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Gossip protocols are popular methods for average consensus problems in distributed computing. We prove new convergence guarantees for a variety of such protocols, including path, clique, and synchronous pairwise gossip. These arise by exploiting the connection between these protocols and the block randomized Kaczmarz method for solving linear systems. Moreover, we extend existing convergence results for block randomized Kaczmarz to allow for a more general choice of blocks, rank-deficient systems, and provide a tighter convergence rate guarantee. Previous results for block randomized Kaczmarz assumed blocks formed a paving of the systems; our analysis, contrary to the title of our paper, generalizes to a broader class of blocks that we call coverings. We furthermore apply this analysis to inconsistent consensus models and obtain similar guarantees. An extensive empirical analysis of these methods is provided for a variety of synthetic and real networks. [ABSTRACT FROM AUTHOR]

The $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ filter design for linear stochastic time-varying delay systems based on the filter velocity constraint is considered in this dissertation. Different from existing $\mathcal {L}_{2}\,-\,\mathcal {L}_{\infty }$ performance analysis and filter design, a new criterion is proposed to make a more accurate judgment, which can not only guarantee the stability of the filtering error system with $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ performance level but also can estimate the convergence speed of the filter. The ideal filter should has the same convergence speed as the original system, so as to ensure the rapid convergence of the error system, but also not to reduce the anti-interference ability and increase the bandwidth of the filter system. By the new filter design method, an ideal filter can be designed, which can regulate the convergence speed of the filter system to the desired effect. A simulation instance is provided to exhibit the validity of the new approach. [ABSTRACT FROM AUTHOR]

A data-driven strategy to estimate the optimal feedback and the value function in an infinite-horizon, continuous-time, linear-quadratic optimal control problem for an unknown system is proposed. The method permits the construction of the optimal policy without any knowledge of the model, without requiring that the time derivatives of the state are available for the design, and without even assuming that an initial stabilizing feedback policy is available. Two alternative architectures are discussed: the first scheme revolves around the periodic computation of some matrix inversions involving the Q-function, whereas the second approach relies on a purely continuous-time implementation of some dynamic systems whose trajectories are uniformly attracted by the solutions to the above algebraic equations. Interestingly, the proposed strategy essentially constitutes a (direct) data-driven implementation of the celebrated Kleinman algorithm, hence subsuming the particularly appealing features of the latter, such as quadratic monotone convergence to the optimal solution. The theory is then validated by the means of practically motivated applications. [ABSTRACT FROM AUTHOR]

This work studies the ${H}_{\infty }$ -based minimal energy control with a preset convergence rate (PCR) problem for a class of disturbed linear time-invariant continuous-time systems with matched external disturbance. This problem aims to design an optimal controller so that the energy of the control input satisfies a predetermined requirement. Moreover, the closed-loop system asymptotic stability with PCR is ensured simultaneously. To deal with this problem, a modified game algebraic Riccati equation (MGARE) is proposed, which is different from the game algebraic Riccati equation in the traditional ${H}_{\infty } $ control problem due to the state cost being lost. Therefore, a unique positive-definite solution of the MGARE is theoretically analyzed with its existing conditions. In addition, based on this formulation, a novel approach is proposed to solve the actuator magnitude saturation problem with the system dynamics being exactly known. To relax the requirement of the knowledge of system dynamics, a model-free policy iteration approach is proposed to compute the solution of this problem. Finally, the effectiveness of the proposed approaches is verified through two simulation examples. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) applies to systems required to track the desired trajectory of finite duration repeatedly. This article considers constrained ILC design for linear time-varying systems, a problem with limited, in relative terms, results in the literature but not uncommon in practical applications. Different design algorithms are developed, and their convergence properties are established. An extension of these designs to point-to-point tracking tasks is given. A high-speed rack feeder typically used in automated warehouses is considered to verify the designs. It represents a flexible beam structure subject to kinematic constraints, such as a maximum velocity and a maximum acceleration with a vertically moving mass causing the time-varying characteristics. Experimental results demonstrate the effectiveness of the designs. [ABSTRACT FROM AUTHOR]

There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically used for image reconstruction within an optimization framework. The technical challenge is to develop a regularizer that can accurately model realistic images and be optimized efficiently along with the loss function. Motivated by the recent plug-and-play paradigm for image regularization, we construct a quadratic regularizer whose reconstruction capability is competitive with state-of-the-art regularizers. The novelty of the regularizer is that, unlike classical regularizers, the quadratic objective function is derived from the observed data. Since the regularizer is quadratic, we can reduce the optimization to solving a linear system for applications such as superresolution, deblurring, inpainting, etc. In particular, we show that using iterative Krylov solvers, we can converge to the solution in few iterations, where each iteration requires an application of the forward operator and a linear denoiser. The surprising finding is that we can get close to deep learning methods in terms of reconstruction quality. To the best of our knowledge, the possibility of achieving near state-of-the-art performance using a linear solver is novel. [ABSTRACT FROM AUTHOR]

