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We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We prove a central limit theorem for the linear spectral statistics of general rank-one spiked Wigner matrices, and based on the central limit theorem, we propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does not require prior knowledge about the distribution of the signal or the noise. When the noise is Gaussian, the proposed test is optimal in the sense that its error matches that of the likelihood ratio test, which minimizes the sum of the Type-I and Type-II errors. If the density of the noise is known and non-Gaussian, the error of the test can be lowered by applying an entrywise transformation to the data matrix. [ABSTRACT FROM AUTHOR]

In this brief, the problem of output consensus in a multi-agent system is considered, where a distributed dynamic output feedback control architecture is proposed. The control architecture consists of two components, one is local controllers for the agents, and another is a gain for the network. The transfer function of local controller is designed based on the number of positive real axis (in the complex plane) zeros of the agent transfer function, and then network gain is selected by sketching the root-locus of a unity feedback system. It is shown that the output consensus can be achieved with an integral type controller for a class of agents, irrespective of their order. Moreover, with the proposed control architecture, there is no need of communication between the local controllers. The effectiveness of the developed approach is demonstrated through numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we present a distributed aperiodic control algorithm for multibus DC microgrids to realize proper current sharing and voltage regulation under denial-of-service (DoS) attacks. To deal with the DoS attacks, an estimation mechanism using only local information is designed when the communication channels are jammed, which avoids persistent load fluctuations or instability of bus voltages caused by malicious attacks. Moreover, an aperiodic communication mechanism is employed using the local and neighbors’ current states stored in the zero-order holder to determine the communication instants. The proposed resilient aperiodic control achieves proportional load current sharing and maintains the weighted average bus voltage invariant simultaneously. Voltage drift under DoS attacks can be avoided. Furthermore, sufficient stability conditions are established for control gains concerning the attack parameters. The Lyapunov synthesis shows that the current sharing error can exponentially converge towards an adjustable set, and the weighted average bus voltage can be maintained at its nominal value. The advantages of the proposed control are illustrated by switch-level simulations and a hardware-in-the-loop experiments. [ABSTRACT FROM AUTHOR]

Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated heterogeneous variance structure. We propose a sequential test which utilizes the edge singular values (i.e., the largest few singular values) of the data matrix. It also naturally leads to a consistent sequential testing estimate of the number of signals. We describe the asymptotic distribution of the test statistic in terms of the Tracy-Widom distribution. The test is shown to be accurate and have full power against the alternative, both theoretically and numerically. The theoretical analysis relies on establishing the Tracy-Widom law for a large class of Gram type random matrices with non-zero means and completely arbitrary variance profiles, which can be of independent interest. [ABSTRACT FROM AUTHOR]

Based on the fact that the traditional probability distribution entropy describing a local feature of the system cannot effectively capture the global topology variations of the network, some indicators constructed by the network adjacency matrix and Laplacian matrix come into being. Specifically, these measures are based on the eigenvalues of the scaled Laplace matrix, the eigenvalues of the network communicability matrix, and the spectral entropy based on information diffusion that has been proposed recently, respectively. In this article, we systematically study the dependence of these measures on the topological structure of the network. We prove from various aspects that spectral entropy has a better ability to identify the global topology than the traditional distribution entropy. Furthermore, the indicator based on the eigenvalues of the network communicability matrix achieves good results in some aspects while, overall, the spectral entropy is able to identify network topology variations from a global perspective. [ABSTRACT FROM AUTHOR]

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) method to approximate them. This instability arises in the presence of eigenvalues that are close to each other. This makes integrating eigendecomposition into deep networks difficult and often results in poor convergence, particularly when dealing with large matrices. While this can be mitigated by partitioning the data into small arbitrary groups, doing so has no theoretical basis and makes it impossible to exploit the full power of eigendecomposition. In previous work, we mitigated this using SVD during the forward pass and PI to compute the gradients during the backward pass. However, the iterative deflation procedure required to compute multiple eigenvectors using PI tends to accumulate errors and yield inaccurate gradients. Here, we show that the Taylor expansion of the SVD gradient is theoretically equivalent to the gradient obtained using PI without relying in practice on an iterative process and thus yields more accurate gradients. We demonstrate the benefits of this increased accuracy for image classification and style transfer. [ABSTRACT FROM AUTHOR]

