACT FROM AUTHOR]

Point set registration is a key problem in intelligent vehicle localization and mapping. This paper presents a rigid point set registration algorithm based on the cubature Kalman filter (CKF). First, the point set registration problem is cast into the state space model assuming that the correspondence between these two point sets is previously unknown. Then, CKF is used to solve this nonlinear filtering problem. At every iterative step, all the points in the moving point set will be considered, and the corresponding points in the model point set will be updated accordingly. In the time update, the scale of the free space that can be explored is significant for this registration algorithm. Herein, continuous simulated annealing (CSA) is adopted to gradually optimize the covariance of the model noise to speed up convergence. Tests on public data sets show that the CKF-based point set registration algorithm is robust to outliers, noise, and initialization misalignment. Then, the application of this algorithm on intelligent vehicles and intelligent transportation systems is demonstrated through mapping and localization experiments. The precision and robustness are both validated compared with the traditional ICP, NDT, and CPD based point set registrations in the localization experiments. Thus, the contributions of this paper are threefold. First, a CKF scheme is utilized in the point set registration problem. Second, CSA serves as the local optimizer to speed up the convergence process and make it more accurate. Third, this filtering-based method is adopted in intelligent vehicles and SLAM applications. [ABSTRACT FROM AUTHOR]

This paper considers a general stochastic resource allocation problem that arises widely in wireless networks, cognitive radio, networks, smart-grid communications, and cross-layer design. The problem formulation involves expectations with respect to a collection of random variables with unknown distributions, representing exogenous quantities such as channel gain, user density, or spectrum occupancy. We consider the constant step-size stochastic dual subgradient descent (SDSD) method that has been widely used for online resource allocation in networks. The problem is solved in dual domain, which results in a primal resource allocation subproblem at each time instant. The goal here is to characterize the non-asymptotic behavior of such stochastic resource allocations in an almost sure sense. It is well known that with a step size of \epsilon , SDSD converges to an \mathcal {O}(\epsilon) -sized neighborhood of the optimum. In practice, however, there exists a trade-off between the rate of convergence and the choice of \epsilon $ . This paper establishes a convergence rate result for the SDSD algorithm that precisely characterizes this trade-off. Toward this end, a novel stochastic bound on the gap between the objective function and the optimum is developed. The asymptotic behavior of the stochastic term is characterized in an almost sure sense, thereby generalizing the existing results for the stochastic subgradient methods. For the stochastic resource allocation problem at hand, the result explicates the rate with which the allocated resources become near-optimal. As an application, the power and user-allocation problem in device-to-device networks is formulated and solved using the SDSD algorithm. Further intuition on the rate results is obtained from the verification of the regularity conditions and accompanying simulation results. [ABSTRACT FROM PUBLISHER]