This article focuses on the adaptive Kalman filtering problem for linear systems with unknown covariances of both dynamic multiplicative noise (multiplicative measurement noise) and additive noises (additive process and measurement noises). A recursive-noise adaptive Kalman filter is proposed to estimate both states and covariances of noises by using the variational Bayesian (VB) inference and an indirect method. First, we characterize inverse Wishart priors for both measurement noise covariance and process noise covariance and employ the Student’s t-distribution to represent the likelihood function, which is non-Gaussian and affected by mixing multiplicative noise and additive measurement noise. Then, an adaptive Kalman filtering for recursive both noise covariance matrices and dynamic state is proposed following VB inference. Performance analysis for VB procedures and the proposed filter is provided to ensure the convergence and stability. A target tracking example is provided to validate the effectiveness of the proposed filtering algorithm. [ABSTRACT FROM AUTHOR]

The generalized minimum residual method (GMRES) is a commonly used iterative Krylov solver for sparse, non-symmetric systems of linear equations. Like other iterative solvers, data movement dominates its run time. To improve this performance, we propose running GMRES in reduced precision with key operations remaining in full precision. Additionally, we provide theoretical results linking the convergence of finite precision GMRES with classical Gram-Schmidt with reorthogonalization (CGSR) and its infinite precision counterpart which helps justify the convergence of this method to double-precision accuracy. We tested the mixed-precision approach with a variety of matrices and preconditioners on a GPU-accelerated node. Excluding the incomplete LU factorization without fill in (ILU(0)) preconditioner, we achieved average speedups ranging from 8 to 61 percent relative to comparable double-precision implementations, with the simpler preconditioners achieving the higher speedups. [ABSTRACT FROM AUTHOR]

In this article, the consensus problem of linear systems is revisited from a novel geometric perspective. The interaction network of these systems is assumed to be piecewise fixed. Moreover, it is allowed to be disconnected at any time but holds a quite mild joint connectivity property. The system matrix is marginally stable and the input matrix is not of full-row rank. By directly examining the subspace determined by the network, we first establish convergence by resorting to an observability condition. Then, according to joint connectivity, we are able to extend this convergence uniformly to the entire orthogonal complement of the consensus manifold. In this way, we work out the necessary and sufficient condition for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly if and only if a jointly $(\delta,T)$ -connected condition and an observability condition relying only on the system and input matrices are satisfied. We also characterize the lower bound of the convergence rate. Simple yet effective examples are presented to illustrate the findings. [ABSTRACT FROM AUTHOR]

This article addresses the robust fixed-time stabilization control problem for generic linear systems with both matched and mismatched disturbances. A new observer-based fixed-time control technique is proposed to solve this robust stabilization problem, provided that the system matrix pair $(A,B)$ is controllable. The ultimate boundedness of the closed-loop system in the presence of mismatched disturbances is proven. An upper bound of the convergence time is provided, which is irrelevant to initial conditions. Finally, a simulation example is presented to show the efficiency of the proposed control design method. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been successfully applied in several data mining tasks. Recently, there is an increasing interest in the acceleration of NMF, due to its high cost on large matrices. On the other hand, the privacy issue of NMF over federated data is worthy of attention, since NMF is prevalently applied in image and text analysis which may involve leveraging privacy data (e.g, medical image and record) across several parties (e.g., hospitals). In this paper, we study the acceleration and security problems of distributed NMF. First, we propose a distributed sketched alternating nonnegative least squares(DSANLS) framework for NMF, which utilizes a matrix sketching technique to reduce the size of nonnegative least squares subproblems with a convergence guarantee. For the second problem, we show that DSANLS with modification can be adapted to the security setting, but only for one or limited iterations. Consequently, we propose four efficient distributed NMF methods in both synchronous and asynchronous settings with a security guarantee. We conduct extensive experiments on several real datasets to show the superiority of our proposed methods. The implementation of our methods is available at https://github.com/qianyuqiu79/DSANLS. [ABSTRACT FROM AUTHOR]

In this work we present a new framework for the analysis and design of randomized gossip algorithms for solving the average consensus problem. We show how classical randomized iterative methods for solving linear systems can be interpreted as gossip algorithms when applied to special systems encoding the underlying network and explain in detail their decentralized nature. Our general framework recovers a comprehensive array of well-known gossip algorithms as special cases, including the pairwise randomized gossip algorithm and path averaging gossip, and allows for the development of provably faster variants. The flexibility of the new approach enables the design of a number of new specific gossip methods. For instance, we propose and analyze novel block and the first provably accelerated randomized gossip protocols, and dual randomized gossip algorithms. From a numerical analysis viewpoint, our work is the first that explores in depth the decentralized nature of randomized iterative methods for linear systems and proposes them as methods for solving the average consensus problem. We evaluate the performance of the proposed gossip protocols by performing extensive experimental testing on typical wireless network topologies. [ABSTRACT FROM AUTHOR]