In this article, the non-negative edge consensus problem is addressed for positive networked systems with undirected graphs using state-feedback protocols. In contrast to existing results, the major contributions of this work included: 1) significantly improved criteria of consequentiality and non-negativity, therefore leading to a linear programming approach and 2) necessary and sufficient criteria giving rise to a semidefinite programming approach. Specifically, an improved upper bound is given for the maximum eigenvalue of the Laplacian matrix and the (out-) in-degree of the degree matrix, and an improved consensuability and non-negativevity condition is obtained. The sufficient condition presented only requires the number of edges of a nodal network without the connection topology. Also, with the introduction of slack matrix variables, two equivalent conditions of consensuability and non-negativevity are obtained. In the conditions, the system matrices, controller gain, as well as Lyapunov matrices are separated, which is helpful for parameterization. Based on the results, a semidefinite programming algorithm for the controller is readily developed. Finally, a comprehensive analytical and numerical comparison of three illustrative examples is conducted to show that the proposed results are less conservative than the existing work. [ABSTRACT FROM AUTHOR]

In this article, an event-triggered control (ETC) law is proposed for auto-scaling of Web servers hosted on a private cloud. The Web server systems are modeled as a discrete-time linear time-invariant (LTI) system where the incoming Web requests act as disturbance inputs. Dealing with such disturbance inputs adds an additional challenge in the design and real-time implementation of the ETC. To address this challenge, we first design an ETC law to ensure ${\mathscr {D}}_{R}$ stability of the nominal system. Second, we derive the conditions which ensure input to state stability of the closed-loop system, under the event-triggered implementation, with respect to disturbance inputs. Then, sufficient conditions are derived, which ensure that the interevent times are nontrivial. Finally, to show the efficacy of the proposed approach, we validate our results on an experimental testbed of a Web server system hosted on a private cloud and provide comparative results. [ABSTRACT FROM AUTHOR]

This article proposes a low-latency parallel Jacobi-method-based algorithm for computing eigenvalues and eigenvectors of $n\times n$ -sized real-symmetric matrix. It is a coordinate rotations digital-computer (CORDIC)-based iterative algorithm that comprises multiple rotations and hence the key contribution of our work is to reduce the time cost of each rotation. Thus, alleviating the total latency for computing eigenvalues and eigenvectors using the parallel Jacobi method. Based on this proposed algorithm and additional architectural optimizations, a new low-latency and highly accurate VLSI-architecture has been presented in this manuscript for computing eigenvalues and eigenvectors of real-symmetric matrix. Subsequently, this work proposes a reconfigurable algorithm and its VLSI-architecture for computing eigenvalues and eigenvectors of complex Hermitian (CH), complex skew-Hermitian (CSH), and real skew-symmetric (RSS) matrices. Performance analysis of the proposed architectures has demonstrated minimal error-percentage of 0.0106% which is adequate for the wide range of real-time applications. The proposed architectures are hardware implemented on Zynq Ultrascale+ field-programmable gate array (FPGA)-board that consumed short latency of $9.377~\mu \text{s}$ while operating at maximum clock frequency of 172.75 MHz. Comparison of our implementation results with the reported works showed that the proposed architecture incurs 43.75% lower latency and 89.4% better accuracy than the state-of-the-art implementation. [ABSTRACT FROM AUTHOR]

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader–follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader–follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained. [ABSTRACT FROM AUTHOR]

The consensusability and global optimality problems are solved for the discrete-time linear multiagent system (MAS) with marginally stable and strictly unstable dynamics. A unified framework is proposed by capturing the maximal disc-guaranteed gain margin (GGM) of the discrete-time linear quadratic regulator (LQR). Sufficient and necessary conditions on consensusability are established. Two bounds of the consensus region are derived only in terms of the unstable eigenvalues of the agent’ dynamics. For the single-input MAS, by proving that the radius of the consensus region exactly equals the reciprocal of the Mahler measure of the agent’ dynamics, we incidentally reveal the relation between the maximal GGM and the intrinsic entropy rate of the system dynamics for single-input discrete-time linear systems. By employing the inverse optimal control approach, it is proved that the globally optimal consensus is achieved, if and only if the associated Laplacian matrix is a simple matrix and all its nonzero eigenvalues can be radially projected into a specific subset of the consensus region. Moreover, the limitation on the eigenvalues vanishes for the marginally stable MAS. As an application of the global optimality, the minimum-energy-distributed consensus control problem is solved for the marginally stable MAS. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Orthogonality of the characteristic modes with respect to the weight operator of the generalized eigenvalue equation (GEE), and in the far-field, is investigated in the case of lossy conducting and dielectric objects. Linking the weight operator to radiated power is shown to provide orthogonal far fields in the lossless case. In the lossy case, both the orthogonality of the characteristic far fields and the weight operator orthogonality of the modal currents are satisfied with respect to the Hermitian inner products only for sufficiently symmetric geometries, such as a sphere. For irregular lossy shapes, independent of the symmetry of the formulation, the far-field orthogonality can be obtained only with respect to the symmetric (non-Hermitian) product. The weight operator orthogonality can be satisfied with (complex) symmetric formulations, but again only with respect to the symmetric product. Since the symmetric products are not related to any physical power quantity, the modes do not form a (radiated) power orthogonal set in the lossy case. Hence, for lossy structures, characteristic modes (CMs) do not satisfy their classical definition and they need to be redefined. [ABSTRACT FROM AUTHOR]