In the first part of this paper, a free-form surface matching method called variance-minimization matching (VMM) was proposed to address uneven/open point distributions and measuring noise. The convergence property and sensitivity to measuring defects were theoretically studied. In the second part of this paper, a series of experiments are presented to verify the feasibility of the proposed method in free-form surface matching. The experiments are divided into four sets: a measuring defects experiment, a noise experiment, a convergence experiment, and an artificial experiment. In the first set of experiments, the existing methods are prone to becoming trapped in a local optimum affected by uneven/open point distributions, which shows that measured points incline toward dense areas. However, in VMM, there is little inclination regardless of the increase in the number of measuring defects. In the second set of experiments, sensitivity to varying noise is tested. The results show that VMM helps prevent unstable sliding in the presence of Gaussian noise. In the third set of experiments, we compare convergence speed and convergence stability under different initial positions. It is verified that VMM exhibits the quadratic convergence. Finally, a set of artificial experiments is implemented, revealing that the proposed method is appropriate for use in automated manufacturing processes such as geometric inspection and allowance distribution. Note to Practitioners—Measuring defects usually occur when using a scanning device to obtain the measured points of a workpiece. Weakening the effect of measuring defects on matching results is critical to promoting manufacturing automation. This paper proposes a new method called variance-minimization matching (VMM) that considers measuring defects. In the first part of this paper, the modeling and theoretical analysis of VMM were introduced. In the second part of this paper, simulated experiments are performed to verify the feasibility of VMM in addressing uneven/open point distributions, measuring noise, and large initial positions. Next, artificial experiments employing VMM in geometric inspection and allowance distribution are presented. The proposed method also applies to other automated manufacturing processes, such as workpiece localization, deformation analysis, and complex parts repair. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the fundamental problem of computing MIMO capacity under per-antenna power constraint (PAPC). Unlike the sum power constraint counterpart which likely admits water-filling-like solutions, MIMO capacity with PAPC has been largely studied under the framework of generic convex optimization. The two main shortcomings of these approaches are 1) their complexity scales quickly with the problem size, which is not appealing for large-scale antenna systems and/or 2) their convergence properties are sensitive to the problem data. As a starting point, we first consider a single user MIMO scenario and propose two provably-convergent iterative algorithms to find its capacity, the first method based on fixed-point iteration and the other based on alternating optimization and minimax duality. In particular, the two proposed methods can leverage the water-filling algorithm in each iteration and converge faster, compared with current methods. We then extend the proposed solutions to multiuser MIMO systems with dirty paper coding-based transmission strategies. In this regard, capacity regions of Gaussian broadcast channels with PAPC are also computed using closed-form expressions. Numerical results are provided to demonstrate the outperformance of the proposed solutions over existing approaches. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) and Kernel principal component analysis (KPCA) are fundamental methods in machine learning for dimensionality reduction. The former is a technique for finding this approximation in finite dimensions and the latter is often in an infinite dimensional reproducing Kernel Hilbert-space (RKHS). In this paper, we present a geometric framework for computing the principal linear subspaces in both (finite and infinite) situations as well as for the robust PCA case, that amounts to computing the intrinsic average on the space of all subspaces: the Grassmann manifold. Points on this manifold are defined as the subspaces spanned by $K$ K -tuples of observations. The intrinsic Grassmann average of these subspaces are shown to coincide with the principal components of the observations when they are drawn from a Gaussian distribution. We show similar results in the RKHS case and provide an efficient algorithm for computing the projection onto the this average subspace. The result is a method akin to KPCA which is substantially faster. Further, we present a novel online version of the KPCA using our geometric framework. Competitive performance of all our algorithms are demonstrated on a variety of real and synthetic data sets. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence speed of the Arimoto-Blahut algorithm. For many channel matrices, the convergence speed is exponential, but for some channel matrices it is slower than exponential. By analyzing the Taylor expansion of the defining function of the Arimoto-Blahut algorithm, we will make the conditions clear for the exponential or slower convergence. The analysis of the slow convergence in this paper is new. Based on this analysis, we will compare the convergence speeds of the Arimoto-Blahut algorithm numerically with the values obtained in our theorems for several channel matrices. The purpose of this paper is to obtain a complete understanding of the convergence speed of the Arimoto-Blahut algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the underlying assumptions that have been used for designing adaptive particle swarm optimization (PSO) algorithms in the past years are theoretically investigated. I relate these assumptions to the movement patterns of particles controlled by coefficient values (inertia weight and acceleration coefficients) and introduce three factors, namely the autocorrelation of the particle positions, the average movement distance of the particle in each iteration, and the focus of the search, that describe these movement patterns. I show how these factors represent movement patterns of a particle within a swarm and how they are affected by particle coefficients (i.e., inertia weight and acceleration coefficients). I derive equations that provide exact coefficient values to guarantee to achieve the desired movement pattern defined by these three factors within a swarm. I then relate these movements to the searching capability of particles and provide a guideline for designing potentially successful adaptive methods to control coefficients in particle swarm. Finally, I propose a new simple time adaptive particle swarm and compare its results with previous adaptive particle swarm approaches. Experiments show that the theoretical findings indeed provide a beneficial guideline for the successful adaptation of the coefficients in the PSO algorithm. [ABSTRACT FROM AUTHOR]

The special section presents the recent advances on sliding mode control and its applications in modern industrial systems. With the increased utilization of modern equipment in wide industry applications such as renewable energy systems, distributed generation, smart grid, transportation, robot manipulators, power systems and automotive, emphasis on better performance in terms of the robustness, optimization, reliability and implementation simplicity has become an important requirement. Sliding mode control is recognized as one of the popular and powerful tools in achieving these requirements in industrial systems. The robustness feature eliminates the burden of the necessity of system parameters required for accurate modelling in most applications. In spite of these attractive advantages, the sliding mode control method suffers from chattering existing due to unmodelled dynamics and switching time delays. The effort of the researchers and industry has led to a rapid development of different sliding mode control methods in terms of sliding surface design, sliding surface coefficient selection, sliding-mode observers, chattering reduction methods, and modulation techniques. Especially, the observer and disturbance estimation techniques are widely studied and substantial new observation and estimation techniques have been proposed in the literature. Hence, the objective of this special section is to share the new ideas of researchers and industry on sliding mode control and its applications in modern industrial systems. The summaries of thirteen papers accepted for publication are given below. [ABSTRACT FROM AUTHOR]

