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This paper presents an extensive study of linear and logistic regression algorithms implemented with 1T1R memristor crossbars arrays. Using a sophisticated simulation platform that wraps circuit-level simulations of 1T1R crossbars and physics-based models of RRAM (memristors), we elucidate the impact of device variability on algorithm accuracy, convergence rate and precision. Moreover, a smart pulsing strategy is proposed for practical implementation of synaptic weight updates that can accelerate training in real crossbar architectures. Stochastic multi-variable linear regression shows robustness to memristor variability in terms of prediction accuracy but reveals impact on convergence rate and precision. Similarly, the stochastic logistic regression crossbar implementation reveals immunity to memristor variability as determined by negligible effects on image classification accuracy but indicates an impact on training performance manifested as reduced convergence rate and degraded precision. [ABSTRACT FROM AUTHOR]

In this paper, a unified framework is proposed to address the synchronization problem of memristor chaotic systems (MCSs) via the sliding-mode control method. By employing the presented unified framework, the finite-time and fixed-time synchronization of MCSs can be realized simultaneously. On the one hand, based on the Lyapunov stability and sliding-mode control theories, the finite-/fixed-time synchronization results are obtained. It is proved that the trajectories of error states come near and get to the designed sliding-mode surface, stay on it accordingly and approach the origin in a finite/fixed time. On the other hand, we develop an image encryption algorithm as well as its implementation process to show the application of the synchronization. Finally, the theoretical results and the corresponding image encryption application are carried out by numerical simulations and statistical performances. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time and fixed-time bipartite average tracking (BAT) problems in multi-agent systems (MASs) subject to bounded disturbances. A novel non-smooth protocol is first constructed on the basis of utilizing the finite-time control method, which can realize the finite-time BAT with structurally balanced graph. Then, the fixed-time BAT problem is dealt with nonlinear fixed-time algorithm, the setting time of which is obtained without depending on initial states. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve the finite-time and fixed-time BAT for MASs with disturbances. Numerical examples are finally developed for illustration. [ABSTRACT FROM AUTHOR]

Piecewise affine (PWA) systems are attractive models that can represent various hybrid systems with local affine subsystems and polyhedral regions due to their universal approximation properties. The identification problem of PWA systems amounts to estimating the number of subsystems, parameters of each subsystem, and the corresponding polyhedral partitions via state-input vectors. In this paper, we propose a novel approach to address the online identification problem of continuous-time PWA systems in state-space form. Specifically, an online active mode recognition algorithm and a generalized integral concurrent learning identifier are presented to acquire the number of subsystems, the switching sequence, and the parameter of each subsystem. In addition, we develop the optimization problem for the polyhedral partition estimation, which is solved by using the estimated switching sequence and subsystem parameters. The effectiveness of the proposed identification approach is demonstrated via simulation results. [ABSTRACT FROM AUTHOR]

Deep Neural Networks (DNNs) are increasingly being used in a variety of applications. However, DNNs have huge computational and memory requirements. One way to reduce these requirements is to sparsify DNNs by using smoothed LASSO (Least Absolute Shrinkage and Selection Operator) functions. In this paper, we show that irrespective of error profile, the sparsity values obtained using various smoothed LASSO functions are similar, provided the maximum error of these functions with respect to the LASSO function is the same. We also propose a layer-wise DNN pruning algorithm, where the layers are pruned based on their individual allocated accuracy loss budget, determined by estimates of the reduction in number of multiply-accumulate operations (in convolutional layers) and weights (in fully connected layers). Further, the structured LASSO variants in both convolutional and fully connected layers are explored within the smoothed LASSO framework and the tradeoffs involved are discussed. The efficacy of proposed algorithm in enhancing the sparsity within the allowed degradation in DNN accuracy and results obtained on structured LASSO variants are shown on MNIST, SVHN, CIFAR-10, and Imagenette datasets and on larger networks such as ResNet-50 and Mobilenet. [ABSTRACT FROM AUTHOR]

Sparsified kernel adaptive filters (SKAFs) is an attractive filtering solution with low memory and computational complexity. Most of existing SKAFs are based on the mean square error (MSE) criterion under Gaussian noise assumption for its simplicity and convenience. When the assumption deviates largely from the underlying truth, the performance of these methods could degrade significantly. In this paper, we propose a novel SKAF, named as projected kernel least mean p-power algorithm (PKLMP), based on the mean p-power error (MPE) criterion and vector projection (VP) method. We provide convergence analyses in terms of the stead-state MSE, based on a Taylor expansion method, and derive the lower and upper bounds for the steady-state excess MSE. We also conduct mean convergence analysis for PKLMP, and derive convergence conditions. To exploit the information in the desired outputs, we further derive a modified PKLMP by smoothing the desired signal. Finally, a simple and effective online variable kernel centers strategy is proposed to improve the filtering performance of the proposed KAFs. Simulation results under a static function estimation, a chaotic time-series prediction, and two real-world time-series predictions are conducted and validate the effectiveness of the proposed PKLMP algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a COordinate Rotation Digital Computer (CORDIC)-based architecture for the computation of Nth root and proves its feasibility by hardware implementation. The proposed architecture performs the task of Nth root simply by shift-add operations and enables easy tradeoff between the speed (or precision) and the area. Technically, we divide the Nth root computation into three different subtasks, and map them onto three different classes of the CORDIC accordingly. To overcome the drawback of narrow convergence range of the CORDIC algorithm, we adopt several innovative methods to yield a much improved convergence range. Subsequently, in terms of convergence range and precision, a flexible architecture is developed. The architecture is validated using MATLAB with extensive vector matching. Finally, using a pipelined structure with fixed-point input data, we implement the example circuits of the proposed architecture with radicand ranging from zero to one million, and achieve an average mean of approximately 10−7 for the relative error. The design is modeled using Verilog HDL and synthesized under the TSMC 40-nm CMOS technology. The report shows a maximum frequency of 2.083 GHz with $197421.00~{\mu }\text{m}^{2}$ area. The area decreases to $169689.98~{\mu }\text{m}^{2}$ when the frequency lowers to 1.00 GHz. [ABSTRACT FROM AUTHOR]