As higher symbol rates are utilized in the intensity modulation and direct detection (IM/DD) scheme to meet the unrelenting growth of data traffic, overcoming the inter-symbol interference (ISI) induced by the limited bandwidth has become increasingly crucial. Channel equalization based on digital signal processing (DSP) is an effective solution, where least-mean squares (LMS) algorithm is adopted to adjust tap coefficients. However, the LMS algorithm usually has slow rate of convergence and requires lots of training symbols. This work proposes a novel training sequence to accelerate the LMS-based equalization. A first-order Markov chain (MC) is employed for sequence generation, which introduces correlation between samples and shapes signal spectrum. Compared with the conventional training sequence that consists of independent and identically distributed (i.i.d.) samples and has a white spectrum, the MC sequence enables faster convergence of tap coefficients and mean-squared error (MSE). Moreover, an experimental demonstration of a 43 Gbaud PAM-4 signal shows that the proposed sequence can achieve a lower pre-forward-error-correction (pre-FEC) bit error rate (BER) than that of the i.i.d. sequence with the same length. When the PAM-4 signal is transmitted over a 5-km standard single mode fiber (SSMF) with 6-dB system bandwidth of 10 GHz, more than 70% training sequence length reduction can be attained. When the fiber length is increased to 10 km and the signal suffers from severe power fading, more than 48% reduction can be achieved. [ABSTRACT FROM AUTHOR]

In the traditional gradient descent (T-GD) algorithm, the convergence rate is strongly depend on the condition number of the information matrix: a larger condition number leads to a poor optimal convergence factor infimum $\mu _{\text{op}}$ , which sets a convergence rate ceiling. That is, once the information matrix is fixed, the convergence factor of the T-GD algorithm reaches at most the infimum $\mu _{\text{op}}$. This article studies a varying infimum gradient descent algorithm, which can move down the infimum by using different order iterative preconditioning methods, as follows: first, for infinite iterative algorithm, the infimum becomes smaller and smaller with the increased iteration numbers; second, for finite iterative algorithm, the infimum is equal to zero, and the parameter estimates can be obtained in only one iteration; third, construct an adaptive interval between zero and $\mu _{\text{op}}$ , which can establish a link between the least squares and T-GD algorithms. Based on the varying infimum gradient descent algorithm, researchers can adaptively choose preconditioning matrices for different kinds of models on a case by case basis. The convergence analysis and simulation examples show effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting a banded structure) or beamforming (widening the spectral null width associated with an interferer). In this paper, the focus is on high-dimensional setting where the dimension $p$ is high, while the data aspect ratio $n/p$ is low. We propose an estimator called Tabasco (TApered or BAnded Shrinkage COvariance matrix) that shrinks the tapered sample covariance matrix towards a scaled identity matrix. We derive optimal and estimated (data adaptive) regularization parameters that are designed to minimize the mean squared error (MSE) between the proposed shrinkage estimator and the true covariance matrix. These parameters are derived under the general assumption that the data is sampled from an unspecified elliptically symmetric distribution with finite 4th order moments (both real- and complex-valued cases are addressed). Simulation studies show that the proposed Tabasco outperforms all competing tapering covariance matrix estimators in diverse setups. An application to space-time adaptive processing (STAP) also illustrates the benefit of the proposed estimator in a practical signal processing setup. [ABSTRACT FROM AUTHOR]

This paper considers the problem of adaptive classification for performing pattern discrimination in varying conditions when new data arrives. A new efficient method is presented to incrementally update features in a Nyström-approximated linearized kernel embedding (LKE). Our method leverages a fast eigendecomposition algorithm for symmetric Arrowhead matrices. The proposed method can also be applied to kernel principal component analysis (KPCA) or similar problems. A mechanism is proposed which allows the incremental linearized kernel embedding to be used for updating of dictionaries in a sparse representation-based classification algorithm. The method is based on transporting the dictionaries into the embedding expanded with new data points and avoids the need to learn new dictionary matrices every time new data becomes available. The effectiveness of the developed methods is illustrated on two handwritten digit image data sets namely MNIST and USPS. Classification performance before and after sequential embedding updates is evaluated and compared. Comparisons are also made between our incremental LKE algorithm and the conventional approach to updating the empirical kernel map in terms of their computational requirements and numerical stability. [ABSTRACT FROM AUTHOR]