This paper introduces a robust generalized point cloud (PC) registration method that utilizes not only the positional but also the orientation information associated with each point. The proposed method solves the rigid PC registration problem in a probabilistic manner, which casts the problem into a maximum likelihood (ML) framework. A hybrid mixture model (HMM) is utilized to represent one generalized PC. In the HMM, a von-Mises–Fisher mixture model (FMM) is adopted to model the orientational uncertainty, while a Gaussian mixture model (GMM) is used to represent the positional uncertainty. An expectation–maximization (EM) algorithm is adopted to solve the optimization problem in an iterative manner to find the optimal rotation matrix and the translation vector between two generalized PCs. In both expectation step (E step) and maximization step (M step), orientational information is utilized, which can potentially improve the algorithm’s robustness to noise and outliers. In the E step, the posterior probabilities that represent the degree of point correspondences in two PCs are computed. In the M step, an efficient closed-form solution to a rigid transformation matrix is developed. E and M steps will iterate until certain convergence criteria are satisfied. Extensive experiments under different noise levels and outlier ratios have been carried out on a data set of femur bone computed tomography images. Experimental results show that the proposed method outperforms the state-of-the-art ones in terms of accuracy, robustness, and convergence speed significantly. Note to Practitioners—This paper was motivated by solving the problem of registering two PCs. Most existing approaches generally use only the positional information associated with each point and thus lack robustness to noise and outliers. This paper suggests a new robust method that also adopts the normal vectors associated with each point. The registration problem is cast into a maximum likelihood (ML) problem and solved under the expectation–maximization (EM) framework. Closed-form solutions for estimating parameters in both expectation and maximization steps are provided in this paper. We have demonstrated through extensive experiments that the proposed registration algorithm achieves improved accuracy, robustness to noise and outliers, and faster convergence speed. [ABSTRACT FROM AUTHOR]

This paper aims at proposing a novel 2D non-linear phase decomposition of images, which performs the image processing tasks better than the traditional Fourier transformation (linear phase decomposition), but further, it has additional mathematical properties allowing more effective image analysis, including adaptive decomposition components and positive instantaneous phase derivatives. 1D unwinding Blaschke decomposition has recently been proposed and studied. Through factorization it expresses arbitrary 1D signal into an infinite linear combination of Blaschke products. It offers fast converging positive frequency decomposition in the form of rational approximation. However, in the multi-dimensional cases, the usual factorization mechanism does not work. As a consequence, there is no genuine unwinding decomposition for multi-dimensions. In this paper, a 2D partial unwinding decomposition based on algebraic transforms reducing multi-dimensions to the 1D case is proposed and analyzed. The result shows that the fast convergence offers efficient image reconstruction. The tensor type decomposing terms are mutually orthogonal, giving rise to 2D positive frequency decomposition. The comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the Fourier category. An application in watermarking is presented to demonstrate its potential in applications. [ABSTRACT FROM AUTHOR]

This paper compares three modern and two classical multiobjective optimizers (MOOs) as applied to real-world problems in electromagnetics. The behavior of sophisticated optimizers on simple test functions has been studied exhaustively. In contrast, the algorithms here are tested on practical applications, where the function evaluations are computationally expensive, making the convergence rate a crucial factor. The examples considered include the optimization of a narrowband slot antenna, a mushroom-type electromagnetic bandgap structure, and an ultrawideband Vivaldi antenna. Another popular topic in the literature is in comparing classical MOOs on electromagnetics problems. The modern optimizers chosen in this paper are state of the art and each has a distinct design philosophy. This paper introduces two unique MOOs to the electromagnetics community: BORG, an auto-adaptive genetic algorithm and the Multi-Objective Covariance Matrix Adaptation Evolutionary Strategy (MO-CMA-ES), an extension of the popular single-objective CMA-ES. These algorithms are compared to the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D), a Chebysheff scalarization algorithm, and two classical MOOs. This paper will study the behavior of these algorithms on problems in electromagnetics with a limited number of function evaluations using five distinct metrics and will provide useful guidelines and recommended optimizer settings. [ABSTRACT FROM AUTHOR]

A recent research paper by Wei et al. proposes a differential privacy algorithm in the context of Federated Learning and provides its performance analysis, mainly focusing on proving a convergence bound for the loss function. In this paper, we show that some of the mathematical derivations given in Wei et al. are not valid. Thus the bounds they prove in the paper do not hold for all loss functions. In this work, we give the correct derivation of the best possible local sensitivity bound, which is valid for all loss functions. We also state the modifications in the bounds for global sensitivity and the standard deviation of the Gaussian noise added, both before and after aggregation. [ABSTRACT FROM AUTHOR]

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input–output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC. [ABSTRACT FROM AUTHOR]