Neural networks as well as the related neural dynamics have been widely exploited to conduct online computing operations for solving various problems in recent years. This article makes progress along this direction by proposing a saturation-allowed neural dynamics (SAND) model for solving the perturbed time-dependent system of linear equations with noise-tolerant capacity. Specifically, by elaborately constructing a new general framework enhanced by the error-integration information and nonlinear projection functions (PFs), a SAND model is proposed and investigated under various additive noises. In addition, theoretical analyses reveal that the proposed SAND model is of global convergence with zero theoretical error. Moreover, when the value of PF is strictly limited by bounds, i.e., a saturation function, the upper bound of the residual errors of the proposed SAND model is subject to the noises and the bounds of PF. Computer simulation results, as well as robot experiments, verify the superior property of the proposed SAND model for solving the perturbed time-dependent system of linear equations, compared with the state of the prior art. [ABSTRACT FROM AUTHOR]

In signed networks, the cooperation and antagonism cause great difficulties for their behavior analysis, especially, when they are subject to time-varying topologies. This is different from unsigned networks involving only cooperations, of which behavior analysis can be feasibly achieved based on the nonnegative matrix theory. With these facts, this article first bridges a relation between signed and unsigned networks and then takes advantage of the relation for the behavior analysis of signed networks under directed switching topologies. In particular, a solution is provided for the connection of signed and unsigned networks via solving a class of linear dynamic systems, which is obtained by separating antagonisms from cooperations. The solution makes it possible to employ the convergence results for unsigned networks to address the convergence issues for signed networks. If the joint spanning tree condition is met, then switching signed networks can achieve the quasi-interval bipartite consensus. Moreover, the established results can be applied to signed networks with both continuous-time and discrete-time dynamics. [ABSTRACT FROM AUTHOR]

With the emergence of the Internet of Things that allows communications and local computations and with the vision of Industry 4.0, a foreseeable transition is from centralized system planning and operation toward decentralization with interacting components and subsystems, e.g., self-optimizing factories. In this article, a new “price-based” decomposition and coordination methodology is developed to efficiently coordinate a system consisting of distributed subsystems such as machines and parts, which are described by mixed-integer linear programming (MILP) formulations, in an asynchronous way. The novel method is a dual approach, whereby the coordination is performed by updating Lagrangian multipliers based on economic principles of “supply and demand.” To ensure low communication requirements within the method, exchanges between the “coordinator” and subsystems are limited to “prices” (Lagrangian multipliers) broadcast by the coordinator and to subsystem solutions sent at the coordinator. Asynchronous coordination, however, may lead to convergence difficulties since the order in which subsystem solutions arrive at the coordinator is not predefined as a result of uncertainties in communication and solving times. Under realistic assumptions of finite communication and solve times, the convergence of our method is proven by innovatively extending the Lyapunov stability theory. Numerical testing of generalized assignment problems through simulation demonstrates that the method converges fast and provides near-optimal results, paving the way for self-optimizing factories in the future. Accompanying CPLEX codes and data are included. Note to Practitioners—In view of a foreseeable transition toward self-optimizing factories whereby machines and parts have communication and computational capabilities, a novel “price-based” distributed and asynchronous method to coordinate a system consisting of distributed subsystems is developed. Under realistic assumptions of finite communication and solve times, method convergence is proven. Numerical testing of generalized assignment problems through simulation demonstrates that the method converges fast and provides near-optimal results, paving the way for self-optimizing factories in the future. Accompanying CPLEX codes and data are included. [ABSTRACT FROM AUTHOR]

Although proportional-integral-derivative control remains one of the most common control schemes used in industry, its tuning still remains inadequately understood in many applications. This task becomes much more challenging when applied to multi-input multi-output (MIMO) systems. This article presents the design of a discrete-time robust multivariable (nonadaptive) tracking controller that comes with a simple structure, requires very limited information on the plant model, and is relatively easy to tune. In addition to being easy to tune and implement, an objective of this controller is to deal with a class of large-scale systems with complex dynamics. We analytically demonstrate the robustness and convergence of the closed-loop system for a class of MIMO linear time-varying systems. The overall superiority of the proposed controller is experimentally validated on a Barrett robot arm in a laboratory environment. The article also provides a stochastic framework of the general setting of the controller. Within this framework, two minimum mean square error optimal solutions of the controller are provided; one is designed for the case where the number of inputs is not greater than the number of outputs, and the other is for the antithesis. [ABSTRACT FROM AUTHOR]

Model predictive iterative learning control (MPILC) is a popular approach to control batch systems with repetitive nature, as it is capable of tracking the plant reference trajectory with high accuracy and guaranteed closed-loop stability. However, varying reference trajectory often happens in batch processes, so that the tracking performance of a general MPILC can be deteriorated. With the reference variation being treated as bounded disturbance, this paper incorporates $H_{\infty } $ control with MPILC to constitute a robust MPILC (RMPILC), so as to restrain the fluctuation of tracking error caused by the varying reference. This RMPILC adopts the linear parameter varying (LPV) model to represent the dynamic property of the nonlinear system. It then solves the input vector of controlled system by optimizing the tracking performance objective function with constraints in the form of linear matrix inequalities. The robust stability and convergence condition of RMPILC are analyzed. The effectiveness of proposed algorithm is verified thorough the simulations on a numerical example, and also a continuous stirred tank reactor (CSTR) system. [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]

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]