In this brief, the almost sure exponential consensus of multi-agent systems is investigated. A consensus protocol is designed with aperiodically intermittent communication noise rather than common continuous communication noise. Based on the consensus protocol, some sufficient conditions are given. Moreover, theoretical results show that the larger the noise control gain is, the larger the convergence rate of exponential convergency becomes in an almost sure sense. Besides, when the consensus protocol with aperiodically intermittent communication noise degenerates into one with periodically intermittent communication noise or one with common continuous communication noise, two corollaries are presented respectively. Then, the main results are used to consider almost sure exponential consensus of oscillator systems, and some simulations are provided. [ABSTRACT FROM AUTHOR]

There are many successful spectral based unsupervised dimensionality reduction methods, including Laplacian Eigenmap (LE), Locality Preserving Projection (LPP), Spectral Regression (SR), etc. We find that LPP and SR are equivalent if the symmetric similarity matrix is doubly stochastic, Positive Semi-Definite (PSD) and with rank $p$ p , where $p$ p is the reduced dimension. Since solving SR is believed faster than solving LPP based on some related literature, the discovery promotes us to seek to construct such specific similarity matrix to speed up LPP solving procedures. We then propose an unsupervised linear method called Unsupervised Large Graph Embedding (ULGE). ULGE starts with a similar idea as LPP but adopts an efficient approach to construct anchor-based similarity matrix and then performs spectral analysis on it. Moreover, since conventional anchor generation strategies suffer kinds of problems, we propose an efficient and effective anchor generation strategy, called Balanced $K$ K -means based Hierarchical $K$ K -means (BHKH). The computational complexity of ULGE can reduce to $O(ndm)$ O (n d m) , which is a significant improvement compared to conventional methods need $O(n^2d)$ O (n 2 d) at least, where $n$ n , $d$ d and $m$ m are the number of samples, dimensions, and anchors, respectively. Extensive experiments on several publicly available datasets demonstrate the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Graph spectral sparsification aims to find a ultrasparse subgraph which can preserve the spectral properties of the original graph. The subgraph can be leveraged to construct a preconditioner to speed up the solution of the original graph’s Laplacian matrix. In this work, we propose feGRASS, a fast and effective graph spectral sparsification approach for the problem of large-scale power grid analysis and other problems with similar graphs. The proposed approach is based on two novel concepts: 1) effective edge weight and 2) spectral edge similarity. The former takes advantage of node degrees and breadth-first-search (BFS) distances, which leads to a scalable algorithm for generating low-stretch spanning trees (LSSTs). Then, the latter concept is leveraged during the recovery of spectrally critical off-tree edges to produce spectrally similar subgraphs. Compared with the most recent competitor , the proposed approach is much faster for producing high-quality spectral sparsifiers. Extensive experimental results have been demonstrated to illustrate the superior efficiency of a preconditioned conjugate gradient (PCG) algorithm based on the proposed approach, for solving large power grid problems and many other real-world graph Laplacians. For instance, a power grid matrix with 60 million unknowns and 260 million nonzeros can be solved (at a 1E-3 accuracy level) within 196 s and 12 PCG iterations, on a single CPU core. [ABSTRACT FROM AUTHOR]

Identification of communication parameters, a major task of intelligent receivers, has important applications in intelligent systems, especially cognitive radio systems. Multiple antennas make the identification problem more challenging. In this paper, we focus on the problem of detecting the number of transmit antennas in multiple-input multiple-output (MIMO) cognitive radio systems. A novel identification algorithm is proposed to determine the number of transmit antennas for MIMO systems in the presence of alpha-stable noise. We first introduce the correlation matrix based on the fractional lower order statistics (FLOS) and provide a particular structure of FLOS-based correlation matrix. Then, the eigenvalues of the FLOS-based correlation matrix are employed to construct a test statistic and the central limit theorem is exploited to obtain the decision threshold. Finally, the transmit-antenna number is detected using a serial binary hypothesis test. Simulation results are demonstrated to evaluate the effectiveness of the proposed transmit-antenna number detection algorithm for MIMO systems in the presence of alpha-stable noise. [ABSTRACT FROM AUTHOR]