Communication systems introduce uncertainties that directly impact power system management. Quantitative analysis of such impact is essential for power system reliability and resilience. This paper establishes rigorous relationships between communication packet delivery ratio and errors on optimal load tracking and allocation (OLTA) in DC microgrids (MGs). By modeling channel uncertainties using packet delivery ratio and communication network topologies, impact of communication packet loss on the distributed OLTA algorithm for DC MGs is studied. It is shown that communication packet loss directly affects the convergence rate of the distributed OLTA algorithm under intermittent renewable generations. The results of this paper quantitatively characterize a practical criterion for securing reliability of OLTA solutions under communication uncertainty. Simulation studies using a real-world DC MG are conducted to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper proves an impossibility result for stochastic network utility maximization for multi-user wireless systems, including multiple access and broadcast systems. Every time slot an access point observes the current channel states for each user and opportunistically selects a vector of transmission rates. Channel state vectors are assumed to be independent and identically distributed with an unknown probability distribution. The goal is to learn to make decisions over time that maximize a concave utility function of the running time average transmission rate of each user. Recently it was shown that a stochastic Frank-Wolfe algorithm converges to utility-optimality with an error of $O(\log (T)/T)$ , where $T$ is the time the algorithm has been running. An existing $\Omega (1/T)$ converse is known. The current paper improves the converse to $\Omega (\log (T)/T)$ , which matches the known achievability result. It does this by constructing a particular (simple) system for which no algorithm can achieve a better performance. The proof uses a novel reduction of the opportunistic scheduling problem to a problem of estimating a Bernoulli probability $p$ from independent and identically distributed samples. Along the way we refine a regret bound for Bernoulli estimation to show that, for any sequence of estimators, the set of values $p \in [{0,1}]$ under which the estimators perform poorly has measure at least 1/6. [ABSTRACT FROM AUTHOR]

As an algorithmic framework, message passing is extremely powerful and has wide applications in the context of different disciplines including communications, coding theory, statistics, signal processing, artificial intelligence and combinatorial optimization. In this paper, we investigate the performance of a message-passing algorithm called min-sum belief propagation (BP) for the vertex-disjoint shortest $k$ -path problem ($k$ -VDSP) on weighted directed graphs, and derive the iterative message-passing update rules. As the main result of this paper, we prove that for a weighted directed graph $G$ of order $n$ , BP algorithm converges to the unique optimal solution of $k$ -VDSP on $G$ within $O(n^{2}w_{max})$ iterations, provided that the weight $w_{e}$ is nonnegative integral for each arc $e\in E(G)$ , where $w_{max}=\max \{w_{e}: e\in E(G)\}$. To the best of our knowledge, this is the first instance where BP algorithm is proved correct for NP-hard problems. Additionally, we establish the extensions of $k$ -VDSP to the case of multiple sources or sinks. [ABSTRACT FROM AUTHOR]

This paper investigates optimal power management in dc microgrids, with its applications to dc dual-source trolleybus systems. High mobility of buses and their impact on power supply networks introduce challenging power management issues. This paper incorporates line power losses in power management strategies and introduces a new distributed optimal power management methodology. A multi-objective optimization model is developed. Using only neighborhood information exchange among feeder lines in the network, the new consensus-type control accommodates both feeder current allocation and power loss reduction with fast convergence. One critical finding of this paper is that our local recursive optimization algorithms achieve the global optimal solution asymptotically. Under random noise on information exchange, convergence and optimality of the proposed method are established rigorously. The power system configurations of the Beijing dual-source trolleybus system are used for simulation case studies on the new power management methods. Feasibility, accuracy, and comparison with global optimization results are demonstrated. [ABSTRACT FROM PUBLISHER]

We study how to efficiently allocate the infinitesimal divisible resource under auction mechanism in a dynamic way. We propose a Vickrey–Clarke–Groves-type auction mechanism with a 2-D bid which specifies a per unit price and a maximum of the demand. Due to the absence of enough information related to the infinite dimensional valuations of individual players in a single-bid strategy, it is challenging to implement the efficient Nash equilibrium (NE) in a dynamic way. In this paper, we introduce a pair of parameters related to players’ valuations, and design a decentralized dynamic process assisted with this pair of values, such that at each iteration, a single player updates its best bid under a constrained set of demand. Under the proposed auction mechanism, we show the incentive compatibility, efficiency, and uniqueness of the NE. Furthermore, our method is guaranteed to converge to the efficient NE, and it presents the enhanced convergence performance compared with those methods proposed in the literature. Case studies are given to demonstrate the results developed in this paper. [ABSTRACT FROM PUBLISHER]