High-order power-flow (PF) solution methods are techniques with higher convergence rate than the standard Newton–Raphson (NR). This feature normally provokes that less iterations are necessary for achieving the required convergence tolerance. This advantage enables important computational savings in realistic large-scale power systems, since some expensive computations may be avoided. This article develops and analyzes a novel family of multistep PF solution techniques. The introduced solution paradigm just involves an LU decomposition along with other cheap computations each iteration. In addition, it is proved that its convergence order is equal to the number of steps considered. A comparison with other high-order PF techniques available in the literature reveals that the introduced paradigm is more efficient when more than three steps are taken. Hence, two PF methods with fourth and fifth convergence rate are developed and validated in 12 systems under different demand conditions. Results prove that the developed PF solution methods are able to notably outperform NR and the other high-order PF solvers proposed in the literature. [ABSTRACT FROM AUTHOR]

Computing time-varying linear systems is widely encountered in engineering practice and scientific computation. Dynamic neural networks, as a class of modeling approaches, have been intensively explored in recent decades for solving linear equations. The time-varying nature of this problem and the noisy workspace for many engineering practice require two features of practical design: 1) fast convergence in time and 2) robustness against noises and disturbance. Existing solutions usually decouple the problem into two steps by designing a fast-convergent neural controller and then topped with an additional low-pass filter to reach noise robustness. However, due to the interplay of the mentioned two dynamical parts, the overall system may lose stability if the parameters are not well tuned. In this paper, we establish the first dynamical neural model for simultaneously achieving fast-convergence, particularly finite-time convergence, and noise-robustness, with the capability to reject the unknown noise when it is constant or varies slowly. To do so, a superior design formula activated by noise-tolerant nonlinear functions is proposed to enhance the capability of zeroing neural networks (ZNNs), achieving denoising and finite-time convergence in a unified design. According to this design formula, a novel recurrent neural network (RNN) with finite-time convergence and inherently noise-suppression performance [thus termed the finite-time robust RNN (FTRRNN)] is developed and applied to robotic motion tracking illustrated via time-varying linear equation system solving. Furthermore, theoretical analyses on the global stability, the finite-time convergence and the denoising ability of the proposed design formula and the corresponding FTRRNN model are presented in details. The upper bound on the convergence time is also analytically derived. A numerical example is supplied to verify the superior property of the FTRRNN model to the ZNN model according to the results of computing time-varying linear equation system in the presence of additive noises. Finally, an application to robotic motion tracking is presented to show that the presented FTRRNN model can successfully realize the ellipse-path tracking control of a planar two-link manipulator in front of the external disturbances, while the conventional ZNN model fails under the same conditions. [ABSTRACT FROM AUTHOR]

This paper considers the problem of data driven iterative learning control (DDILC) for a class of nonaffine nonlinear systems subject to data quantization and sensor saturation. Two novel quantized DDILC (QDDILC) algorithms are proposed based on saturated and quantized information of system outputs. The convergence of the proposed QDDILC algorithms is strictly proved and the effects of output saturation and data quantification are also analyzed. It is shown that sensor saturation does not change the convergence property, thus it causes the convergence rate to slow down. For the QDDILC algorithm, data quantization will cause the tracking error to converge to a bound depending on the quantization level. However, the modified QDDILC algorithm, which using the different quantization scheme from QDDILC algorithm, can ensure that the tracking error converges to zero. Illustrative simulations are exploited to verify the theoretical results. [ABSTRACT FROM AUTHOR]

It is usually considered in power systems that the B matrices in fast decoupled power flow (B’ and B”) are symmetric and positive-definite. The fast decoupled power flow (FDPF) based on the conjugate gradient (CG) iterative method was well developed, because the CG iterative method has a good convergence property and a lower memory requirement which can be easily implemented in the parallel computation. However, a rare yet important phenomenon hasn’t been well addressed in that “negative reactance” may exist in the practical power system models, which could affect the definiteness of B matrices in FDPF and the CG convergence performance. In this brief, the eigenvalues of B matrices with negative reactance are investigated and the convergence of CG for FDPF is discussed. Several large-scale practical systems are tested, which could provide some insights for the study of the FDPF using the CG method with negative reactances. [ABSTRACT FROM AUTHOR]

For leader-following multiagent systems with input saturation, the existing protocols use a low gain feedback approach to achieve semi-global consensus. The main drawback of this approach is the ineffective utilization of the actuator potential, resulting in bad performance. To improve the transient performance of the consensus tracking, this paper proposes a gain scheduled approach for multiagent systems subject to the saturator saturations. A novel kind of scheduler-based protocols are proposed, which consists of state feedback controllers with time-varying gain and parameter schedulers. The role of the controllers is to achieve the consensus tracking, while the schedulers can accelerate this consensus progress by enlarging the gain parameter. To remove the dependence of the schedulers on global information, a minimum-value-based consensus algorithm is put forward, with idea of driving all values of agents throughout the network to their minimum value. Its implementation is guaranteed by the network-topology connectivity. Finally, our approach is further extended to the case where the leader’s control input is nonzero, time-varying, and bounded. The discontinuous protocol and its continuous approximation counterpart are designed, yielding the exact- and quasi-consensus tracking, respectively. Simulation results verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new one-step-ahead numerical differentiation rule termed 5-instant discretization formula is proposed for the first-order derivative approximation with higher computational precision. Then, by exploiting the proposed formula to discretize the continuous-time zeroing neural network [or termed, continuous-time Zhang neural network (ZNN)] models, two new discrete-time zeroing neural network [or termed, discrete-time ZNN (DTZNN)] models are proposed, analyzed and investigated for solving systems of discrete time-variant inequalities, including the system of discrete time-variant linear inequalities and the system of discrete time-variant nonlinear inequalities. For comparative purposes, the recently developed Taylor-type DTZNN models and the widely used Euler-type DTZNN models are also presented. Theoretical analyses show that the proposed DTZNN models are convergent, and their steady-state residual errors have an $O(g^{4})$ pattern with $g$ denoting the sampling gap. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed DTZNN models for solving the systems of discrete time-variant inequalities. [ABSTRACT FROM AUTHOR]