This brief investigates the leader-follower consensus problem of linear multiagent systems (MASs) with nonzero leader input under the directed graph. By proposing the innovative adaptive event-triggered mechanism, the proposed control protocol does not need continuous communication among neighbors, and the control protocol can be updated intermittently for each follower. Moreover, Zeno behavior can be excluded for each agent. Note that the existence of the leader’s nonzero bounded input enormously increases the difficulty of solving the leader-follower consensus problem. At last, two numerical examples are introduced to show the effectiveness and advantages of the designed protocol. [ABSTRACT FROM AUTHOR]

This brief studies the optimal control problem of linear singularly perturbed systems (SPSs) via reinforcement learning (RL). We first present an offline model-based algorithm on the basis of Kleinman algorithm to solve the underlying algebraic Riccati equation with singular perturbation parameter and its convergence is proven. This revised version of Kleinman algorithm is the key to develop the subsequent learning algorithm. Then, by means of two time-scale characteristics of SPSs, we present a novel model-free learning algorithm relating to the online measurement of state and input to design the optimal controller. Compared with the existing learning approaches, the obtained RL algorithm is free of ill-conditioned numerical issues caused by the co-existence of fast and slow modes in SPSs and thus is more robust with respect to the computation and measurement errors. Finally, we verify the effectiveness of the developed results by a simulation example. [ABSTRACT FROM AUTHOR]

This brief studies the fully distributed consensus control problem for linear multiagent systems (MASs) with a novel dynamic double-event-triggered mechanism (DDETM). The proposed DDETM can not only reduce the resource consumption of communication, but also reduce the frequency of controller update. Meanwhile, larger triggering time intervals are obtained by introducing two sets of dynamic variables in DDETM compared with the static double-event-triggered mechanism (SDETM). Then a fully distributed DDETM-based control protocol is designed, which is independent of any global information. Next, rigorous proofs are given to assure the realization of consensus control and the exclusion of Zeno behavior. Finally, an illustrative example is presented to verify the proposed protocol. [ABSTRACT FROM AUTHOR]

This brief studies the robust semiglobal multi-agent consensus with linear subsystems subject to nonidentical parameter uncertainties and input saturation. A distributed low-gain-based nonlinear feedback law that avoids eigenvalues of the Laplacian matrix is established. It is proved that under the provided procedure, semiglobal multi-agent consensus is achieved when the lower bound of input saturation and the upper bound of parameter uncertainties satisfy certain relationship, which is shown as a design constraint in the provided method. The event-triggered scenario of the proposed protocol is further studied; the designs for the control law and the updating rule based on node-based event-driven mechanisms are provided and analyzed. [ABSTRACT FROM AUTHOR]

This article mainly solves the consensus issue of parabolic partial differential equation (PDE) agents with switching topology by output feedback. A novel edge-based adaptive control protocol is designed to reach consensus under the condition that the switching graphs are always connected at any switching instants. Different from the existing adaptive protocol associated with partial differential dynamics, the proposed adaptive observer-type law relies on the relative output information rather than relative state information. A proper Lyapunov functional is constructed and some important lemmas are used, then a sufficient condition is obtained for the consensus of parabolic PDE agents on switching graphs. Besides, a corollary about the distributed adaptive consensus of parabolic PDE agents on fixed undirected communication networks is given. Finally, the theoretical results are demonstrated by two numerical simulations. [ABSTRACT FROM AUTHOR]

A novel, general circuit-level description of coupled-resonator microwave filters is introduced in this article. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary reactive frequency-variant coupling (AFVC) networks is proposed. The engineered formulation is more general than prior-art ones—with the only restriction that the coupling network is a reactive-type two-port circuit—and can be treated as an extension of previous synthesis models since constant or linear couplings are special cases of arbitrary frequency dependence. The suggested model is fully general, which allows for AFVCs with highly nonlinear (even singular) characteristics, loaded or unloaded nonresonating nodes (NRNs), frequency-dependent source–load coupling, multiple frequency-variant cross couplings, and/or multiple dispersive couplings for connecting the source and load to the filter network. The model is accompanied by a powerful synthesis technique that is based on the zeros and poles of the admittance or scattering parameters and the eigenvalues of properly defined eigenproblems. In the most general case, the zeros and poles of the admittance or scattering parameters are related to solutions of nonlinear eigenvalue problems. The synthesis is defined as an inverse nonlinear eigenvalue problem (INEVP) where the matrix is constructed from three sets of eigenvalues. This is accomplished by optimization using an iterative nonlinear least-squares solver with excellent convergence property. Finally, the third- and fifth-order examples of bandpass filter topologies involving AFVCs are shown, and the experimental validation of the proposed theory is presented through the manufacturing and characterization of a microstrip filter prototype with transmission zeros (TZs). [ABSTRACT FROM AUTHOR]