This paper is concerned with iterative learning control (ILC) algorithms for two-dimensional (2-D) linear discrete systems described by the first Fornasini–Marchesini model (FMMI) with iteration-varying reference trajectories/profiles. The variation of reference trajectories in iteration domain is represented by a high-order internal model (HOIM) formula. Robustness and convergence of two types of HOIM-based ILC laws with different boundary conditions are investigated, respectively. A strategy employed in this paper is to reconstruct the HOIM-based ILC process of the 2-D linear FMMI system into a set of 2-D linear inequalities or a 2-D linear Roesser model such that sufficient robustness/convergence conditions of the HOIM-based ILC laws are obtained. Under random boundary conditions, the designed ILC law (9) is capable to drive the ILC tracking error into a bounded range. Moreover, under the HOIM-based boundary conditions, a perfect tracking to the iteration-varying reference trajectories can be achieved by utilizing the proposed ILC law (32). Two simulation examples are given to validate the effectiveness of the two proposed ILC algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time sliding mode inventory management strategy based on a novel non-switching type reaching law is introduced. The proposed reaching law eliminates undesirable chattering, and ensures that the sliding variable rate of change is upper bounded by a design parameter which does not depend on the system initial conditions. This approach guarantees fast convergence with non-negative, upper limited supply orders, and ensures that the maximum stock level may be specified a priori by the system designer. Furthermore, a sufficient condition for 100% customers' demand satisfaction is derived. The inventory replenishment system considered in this paper involves multiple suppliers with different lead times and different transportation losses in the delivery channels. [ABSTRACT FROM AUTHOR]

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This work investigates energy-optimal motion planning for a class of multiaxis motion systems where the system dynamics are linear time-invariant and decoupled in each axis. Solving the problem in a reliable and efficient manner remains challenging owing to the presence of various constraints on control and states, nonconvexity in its cost function, and obstacles. This paper shows how the cost function can be convexified by considering the system dynamics, while decomposing decision variables to obtain a convex representation of collision avoidance constraints. With the convexified cost function and constraints, the original problem is decomposed into two quadratic programming (QP) problems. An alternating quadratic programming (AQP) algorithm is proposed to solve both the QP problems alternatingly and iteratively till convergence. Requiring an initial feasible trajectory as a guess, AQP necessarily converges to an energy-efficient solution that is homotopic to the initial guess. Under certain circumstances, AQP is guaranteed to produce a local optimum. Simulation demonstrates that AQP is computationally efficient and reliable while claiming comparable energy saving as the mixed-integer QP approach. Note to Practitioners—This paper presents an energy-optimal motion planning algorithm that can be easily implemented on a class of multiaxis motion systems. Main advantages of the proposed algorithm are: 1) it produces a trajectory resulting in lower but comparable energy efficiency as the global optimum; 2) it is guaranteed to provide an energy-efficient and constraint-compliant trajectory, and thus is reliable; 3) it requires a low computational load and can be deployed on a wide range of applications; and 4) its implementation is straightforward to any engineer with basic knowledge of numerical methods. [ABSTRACT FROM AUTHOR]

This paper considers a low-complexity Gaussian message passing (GMP) Multi-User Detection (MUD) scheme for a coded massive multiple-input multiple-output (MIMO) system with non-orthogonal multiple access (massive MIMO-NOMA), in which a base station with $N_{s}$ antennas serves $N_{u}$ sources simultaneously in the same frequency. Both $N_{u}$ and $N_{s}$ are large numbers, and we consider the overloaded cases with $N_{u}>N_{s}$. The GMP for MIMO-NOMA is a message passing algorithm operating on a fully-connected loopy factor graph, which is well understood to fail to converge due to the correlation problem. The GMP is attractive as its complexity order is only linearly dependent on the number of users, compared to the cubic complexity order of linear minimum mean square error (LMMSE) MUD. In this paper, we utilize the large-scale property of the system to simplify the convergence analysis of the GMP under the overloaded condition. We prove that the variances of the GMP definitely converge to the mean square error (MSE) of the LMMSE multi-user detection. Second, the means of the traditional GMP will fail to converge when $N_{u}/N_{s}< (\sqrt {2}-1)^{-2}\approx 5.83$. Therefore, we propose and derive a new convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the LMMSE multi-user detection performance for any $N_{u}/N_{s}>1$ , and show that it has a faster convergence speed than the traditional GMP with the same complexity. Finally, the numerical results are provided to verify the validity and accuracy of the theoretical results presented. [ABSTRACT FROM AUTHOR]

In many different applications, it is important to determine the Hilbert transform of a given function. However, it is generally impossible to calculate it in closed form. Therefore Hilbert transform approximations are used. This paper studies the convergence and divergence behavior of general classes of such approximation methods. These classes are characterized by two very natural axioms and they include basically all known traditional numerical algorithms. The convergence of these methods is investigated on a family of signal spaces of continuous functions with finite energy. These spaces are parametrized by a number which measures the energy concentration in the low frequency components of the signal. It is shown that stable methods only exist on signal spaces with a sufficient energy concentration and this paper gives some explicit examples of convergent methods. On all other spaces in the family of signal spaces, every sampling-based Hilbert transform approximation shows a blowup behavior of its peak value, i.e., on these spaces, every sampling-based Hilbert transform approximation diverges. [ABSTRACT FROM AUTHOR]