We propose Weighted SBL (WSBL) for sparse signal recovery, inspired by the Sparse Bayesian Learning (SBL) method. Unlike SBL, where all hyperparameter priors follow Gamma distributions with identical parameters, in WSBL, the hyperparameters are Gamma distributed with distinct parameters. These parameters, guided by some known weights, give more importance to some hyperparameters over others, thus introducing more degrees of freedom to the problem and leading to better recovery performance. The weights can be determined based on a low-resolution estimate of the sparse vector, for example, an estimate obtained via a method that does not encourage sparsity. The choice of the MUSIC estimate as weight is analyzed. Unlike in SBL, the WSBL hyperparameters are upper bounded; this makes it easy to select a threshold to separate zero from non-zero elements in the recovered sparse vector, which makes the iterative recovery process converge faster. Theoretical analysis based on variational approximation theory and also simulation results demonstrate that WSBL results in substantial improvement in terms of probability of detection and probability of false alarm, especially in the low signal to noise ratio regime, as compared to existing approaches, such as SBL, Sparse Bayesian Support knowledge (BSN), and Multiple response Sparse Bayesian Learning (MSBL). The performance of WSBL is evaluated for Direction of Arrival (DOA) estimation in colocated Multiple Input Multiple Output (MIMO) radar. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mapping operator generation method for the subspace correction to accelerate transient and/or nonlinear eddy-current analyses. In these analyses, a sequence of linear systems whose coefficient matrices are similar or identical is solved. In our method, we automatically construct the operator using the information obtained in the preceding solution steps. The operator is generated with minimum additional memory requirement through the sampling of approximate solution vectors and the use of the Rayleigh–Ritz’s method. Numerical tests using transformer and box-shield models demonstrate that the subspace correction based on the proposed method significantly reduces the number of iterations and the computational time. [ABSTRACT FROM AUTHOR]

Convolution sum system representations are commonly used in signal processing. It is known that the convolution sum, treated as the limit of its partial sums, can be divergent for certain continuous signals and stable linear time-invariant (LTI) systems, even when the convergence of the partial sums is treated in a distributional setting. In this paper, we ask a far more general question: is it at all possible to define a generalized convolution sum with natural properties that works for all absolutely integrable continuous signals that vanish at infinity and all stable LTI systems? We prove that the answer is “no.” Further, for certain subspaces, we give a sufficient and necessary condition for uniform convergence. Finally, we discuss the implications of our results on the effectiveness of window functions in the convolution sum. [ABSTRACT FROM AUTHOR]

To realize the high data rates with low complexity in MIMO systems, linear detections are commonly used where the received signal vector is first transformed to a new vector and then detected on per symbol basis. However, the typical linear detectors such as zero forcing detector and minimum mean-square error detector are not optimal in terms of maximizing the achievable data rate of MIMO system under linear detection constraint. In this letter, we investigate the optimal linear transformer that can maximize such rate with finite constellation inputs. By capitalizing on the relationship between mutual information and the MMSE between channel inputs and outputs, the optimal linear detector (OLD) can be expressed as a fixed-point equation and be solved iteratively. Analytical results prove the consistence between the proposed OLD and the joint maximum likelihood detector (JMLD) in the low- and high-SNR region. The further simulation results verify the consistence, and moreover, at moderate SNR, OLD can significantly improve the achievable data rate and is close to that of JMLD. [ABSTRACT FROM AUTHOR]

This brief presents a novel direct adaptive optimal controller design for uncertain continuous-time linear time-invariant systems. The optimal gain parameter, obtained from the Riccati equation, is continuously estimated without using knowledge of the system dynamics, rather information rich past, and current data along the system trajectory is used for parameter estimation. This approach guarantees parameter convergence to the close neighborhood of the optimal controller by relaxing the restrictive persistence of excitation condition, typically required for achieving parameter convergence in approximate/adaptive optimal control methods. A Lyapunov-based analysis establishes the uniformly ultimately bounded stability of the designed controller. Further a simulation example demonstrates the efficacy of the proposed result. [ABSTRACT FROM AUTHOR]