Distributed formation control is presented for networked Euler–Lagrange systems (ELSs) over a directed interaction topology. This problem is defined by a layered framework in which information flow both among the leaders and among the followers is described by different layers. To empower the formation to make a variety of geometric transformations, we present the necessary and sufficient conditions for affine maneuverability under a directed graph. Unlike most existing results using a diagonal stabilizing matrix to achieve the stabilizability of affine formation, this fully distributed approach is feasible without any global information. Next, we propose an adaptive control law for agents in each layer, where the closed-loop errors are driven to a neighborhood of the origin in finite time. Adaptive neural networks are integrated to tackle the model uncertainties in ELSs by updating the norm of the weight matrix, which can simplify the control design and alleviate the computational burden compared with traditional ones. The simulation results are given to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider minimizing a sum of local convex objective functions in a distributed setting, where the cost of communication and/or computation can be expensive. We extend and generalize the analysis for a class of nested gradient-based distributed algorithms [NEAR-DGD, (Berahas et al., 2019)] to account for multiple gradient steps at every iteration. We show the effect of performing multiple gradient steps on the rate of convergence and on the size of the neighborhood of convergence, and prove R-Linear convergence to the exact solution with a fixed number of gradient steps and increasing number of consensus steps. We test the performance of the generalized method on quadratic functions and show the effect of multiple consensus and gradient steps in terms of iterations, number of gradient evaluations, number of communications and cost. [ABSTRACT FROM AUTHOR]

This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: 1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the associated eigenvalue and the rest of the spectrum) is particularly small; 2) how to perform estimation and inference on linear functionals of an eigenvector—a sort of “fine-grained” statistical reasoning that goes far beyond the usual $\ell _{2}$ analysis. We investigate how to address these challenges in a setting where the unknown $n\times n$ matrix is symmetric and the additive noise matrix contains independent (and non-symmetric) entries. Based on eigen-decomposition of the asymmetric data matrix, we propose estimation and uncertainty quantification procedures for an unknown eigenvector, which further allow us to reason about linear functionals of an unknown eigenvector. The proposed procedures and the accompanying theory enjoy several important features: 1) distribution-free (i.e. prior knowledge about the noise distributions is not needed); 2) adaptive to heteroscedastic noise; 3) minimax optimal under Gaussian noise. Along the way, we establish valid procedures to construct confidence intervals for the unknown eigenvalues. All this is guaranteed even in the presence of a small eigen-gap (up to $O(\sqrt {n/\mathrm {poly}\log (n)}\,)$ times smaller than the requirement in prior theory), which goes significantly beyond what generic matrix perturbation theory has to offer. [ABSTRACT FROM AUTHOR]

This brief studies distributed event-triggered law design of the Nash equilibrium seeking for noncooperative games under strongly connected graphs. Each player is desired to maximize its payoff function by updating its own action based on other players’ actions. An event-triggered law is proposed, and each player estimates all other players’ actions and exchanges the estimated information with their neighbors only when the triggering conditions are satisfied. Theoretical demonstration is presented to verify that the actions and estimates of players all converge to the unique Nash equilibrium under the proposed event-triggered law and Zeno behavior is excluded. Simulations are provided to show the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Passivity is a fundamental requirement for rational models to guarantee stable behavior when included in general time domain simulations. This paper introduces a new variant of one passivity enforcement scheme that is based on residue matrix perturbation. The constrained least squares problem associated with the passivity condition is transformed into a least distance problem which is solved as a non-negative least squares problem while utilizing the sparsity pattern that arises with multi-terminal problems. The resulting method is very fast and requires only a small amount of computer memory, thereby being applicable to models with many terminals and high orders. The method is demonstrated to be suitable for frequency-dependent modeling of subnetworks, transformer winding branch impedances, and measured transformer admittance data. [ABSTRACT FROM AUTHOR]