The problem of the leader-following formation control of nonholonomic mobile robots is addressed in this paper. A distributed formation control strategy using explicitly the coordination errors among robots is proposed without assuming that each follower robot knows the full state of the leader. First, a distributed estimation law is proposed for each follower robot to estimate the states, including the position, orientation, and linear velocity of the leader. The distributed formation control law is then designed based on the estimated states of the leader, and the neighborhood formation tracking error. Under some mild assumptions on the interaction graph among the leader and the follower robots, and the velocity of the leader, asymptotic convergence of formation tracking errors to zero can be achieved. Finally, some numerical simulations and experiments on a group of nonholonomic mobile robots are presented to demonstrate the effectiveness of the proposed strategy. Note to Practitioners—The motivation of this paper is to investigate a practical control strategy for the leader-following formation of multiple autonomous mobile robots subjected to nonholonomic constraints. In most of the existing leader-following formation control schemes for nonholonomic mobile robots, having access to the full state of the leader is a requirement. However, due to limitations in communication bandwidth and range, it is reasonable to assume that the information of the leader is available only to a subset of followers. Hence, this paper suggests a new distributed leader-following formation control strategy based on the distributed estimation of the leader’s states. Moreover, the coordination error between a pair of interacting robots is explicitly used in the control design to weaken the dependence on the estimated state of the leader, and enhance the decentralized nature of the proposed control scheme. The stability and convergence of the system are analyzed mathematically and the experiment using unicycles provides promising results. In ongoing research, we are addressing the issues of collision avoidance and communication delays to provide more realistic setup for the industrial applications of multivehicle systems. [ABSTRACT FROM AUTHOR]

This paper proposes a momentum algorithm based on Borges difference and an adaptive momentum (Adam) algorithm based on Borges difference to update parameters, which can adjust the momentum information more flexibly. The Borges difference is proposed from the definition of Borges derivative to be combined with the gradient algorithm in convolutional neural networks. The proposed momentum algorithm based on Borges difference and Adam algorithm based on Borges difference can be adjusted more flexibly in order to speed up the convergence. The parameter optimization algorithm with the Borges difference presents a better performance compared with the integer-order momentum algorithm and integer-order Adam algorithm, with the proposed nonlinear adjustment method for the parameter tuning of convolutional neural networks. By analyzing experimental results of Fashion-MNIST dataset and CIFAR-10 dataset, the optimization algorithms based on Borges difference proposed in this paper gain better effects on the optimization model compared with the corresponding ones based on the integer-order difference, and can speed up the convergence speed and recognition accuracy of the image recognition. [ABSTRACT FROM AUTHOR]

A rectangular-window sidelobe magnitude reduction method by widening the main lobe width was proposed by Saramäki. A technique for trading off main lobe width against sidelobe magnitude for any arbitrary window was reported by Lim et al.; a fast convergence algorithm for its implementation was proposed by the same authors in another article, where the derivatives of the window function are expressed in Chebyshev polynomials which have high arithmetic complexity. All the coefficients of a rectangular-window are equal; this special property is exploited, in this paper, for deriving the window function’s derivatives without the use of Chebyshev polynomials resulting in a great reduction in the arithmetic complexity. [ABSTRACT FROM AUTHOR]

Total variation (TV) is a one of the most popular regularizers for stabilizing the solution of ill-posed inverse problems. This paper proposes a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functionals. Unlike traditional methods that require nested iterations for computing the proximal step of TV, our algorithm approximates the latter with several simple proximals that have closed form solutions. We theoretically prove that the proposed parallel proximal method achieves the TV solution with arbitrarily high precision at a global rate of converge that is equivalent to the fast proximal-gradient methods. The results in this paper have the potential to enhance the applicability of TV for solving very large-scale imaging inverse problems. [ABSTRACT FROM AUTHOR]

This paper proposes a united-based imperialist competitive algorithm (UICA) for compensatory neural fuzzy systems. The original imperialist competitive algorithm (ICA) comprises numerous empires in the population, and each empire comprises one imperialist and some colonies. Each country represents a feasible solution in the empire, and the more favorable solutions become imperialists, taking over less favorable solutions (i.e., colonies). In the ICA, each colony moves toward its relevant imperialist according to an assimilation policy. This paper proposes a UICA that focuses on this assimilation policy to explore the characteristics of the colonies. The assimilation policy consists of three major parts in this paper. In the first part, a colony searches for the best previous position of the colony. In the second part, the colony faces the best-so-far imperialist. In the third part, the colony moves toward the corresponding imperialist of the colony. The proposed UICA was applied to nonlinear system problems, and the experimental results indicated that the proposed UICA is effective. [ABSTRACT FROM PUBLISHER]