This paper presents a family of robust set-membership normalized subband adaptive filtering (RSM-NSAF) algorithms for acoustic echo cancellation (AEC). By using a new robust set-membership error bound, the RSM-NSAF algorithm obtains improved robustness against impulsive noises and decreased steady-state misalignment relative to the conventional set-membership NSAF (SM-NSAF) algorithm. To exploit the sparsity of the impulse response, the L0 norm constraint robust set-membership NSAF ( L0 -RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and L0 norm constraint robust set-membership improved proportionate NSAF ( L0 -RSM-IPNSAF) algorithms are derived by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L0 norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance. [ABSTRACT FROM PUBLISHER]

This article proposes a robust method for the synthesis and design of optimal linear group delay filters with prescribed bandwidth and dispersion properties. The proposed filters are based on a cascade of second-order all-pass filter cells, for which all the parameters are optimized in order to reach the desired wideband linear group delay characteristic with positive slope. Compared to the previously published synthesis method, the proposed approach offers appropriate initialization enabling convergence and aiming for the optimal solution. The method’s convergence and robustness are proved through a 21-cells synthesis, which is the highest number of cascaded cells reported to date, due to the usual convergence problem. Then the electronic feasibility is illustrated through the measurement results of a lumped-elements linear group-delay filter prototype dimensioned with this method. The measured group delay presents a positive slope of 8 ns GHz−1 in the frequency range [100–725] MHz. It is, to the best of our knowledge, the highest positive slope reported to date with an electronic implementation (i.e except SAW and waveguide devices). [ABSTRACT FROM AUTHOR]

The convergence of the waveform relaxation (WR) method is demonstrated for a class of circuits: Chains of identical and symmetrical passive subcircuits. The WR algorithm uses resistive coupling to implement the iteration. Every part is modeled as a symmetric and reciprocal linear two-port network. The iteration matrices of the WR operator are constructed for the Gauss-Jacobi and Gauss-Seidel relaxations in the Fourier domain. An upperbound estimate of the spectral radius of the WR operator is presented. It demonstrates the convergence of the method independently of the number of cascaded parts in the chain and the coupling resistance. [ABSTRACT FROM AUTHOR]

Predefined mymargin finite-time output containment control problem for nonlinear multi-agent systems with multiple dynamical leaders under directed topology is investigated, where the outputs of followers can converge to the predefined convex hull formed by the multiple leaders within a finite time, and the leaders can have unknown control inputs. Firstly, for the directed topological structure among the followers, a distributed adaptive observer is designed to estimate the whole states of all the leaders under the influences of the leaders’ unknown inputs. By utilizing Hardy’s inequality and common Lyapunov theory, the finite-time convergence of the proposed observer is proved. On the basis of this conclusion, a predefined distributed containment control protocol including the desired convex combinations of the leaders is developed for each follower by using the given weights. Then an algorithm is proposed to design the control parameters in the proposed containment control protocol. With the help of the output regulation theory, the finite-time output containment criterion for nonlinear multi-agent systems in the presence of the leaders’ unknown inputs is derived. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

CORDIC algorithm is suitable to implement sine/cosine function, but the large number of iterations lead to great delay and overhead. Moreover, due to finite bit-width of operands and number of iterations, the relative error of floating-point sine or cosine is terrible when the input angle is close to 0 or $\pi /2$ , respectively. To overcome these shortcomings, TCORDIC algorithm, which combines low latency CORDIC and Taylor algorithm, is presented. After analyzing the latency of traditional CORDIC, low latency CORDIC is proposed, which adopts the technique of sign prediction, compressive iterations, and parallel iterations. Besides, the calculating boundary ( N$ ), which is used for determining whether Taylor algorithm is selected or not in TCORDIC algorithm, is evaluated to achieve a trade-off between area and delay. Truncated multipliers are used to reduce the area further. Finally, Using TCORDIC algorithm, pipelined and iterative structures are implemented for IEEE-754 double precision floating-point sine/cosine with the input Z\epsilon [0,\pi /2]$ . Under typical condition (1V, 25 °C), our designs are synthesized with 40 nm standard cell library. For a pipelined structure, the frequency is up to 1.70 GHz and area . Frequency decreases to 1.45 GHz for iterative structure, but the area requires only 110590.81~\mu {\mathrm { m}}^{2} . TCORDIC is efficient in controlling relative error, and achieves the accuracy within one ulp (unit in the last place) for floating-point sine/cosine function. [ABSTRACT FROM AUTHOR]