Ideal sensor response is always desirable in multiple-input multiple-output (MIMO) system. In practical application, however, sensors may be susceptible to unknown mutual coupling (MC), which seriously decreases the angle estimation accuracy. This letter addresses the scenario where MIMO sensors are corrupted by the direction-dependent MC effect. Taking the banded symmetric and Toeplitz characteristics of the MC matrices into consideration, a closed-form algorithm is introduced for angle estimation. The core of the proposed algorithm is to release the MC effect via selection matrices, and then obtain the angle by exploiting rotational invariance techniques. The proposed algorithm is capable of automatically paired angle estimation in MIMO system with direction-dependent MC, and it is much more efficient than current spectrum search approach. The numerical results show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the problem of distributed robust fault estimation (FE) for leader–follower multiagent systems using relative measurements is considered. A distributed intermediate-based fault estimator is constructed using the local relative measurements and the state estimation from neighbors. The gain matrices of the fault estimator are calculated based on $H_{\infty }$ performance in terms of linear matrix inequality (LMI) to improve the robustness of the estimator. Then, the LMI is separated and simplified by spectral decomposition, and its equivalent condition is proposed based on the maximum and minimum eigenvalue. A distributed eigenvalue estimation algorithm based on the power method is presented to fully distribute the proposed FE scheme. Finally, the numerical simulations are provided to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A subgridding unconditionally stable finite-element time-domain method based on local eigenvalue solution (SUSL-FETD) is proposed to solve multiscale modeling. In this method, subgridding elements are used to discrete a multiscale computational domain, and the explicit central-difference method is applied for temporal discretization. Compared with traditional elements, the subgridding elements have a more complex distribution of edges and nodes. Therefore, an efficient subgridding scheme is given to form the element matrix for each subgridding element. Such system matrices assembled by all element matrices are symmetric. The subgridding FETD (S-FETD) is then further developed into the subgridding unconditionally stable FETD (SUS-FETD) by filtering spatial unstable modes. It is time-consuming to obtain the unstable modes by global eigenvalue decomposition. In this article, the local eigenvalue decomposition is proposed to get the unstable modes, which further reduces the memory storage and computing time. Numerical examples certify that the proposed SUSL-FETD has high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This brief presents an even-triggered control framework for networked Euler-Lagrange systems to achieve bipartite consensus even in the presence of external disturbance. In particular, an adaptive protocol with simple distributed updating laws is proposed by combining the disturbance compensator technique. The new event-triggered control algorithm is constructed without utilizing velocity information, which mitigates the cost on distributed bipartite consensus protocol design. Additionally, there is no Zeno behaviors by giving the positive lower bounds of execution intervals. Numerical examples are applied in the end to verify the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

Robust bearing fault detection is significant to reduce the machinery down-time and to prevent catastrophic failure. Many algorithms are proposed for the faults feature extraction, but it remains challenging to monitors the condition of the mechanical systems from the overwhelming interference noise contained signal in a short response time. To address this problem, as an extension of our recent work, this article introduces an enhanced framework using acquired time-series signals. Specifically, an improved Hankel matrix-based method is proposed for the identification of the state from the sampled vibration signal for each spindle turn, where matrix similarity is employed for the mechanical operation state monitoring. The experimental results indicate that the proposed method performs considerably well in fault identification (100% identification accuracy in three tests) even with a few data samples and phase shift. This work, therefore, would have more hopeful prospects in a variety of engineering fault detection applications. [ABSTRACT FROM AUTHOR]

The distributed optimal consensus based on an event-triggered scheme for Euler–Lagrange (EL) multiagent systems is investigated in this article. The objective is to minimize the global cost function in a distributed manner while achieving consensus, where the local cost function of each agent is only known by itself. First, the distributed optimization algorithms based on the event-triggered scheme are proposed to achieve optimal consensus as well as reduce communication costs for the EL multiagent systems when the model parameters are available. Second, when the model parameters are unavailable, the tracking controllers are developed to solve the optimization problem for the EL multiagent systems. Then, the distributed optimization problem for EL systems can be transformed into the tracking problem for double-integrator multiagent systems. With the proposed algorithms, global optimization can be achieved with the exponential convergence rate. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Eigenvalue decomposition is widely used in dimensionality reduction for knowledge engineering, in particular principal component analysis and other similar spectral methods. Traditional eigenvalue decomposition algorithms for decomposing a matrix of size n × n are usually of complexity O(n3), due to a bottleneck in using Householder/Givens transforms to convert a general matrix to a tri-diagonal one. It is proposed in this article a new algorithm that takes only O(n2.584963 log 1/ɛ) computational complexity to achieve accuracy ɛ of eigenvalue decomposition for any ɛ > 0 . The basic idea of our algorithm is to convert a matrix into a diagonal form in multi-scale divide and conquer scheme, and the conversion is to iteratively and recursively apply two phases of operations called diagonal attractions and diagonal absorptions respectively. In a diagonal attraction, it attracts the off-diagonal entries to make the entries nearer to the diagonal larger in magnitude than those farther away from the diagonal. In a diagonal absorption, it absorbs the near-to-diagonal nonzero entries into the diagonal. In such a scheme, no Householder or Givens transforms are involved. Moreover, diagonal attractions and diagonal absorptions can be implemented with fast matrix multiplications. The scheme’s divide and conquer pattern also allows our algorithm to be easily mapped to modern computer hardware. Our algorithm also complements well the family of randomized eigenvalue/SVD algorithms using sampling techinques, which are of complexity O(nα polylog (1/ɛ)) with small α but very large overheads in the polylog. Their strength in the small exponent α of n in complexity was easily cancelled by the exploding overheads in the polylog. Now, with their low-accuracy estimate refined by our algorithm for high accuracy, their strength can be boosted significantly. [ABSTRACT FROM AUTHOR]