This paper addresses network anomography, that is, the problem of inferring network-level anomalies from indirect link measurements. This problem is cast as a low-rank subspace tracking problem for normal flows under incomplete observations and an outlier detection problem for abnormal flows. Since traffic data is large-scale time-structured data accompanied with noise and outliers under partial observations, an efficient modeling method is essential. To this end, this paper proposes an online subspace tracking of a Hankelized time-structured traffic tensor for normal flows based on the Candecomp/PARAFAC decomposition exploiting the recursive least squares algorithm. We estimate abnormal flows as outlier sparse flows via sparsity maximization in the underlying under-constrained linear-inverse problem. A major advantage is that our algorithm estimates normal flows by low-dimensional matrices with time-directional features as well as the spatial correlation of multiple links without using the past observed measurements and the past model parameters. Extensive numerical evaluations show that the proposed algorithm achieves faster convergence per iteration of model approximation and better volume anomaly detection performance compared to state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

This paper revisits the temporal difference (TD) learning algorithm for the policy evaluation tasks in reinforcement learning. Typically, the performance of TD(0) and TD($\lambda$ λ ) is very sensitive to the choice of stepsizes. Oftentimes, TD(0) suffers from slow convergence. Motivated by the tight link between the TD(0) learning algorithm and the stochastic gradient methods, we develop a provably convergent adaptive projected variant of the TD(0) learning algorithm with linear function approximation that we term AdaTD(0). In contrast to the TD(0), AdaTD(0) is robust or less sensitive to the choice of stepsizes. Analytically, we establish that to reach an $\epsilon$ ε accuracy, the number of iterations needed is $\tilde{O}(\epsilon ^{-2}\ln ^4\frac{1}{\epsilon }/\ln ^4\frac{1}{\rho })$ O ˜ (ε - 2 ln 4 1 ε / ln 4 1 ρ) in the general case, where $\rho$ ρ represents the speed of the underlying Markov chain converges to the stationary distribution. This implies that the iteration complexity of AdaTD(0) is no worse than that of TD(0) in the worst case. When the stochastic semi-gradients are sparse, we provide theoretical acceleration of AdaTD(0). Going beyond TD(0), we develop an adaptive variant of TD($\lambda$ λ ), which is referred to as AdaTD($\lambda$ λ ). Empirically, we evaluate the performance of AdaTD(0) and AdaTD($\lambda$ λ ) on several standard reinforcement learning tasks, which demonstrate the effectiveness of our new approaches. [ABSTRACT FROM AUTHOR]

Orthogonal/vector approximate message-passing (AMP) is a powerful message-passing (MP) algorithm for signal reconstruction in compressed sensing. This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the large system limit. The proof strategy is based on a novel long-memory (LM) MP approach: A first step is a construction of LM-MP that is guaranteed to converge systematically. A second step is a large-system analysis of LM-MP via an existing framework of state evolution. A third step is to prove the convergence of state evolution recursions for Bayes-optimal LM-MP via a new statistical interpretation of existing LM damping. The last is an exact reduction of the state evolution recursions for Bayes-optimal LM-MP to those for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution recursions for Bayes-optimal LM-MP implies that for Bayes-optimal orthogonal/vector AMP. Numerical simulations are presented to show the verification of state evolution results for damped orthogonal/vector AMP and a negative aspect of LM-MP in finite-sized systems. [ABSTRACT FROM AUTHOR]

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable (e.g., perform poorly or even diverge) for other matrix ensembles, especially for ill-conditioned ones. To solve this issue, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear minimum mean square error (MMSE) estimator. This prevents OAMP/VAMP from being used in large-scale systems. To address the drawbacks of AMP and BO-OAMP/VAMP, this paper offers a memory AMP (MAMP) framework based on the orthogonality principle, which ensures that estimation errors in MAMP are asymptotically IID Gaussian. To realize the required orthogonality for MAMP, we provide an orthogonalization procedure for the local memory estimators. In addition, we propose a Bayes-optimal MAMP (BO-MAMP), in which a long-memory matched filter is used for interference suppression. The complexity of BO-MAMP is comparable to AMP. To asymptotically characterize the performance of BO-MAMP, a state evolution is derived. The relaxation parameters and damping vector in BO-MAMP are optimized based on state evolution. Most crucially, the state evolution of the optimized BO-MAMP converges to the same fixed point as that of the high-complexity BO-OAMP/VAMP for all right-unitarily-invariant matrices, and achieves the Bayes optimal MSE predicted by the replica method if its state evolution has a unique fixed point. Finally, simulations are provided to verify the theoretical results’ validity and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, detectability analysis is studied and extended to guide selection of measurements for the dynamic state estimation (DSE) of a synchronous machine. To make sure that the DSE converges, past studies suggested that enough measurements must be available to make the system observable. In this paper, the convergence condition is relaxed via detectability analysis to reduce the number of required measurements. Because the objective of the DSE is to estimate the current states as time progresses, it is shown that a DSE observer can converge not only for an observable system but also for an unobservable system if the eigenvalues corresponding to the unobservable states are stable. Simulation results using the IEEE 10-machine, 39-bus system show that the unscented-Kalman-filter-based DSE can converge when measurements are chosen such that the unobservable states have stable eigenvalues. In comparison with observability analysis, the proposed application of detectability analysis can reduce the number of measurements required for the existence of a DSE observer. [ABSTRACT FROM AUTHOR]