In this paper, we study the validity of the usual convolution sum sampling representation of linear time-invariant (LTI) systems. We consider continuous input signals with finite energy that are absolutely integrable and vanish at infinity. Even for these benign signals, the convolution sum does not always converge. There exist LTI systems and signals such that the convolution sum diverges even in a distributional sense. This result shows that the practice of multiplying a signal with a Dirac comb and convolving subsequently with the impulse response of the LTI system is not valid for this signal space. We further fully characterize the LTI systems for which we have convergence for all signals in the space, and establish a connection between the pointwise, uniform, and distributional convergence. In particular, we show that the convolution sum converges in a distributional sense if and only it converges in a classical pointwise sense. Hence, for this signal space, nothing can be gained by treating the convergence in a distributional sense. [ABSTRACT FROM AUTHOR]

Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations, blocking communication requests are avoided, which makes it hard to isolate and handle any global vector. While some termination protocols were proposed for asynchronous iterations, only very few of them are based on global residual computation and guarantee effective convergence. But the most effective and efficient existing solutions feature two reduction operations, which constitutes an important factor of termination delay. In this paper, we present new, non-intrusive, protocols to compute a residual error under asynchronous iterations, requiring only one reduction operation. Various communication models show that some heuristics can even be introduced and formally evaluated. Extensive experiments with up to 5,600 processor cores confirm the practical effectiveness and efficiency of our approach. [ABSTRACT FROM AUTHOR]

We present an effective technique to solve eddy current problems on the conductors of arbitrary topology by an iterative geometric formulation suitable for an arbitrary polyhedral mesh. The formulation is based on the reformulation of the volume integral formulation in a form suitable to be solved by fixed point iterations. Given that nowadays, the computation of Biot–Savart fields can be performed efficiently on graphics processing units, the right-hand side of the systems is constructed at each fixed point iteration without computing the inductance matrix, which is fully populated. The proposed technique is useful in eddy current problems at industrial frequency where meshing the complement of conductors is hard, thus representing a sound alternative to integral formulations. [ABSTRACT FROM AUTHOR]

The block incomplete-Cholesky (IC) preconditioner is often used for parallel preconditioner in finite-element method (FEM) supported by distributed computing. When many thin elements are included in an analyzed mesh such as magnetic shielding, the convergence characteristic of preconditioned conjugate gradient method would be deteriorated. At that time, IC preconditioner with fill-in makes the convergence characteristic of linear solver much better. This paper demonstrates the validity of block IC with fill-in on linear systems arising in FEM with many flat elements. First, the ability to improve the convergence property using the fill-in strategy is verified by the simulation of magnetic shielding. Next, the parallelization performance of block IC with fill-in is illustrated by using finite-element mesh of laminated core model and induction heating cooker. [ABSTRACT FROM AUTHOR]

A nonconformal and nonoverlapping domain decomposition (DD) scheme for surface integral equations is presented to analyze electromagnetic scattering from electrically large and complex perfect electric conducting objects. In this work, a discontinuous Galerkin approach is employed to avoid the introduction of artificial touching faces between adjacent subdomains. To weakly enforce the current continuity at the cutting contours of these subdomains, a novel interior penalty term is defined so that the error energy associated with the error charges can be minimized. Consequently, without the introduction of a stabilization term that relies on the line integral over interactions of nonmatching meshes, the proposed method provides an effective DD preconditioner and requires no effort to be extended to curvilinear elements for higher modeling accuracy. To show this, curvilinear Rao–Wilton–Glisson basis functions defined over curvilinear elements are employed in this work to demonstrate the accuracy and efficiency of the proposed DD scheme. [ABSTRACT FROM AUTHOR]

Many power systems applications such as power flow and short-circuit analysis require very large sparse matrix computations. With the increase in reliance on our electric infrastructure, power systems are continually growing in size, creating greater computational complexity in solving these large linear systems within reasonable time. For sparse matrix applications, it is desirable to have an algorithm with low runtime complexity in terms of the number of nonzeros in the matrix. There have been several recent advances in computational methods in other fields that, if applied to power system, could make real-time dynamic simulation a reality. Much work has been done for specific types of these problems where the system is symmetric and diagonally dominant, similar to the form of power system matrices. This paper details an expansion on the current work in fast linear solvers to develop power system specific methods that show potential for accurate solutions in $O(m \log ^2 n)$ run times, where $n$ represents the number of nodes and $m$ represents the number of nonzeros in the power system matrix. This paper presents the simulation validation of a recently developed recursively solved iterative chain method for sparse matrices using a low stretch spanning tree preconditioner. [ABSTRACT FROM PUBLISHER]

The approximation of stable linear time-invariant (LTI) systems is studied for the Paley–Wiener space \mathcal PW\pi ^{1} of bandlimited functions with absolutely integrable Fourier transform. For pointwise sampling, it is known that there exist stable LTI systems and functions such that the approximation process diverges, regardless of the oversampling factor. Recently, it was shown that the divergence can be overcome by using more general measurement functionals that are based on a complete orthonormal system. However, this approach requires the approximation process to have an increased bandwidth. In this paper, a two channel approximation process is presented that is uniformly convergent for all stable LTI systems and all functions in \mathcal PW\pi ^{1} . An advantage of the two channel approach compared with the one channel approach is the reduction of the approximation bandwidth, which can be exactly the same as the input function bandwidth. [ABSTRACT FROM AUTHOR]