We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of multiple networks can contribute to synchronization. We illustrate how the effectiveness of a collection of networks to synchronize the coupled systems depends on the graph topology. In particular, we show that if the graph sum is a directed graph whose reversal contains a spanning directed tree, then the network synchronizes if the coupling is strong enough. This is intuitive as there is a root node that influence every other node via a set of edges where each edge in the set is in one of the networks. [ABSTRACT FROM AUTHOR]

We aim to solve the consensus problem of linear multiagent systems (MASs) with input saturation under directed interaction graphs in this article, where only local output information of neighbors is available for each agent. By introducing the multilevel saturation feedback control approach, a fully distributed adaptive anti-windup protocol is proposed, where a local observer, a distributed observer, as well as an anti-windup observer are separately constructed for each agent to estimate consensus error, achieve consensus for a certain internal state, and provide anti-windup compensator, respectively. A dual protocol is further presented with the distributed observer designed based on the input matrix, which gives a thorough view on the connection between the distributed observer and the anti-windup observer, and provides the opportunity to reduce the order of the controller by designing the integrated distributed anti-windup observer. Then, three types of distributed anti-windup protocols are proposed based on the integrated distributed anti-windup observer, which requires different assumptions. Specifically, the first protocol needs two-hop relay information to generate the local observer to estimate consensus error; the second protocol designs the local observer with absolute output information to estimate the state instead; while the last protocol introduces certain assumption on transmission zero of agents’ dynamics to design the unknown input observer to estimate consensus error. All of the protocols are validated by strictly theoretical proof, and are illustrated by performing simulation examples. [ABSTRACT FROM AUTHOR]

This brief studies the synchronization of second-order phase-coupled Kuramoto oscillators. Under the effects of non-uniformity among the system parameters, we propose novel spanning-tree-based conditions for the oscillators to remain phase cohesive over time, which further guarantees the synchronization. First, by choosing a spanning tree in the underlying network graph, we consider the phase cohesiveness as a 2-norm bound on the tree-induced phase differences and an infinity norm bound on the relative phases that are excluded from the spanning tree. Energy functions are constructed to derive two sets of conditions on achieving these two types of boundedness, respectively. Then, we prove that presented phase cohesive conditions guarantee the asymptotic synchronization for a second-order Kuramoto network. Our method is less conservative than those in literature on estimating a region of permissible initial states for oscillators to achieve synchronization, which is verified by numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered containment control (CC) problem of multiagent systems with a directed graph, where the followers’ communication graph is an undirected graph. A novel event-triggered CC protocol is presented to schedule communications between agents, which depends on both local states and control inputs. Different from traditional approaches using broadcasts, a unique property of the proposed protocol is that it enables agent-to-agent data transmission. To do so, each communication link is associated with a specific local event. The estimated relative interagent states are transmitted over a specific link only when the related input-based event is detected. We develop sufficient conditions to solve CC problem under this protocol and extend it to the adaptive event-triggered protocol that does not require the global knowledge on the smallest positive eigenvalue of the Laplacian. For both protocols, we derive positive low bounds on the interevent time intervals generated by individual events, which eliminate the “Zeno phenomenon.” Feasibility of the proposed algorithm is verified by an example. [ABSTRACT FROM AUTHOR]

In this article, a distributed observer-based tracking control protocol is proposed for linear multiagent systems having a leader with unknown nonzero input. The leader is assumed to be uncooperative, i.e., no communication link is available for the leader to transmit its state or control input to the followers. Based on the relative output measurements and the information received from the neighbors, a local controller for each follower is designed, such that the states of the followers converge to the states of the leader. In the proposed algorithm, no global information of the network topology is needed for the controller design. Two simulation examples are presented to illustrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]