DC Microgrids have been widely used due to their high efficiency, high reliability and flexibility. A sine qua non condition for the correct operation of systems is the existence of a feasible power-flow solution. This paper analyzes the existence of the feasible power-flow solution of the DC microgrid under droop control. Firstly, the power-flow mathematical model of DC microgrid is established. Then, based on the nested interval theorem, we obtain the sufficient conditions of the existence of the feasible power-flow solution, and the uniqueness of the feasible power-flow solution is proved. Moreover, the iterative algorithm of the feasible power-flow solution is proposed, which is proved to be monotonically exponentially convergent. The proposed algorithm’s domain of attraction is derived, thus, the initial iterative value of which can easily be chosen to guarantee its convergence. Finally, case studies are given in this paper to verify the correctness and effectiveness of the proposed theorems. [ABSTRACT FROM AUTHOR]

A specific class of nonlinear systems, admitting finite-duration attractors (FDAs), is introduced in this paper, and used for consensus of multiagent systems (MASs). The advantage is that one can obtain a closed-form solution for the settling time function of the presented nonlinear systems. Such a system exhibits a two-phase convergence process, and its settling time function takes values over a finite duration. However, the duration width changes with respect to the initial condition. The FDA-based consensus protocol is shown to make the MAS undertaken achieve finite-duration convergence. With illustrative examples, the perfect consensus property is verified for MASs with or without a leader agent. [ABSTRACT FROM AUTHOR]

The coordinated solution of AC optimal power flow (ACOPF) in the integrated transmission and distribution grid utilizes controllable energy resources in distribution grids for introducing additional operational economy and security benefits of power grids. However, it is rather impractical to compute the ACOPF centrally considering the information privacy in the operation of transmission and distribution grids. Due to the large capacity of distributed generators integrated to distribution grids, existing decentralized methods may encounter numerical problems and fail to converge when nonlinear ACOPF models are applied. In this paper, we propose a decentralized method to solve the ACOPF for integrated transmission and distribution grids. The proposed ACOPF model is characterized through polar-coordinate equations and branch flow equations for transmission grids and distribution grids respectively. A distribution-cost-correction framework is developed for a fast-convergent solution which is based on approximated distribution cost functions. A rigorous proof is provided for convergence and numerical simulations are analyzed for standard IEEE systems which demonstrate the advantages of the coordinated approach in reducing generation dispatch costs and mitigating overvoltage problems. The paper validates through simulations that the accuracy, computational efficiency, and scalability of the proposed approach are superior to those of traditional methods. [ABSTRACT FROM AUTHOR]

Truck-mounted mobile emergency resources (MERs) play a significant role in microgrid formation and regulation for power system resilience enhancement. This paper proposes a distributed fixed-time secondary control (DFSC) scheme to regulate the frequency and active power sharing in islanded microgrids with MERs. The proposed DFSC scheme is designed based on a general directed communication graph which considers MER characteristics (e.g., mobility, flexibility, and potential cyber threats). Each DER receives data from its neighbors through directional communication links. The proposed pinning control strategy selects only a small number of DERs for pinning, which have access to the reference frequency information and would guide the operation of remaining local DERs and MERs. In addition, the guaranteed convergence time is determined by control parameters and communication graph without applying the initial operation states. The paper demonstrates that the desired control performances (i.e., frequency restoration and accurate active power sharing) are realized in a timely fashion considering frequent operations of MERs. Case studies are tested and discussed for load variations, different control parameters, communication link failures, and MER operations through time-domain simulations in PSCAD/EMTDC platform. [ABSTRACT FROM AUTHOR]

We investigate the matrix function optimization under the orthonormal constraint on the matrix variable. By introducing an index-notation-arrangement-based chain rule (I-Chain rule), we obtain the gradient of the cost function and propose a revisited orthonormal-constraint-based projected gradient method to locate a minimum of an objective/cost function of matrix variables iteratively subject to orthonormal constraint. To guarantee the convergence the proposed method, existing schemes require the gradient can be represented by the multiplication of a symmetrical matrix and the matrix variable itself. This condition has been relaxed in this paper. New techniques are proposed to establish the convergence property of the iterative algorithm. Simulation results show the effectiveness of our framework. This paper allows more extensive applications of matrix function optimization problems in science and engineering. [ABSTRACT FROM AUTHOR]