The frequency-domain wave propagation problem is notoriously difficult to solve through iterative methods because it leads to a symmetric but indefinite linear system. For this reason, direct methods are usually employed at the expense of great memory usage. Convergence of iterative methods, however, could be obtained by regularizing the wave equation. We introduce such regularization in discrete geometric approach framework on polyhedral grids. Moreover, we extend the regularization to the impedance boundary condition. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of a network-based data-driven filter design for discrete-time linear systems with bounded noises and packet dropouts. One favorable feature is that the designed filter can be directly employed without identifying the unknown system model. To compensate the negative effects of packet dropouts, an output predictor is first designed to reconstruct the missing data based on the received outputs and the inputs of the system. The asymptotic convergence of the output prediction error is established, of which the rate can be adjusted by the parameter. Then utilizing the predicted outputs and the received measurements, an almost-optimal data-driven filter with tractability is proposed within the set membership (SM) framework and the bound on the worst case estimation error is derived. Finally, two illustrative examples, including a comparison example and an application example, are presented to show the advantages of the proposed design and the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Any sequence of uniformly bounded N\times N Hermitian Toeplitz matrices \{H_{N}\} is asymptotically equivalent to a certain sequence of N\times N circulant matrices \CN\ derived from the Toeplitz matrices in the sense that \left \|{HN- CN }\right \|F = o(\sqrt {N}) as $N\rightarrow \infty $ . This implies that certain collective behaviors of the eigenvalues of each Toeplitz matrix are reflected in those of the corresponding circulant matrix and supports the utilization of the computationally efficient fast Fourier transform (instead of the Karhunen-Loève transform) in applications like coding and filtering. In this paper, we study the asymptotic performance of the individual eigenvalue estimates. We show that the asymptotic equivalence of the circulant and Toeplitz matrices implies the individual asymptotic convergence of the eigenvalues for certain types of Toeplitz matrices. We also show that these estimates asymptotically approximate the largest and smallest eigenvalues for more general classes of Toeplitz matrices. [ABSTRACT FROM AUTHOR]

Adaptive filters are commonly used in many signal processing and communications systems. In many practical digital communications scenarios, including, for example, interference-limited wireless and wireline communications, as well as narrowband power line communications, the considered signals are jointly cyclostationary. Yet, most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals, e.g., the least-mean-squares (LMS). It is known that these algorithms may not converge for jointly cyclostationary signals. In this paper, we rigorously study the optimal adaptive filtering of jointly cyclostationary signals. We first identify the relevant objective as the time-averaged mean-squared error criterion (TA-MSE), and obtain an adaptive algorithm as the stochastic approximation of the TA-MSE minimizer. When the considered signals are jointly stationary, the algorithm specializes to the standard LMS algorithm. We provide a comprehensive transient and steady-state performance analysis without imposing a specific distribution on the considered signals, and derive conditions for convergence and stability. The algorithm, which we call time-averaged LMS, is applied to practical scenarios in a simulations study, and an excellent agreement between the theoretical and the empirical performance is observed. [ABSTRACT FROM PUBLISHER]

SimRank is a widely adopted similarity measure for objects modeled as nodes in a graph, based on the intuition that two objects are similar if they are referenced by similar objects. The recursive nature of SimRank definition makes it expensive to compute the similarity score even for a single pair of nodes. This defect limits the applications of SimRank. To speed up the computation, some existing works replace the original model with an approximate model to seek only rough solution of SimRank scores. In this work, we propose a novel solution for computing all-pair SimRank scores. In particular, we propose to convert SimRank to the problem of solving a linear system in matrix form, and further prove that the system is non-singular, diagonally dominate, and symmetric definite positive (for undirected graphs). Those features immediately lead to the adoption of Conjugate Gradient (CG) and Bi-Conjugate Gradient (BiCG) techniques for efficiently computing SimRank scores. As a result, a significant improvement on the convergence rate can be achieved; meanwhile, the sparsity of the adjacency matrix is not damaged all the time. Inspired by the existing common neighbor sharing strategy, we further reduce the computational complexity of the matrix multiplication and resolve the scalable issues. The experimental results show our proposed algorithms significantly outperform the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

There are several types of ILU preconditioners based on different fill-in dropping rules that can be used. One must assure that the chosen preconditioner is suitable for the problem, but this is not frequently an easy task. A bad choice will lower the GMRES convergence rate, increasing the floating point operations and GMRES iteration as well, or even fail. Based on that, this paper proposes a fill-in dropping rule to construct an ILU preconditioner for solution of linear equations via GMRES. The rule is based on reducing error in incomplete triangular factors related to full factors and on Doolittle's Method for LU factorization and allows efficient control of nonzero elements (fill-in) in order to improve the preconditioner quality and GMRES performance as well. The resulting preconditioner is referred to as ILUD (D stands for Doolittle) and it is tested on real power systems; single and sequential load flows (associated to multiple simulations - contingency analysis). The results corroborate the simplicity, efficiency, high quality, and robustness of the ILUD preconditioner. [ABSTRACT FROM AUTHOR]

We present a fast iterated orthogonal projection (IOP) framework for smoke simulations. By modifying the IOP framework with a different means for convergence, our framework significantly reduces the number of iterations required to converge to the desired precision. Our new iteration framework adds a divergence redistributor component to IOP that can improve the impeded convergence logic of IOP. We tested Jacobi, GS and SOR as divergence redistributors and used the Multigrid scheme to generate a highly efficient Poisson solver. It provides a rapid convergence rate and requires less computation time. In all of our experiments, our method only requires 2-3 iterations to satisfy the convergence condition of 1e-5 and 5-7 iterations for 1e-10. Compared with the commonly used Incomplete Cholesky Preconditioned Conjugate Gradient(ICPCG) solver, our Poisson solver accelerates the overall speed to approximately 7- to 30-fold faster for grids ranging from $128^3$ to $256^3$ . Our solver can accelerate more on larger grids because of the property that the iteration count required to satisfy the convergence condition is independent of the problem size. We use various experimental scenes and settings to demonstrate the efficiency of our method. In addition, we present a feasible method for both IOP and our fast IOP to support free surfaces. [ABSTRACT FROM PUBLISHER]

This paper discusses Krylov subspace methods to solve a linear system whose coefficient matrix is represented by a hierarchical matrix. We propose a preconditioning technique using a part of the original hierarchical matrix to accelerate the convergence of the Krylov subspace methods. The proposed preconditioning technique is based on the assumption that the submatrices on the original hierarchical matrix are approximated using the adaptive cross approximation or variants thereof. The performance of Krylov subspace methods with the proposed preconditioning technique is examined through numerical experiments on an electrostatic field analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Markov chain Monte Carlo (MCMC) algorithm using Gibbs sampling for signal detection in multiple input multiple output (MIMO) or code division multiple access (CDMA) systems. It is shown that the MCMC detector can be seen as a stochastic linear system solver. Based on this point of view, we generalize the MCMC detector using a relaxation factor that can improve the convergence rate. For the MCMC detector, since a faster convergence rate implies a lower computational complexity, it is important to have a faster convergence rate especially for large MIMO systems, which can also be achieved by optimizing the temperature parameter. While the optimal temperature parameter heavily depends on the signal-to-noise ratio (SNR), it is shown that a good relaxation factor can be found for wide range of the SNR and other parameters. [ABSTRACT FROM PUBLISHER]

Field tracing provides the flexible and fully vectorial calculation of the dominant transversal resonator mode. Therefore, the eigenvalue problem formulated in a set of coupled, nonlinear operator equations has to be solved. Up to now, only the iterative power method, also known as Fox and Li algorithm, was used for the eigenvector calculation, where serious convergence problems can occur. We accelerate the convergence speed by applying two polynomial-type vector extrapolation methods, namely, the minimal polynomial extrapolation and the reduced rank extrapolation. Numerical examples show that the convergence speed and, consequently, the computational time required for the calculation of the fully vectorial transversal resonator eigenmode, could be reduced by up to 70% compared with the Fox and Li algorithm. Furthermore, it is shown that the calculated eigenmode is in good agreement with the experimental results. [ABSTRACT FROM PUBLISHER]

This paper is dedicated to the design of unknown input (UI) observers for linear parameter-varying (LPV) systems using algebraic matrix manipulation. First, a discussion is provided concerning the classical design approach, which requires the matching condition. This condition is satisfied for a class of systems having relative degree 1. Second, for the same class of systems, a new generalized approach is proposed for simultaneous state and UI estimation. It is demonstrated that the proposed approach is more general than the classical approach. Finally, an extension of the approach is provided for LPV systems with arbitrary relative degree. Simulation examples are provided to illustrate the main results of the paper. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel class of adaptive extended state observers (AESOs) that significantly expand the applications of extended state observers (ESOs) to nonlinear disturbed systems. An AESO is designed as a linear time-varying form that, as a result, combines both the advantages of theoretical completeness in a conventional linear ESO (LESO) and good practical performance in a conventional nonlinear ESO (NESO). To tune the time-varying observer gains, AESO error dynamics is first transformed into a canonical (phase-variable) form. Then, time-varying PD-eigenvalues are assigned for the canonical system based on differential algebraic spectral theory. Theorems for stability and estimate error bounds of the AESO are given in the presence of unknown disturbances. These theorems also offer some important guidelines for assigning the PD-eigenvalues. To demonstrate the effectiveness of this new observer, two representative applications, including a numerical single-input–single-output example and a practical multiple-input–multiple-output hypersonic vehicle application, are exemplified, and comparison simulations are conducted among AESO, LESO, and NESO. Future work is pointed out in the end. [ABSTRACT FROM PUBLISHER]

We present a domain decomposition (DD) framework for the analysis of impenetrable structures; it allows for the electric field integral equation (EFIE) and combined field integral equation (CFIE), and for open, closed, and open–closed structures. The DD results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations. The DD employs specialized transmission conditions among the domains, and the use of discontinuous Galerkin (DG) allows conformal as well as nonconformal discretizations of domain boundaries; the nonconformal nature of the decomposition gives considerable flexibility in the meshing. The strategy is highly parallelizable, as all the operations involving the subdomains can be performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes. [ABSTRACT FROM PUBLISHER]