A New Event-Triggered Type-3 Fuzzy Control System for Multi-Agent Systems: Optimal Economic Efficient Approach for Actuator Activating

This study presents a new approach for multi-agent systems (MASs). The agent dynamics are approximated by the suggested type-3 (T3) fuzzy logic system (FLS). Some sufficient conditions based on the event-triggered scheme are presented to ensure the stability under less activation of the actuators. New tuning rules are obtained for T3-FLSs form the stability and robustness examination. The effect of perturbations, actuator failures and approximation errors are compensated by the designed adaptive compensators. Simulation results show that the output of all agents well converged to the leader agent under disturbances and faulty conditions. Additionally, it is shown that the suggested event-triggered scheme is effective and the actuators are updated about 20–40% of total sample times.

An Improved Imaging Algorithm for Multi-Receiver SAS System with Wide-Bandwidth Signal

When the multi-receiver synthetic aperture sonar (SAS) works with a wide-bandwidth signal, the performance of the range-Doppler (R-D) algorithm is seriously affected by two approximation errors, i.e., point target reference spectrum (PTRS) error and residual quadratic coupling error. The former is generated by approximating the PTRS with the second-order term in terms of the instantaneous frequency. The latter is caused by neglecting the cross-track variance of secondary range compression (SRC). In order to improve the imaging performance in the case of wide-bandwidth signals, an improved R-D algorithm is proposed in this paper. With our method, the multi-receiver SAS data is first preprocessed based on the phase center approximation (PCA) method, and the monostatic equivalent data are obtained. Then several sub-blocks are generated in the cross-track dimension. Within each sub-block, the PTRS error and residual quadratic coupling error based on the center range of each sub-block are compensated. After this operation, all sub-blocks are coerced into a new signal, which is free of both approximation errors. Consequently, this new data is used as the input of the traditional R-D algorithm. The processing results of simulated data and real data show that the traditional R-D algorithm is just suitable for an SAS system with a narrow-bandwidth signal. The imaging performance would be seriously distorted when it is applied to an SAS system with a wide-bandwidth signal. Based on the presented method, the SAS data in both cases can be well processed. The imaging performance of the presented method is nearly identical to that of the back-projection (BP) algorithm.

Synchronization of Chaotic Systems: A Generic Nonlinear Integrated Observer-Based Approach

The purpose of this research is to study the synchronization of two integrated nonlinear systems with time delay and disturbances. A nonlinear system is a system in which the difference in output is not relative to the difference in input. A new control methodology for synchronization of the two chaotic systems master and slave is recognized by means of the unique integrated chaotic synchronous observer and the integrated chaotic adaptive synchronous observer. The instantaneous approximation states of the master and slave systems are accomplished by means of methods for suggesting observers for every one of the master and slave systems and by the production of error signals between these approximated states. This approximated synchronization error signal and state approximation errors meet at the origin by means of methods involving a particular observer-based feedback control signal to ensure synchronization and state approximation. Using Lyapunov stability theory, adaptive and nonadaptive laws for control systems, and nonlinear properties, the intermingling conditions for state approximation errors and approximated synchronization errors are established as nonlinear matrix inequalities. A solution to the resulting inequality constraints using a two-step linear matrix inequality (LMI)-based approach is introduced, giving essential and adequate conditions to extract values from the controller gain and observer gain matrices. Simulation of the suggested synchronization procedure for FitzHugh–Nagumo neuronal systems is demonstrated to expand the viability of the suggested observer-based control techniques.

Efficient Semidefinite Programming with Approximate ADMM

Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting approximately to the Semidefinite cone. Instead of computing the projections via “exact” eigendecompositions that scale cubically with the matrix size and cannot be warm-started, we suggest using state-of-the-art factorization-free, approximate eigensolvers, thus achieving almost quadratic scaling and the crucial ability of warm-starting. Using a recent result from Goulart et al. (Linear Algebra Appl 594:177–192, 2020. https://doi.org/10.1016/j.laa.2020.02.014), we are able to circumvent the numerical instability of the eigendecomposition and thus maintain tight control on the projection accuracy. This in turn guarantees convergence, either to a solution or a certificate of infeasibility, of the ADMM algorithm. To achieve this, we extend recent results from Banjac et al. (J Optim Theory Appl 183(2):490–519, 2019. https://doi.org/10.1007/s10957-019-01575-y) to prove that reliable infeasibility detection can be performed with ADMM even in the presence of approximation errors. In all of the considered problems of SDPLIB that “exact” ADMM can solve in a few thousand iterations, our approach brings a significant, up to 20x, speedup without a noticeable increase in ADMM’s iterations.

Adaptive Segmentation of Streaming Sensor Data on Edge Devices

Sensor data streams often represent signals/trajectories which are twice differentiable (e.g., to give a continuous velocity and acceleration), and this property must be reflected in their segmentation. An adaptive streaming algorithm for this problem is presented. It is based on the greedy look-ahead strategy and is built on the concept of a cubic splinelet. A characteristic feature of the proposed algorithm is the real-time simultaneous segmentation, smoothing, and compression of data streams. The segmentation quality is measured in terms of the signal approximation accuracy and the corresponding compression ratio. The numerical results show the relatively high compression ratios (from 135 to 208, i.e., compressed stream sizes up to 208 times smaller) combined with the approximation errors comparable to those obtained from the state-of-the-art global reference algorithm. The proposed algorithm can be applied to various domains, including online compression and/or smoothing of data streams coming from sensors, real-time IoT analytics, and embedded time-series databases.

B-spline based corner smoothing method to decrease the maximum curvature of the transition curve

Toolpath represented by linear segments leads to tangency discontinuity between blocks, which results in fluctuation of feedrate and reduction of machining efficiency and quality. To eliminate these unwanted external factors, optimal corner smoothing operation is essential for CNC systems to achieve a smooth toolpath. This work proposes a corner smoothing approach by generating a B-spline transition curve with 7 control points. By adjusting the position of the control points, the resulting transition curve is not limited to smooth the corner in the convex side of the corner, but shuttles back and forth between the convex and concave sides to decrease the maximum curvature, while respecting the given error tolerance. The approximation errors in convex and concave sides can be analytically calculated. Experimental results demonstrate the effectiveness of the proposed method on machining efficiency improvement.

Local clustering via approximate heat kernel PageRank with subgraph sampling

Graph clustering, a fundamental technique in network science for understanding structures in complex systems, presents inherent problems. Though studied extensively in the literature, graph clustering in large systems remains particularly challenging because massive graphs incur a prohibitively large computational load. The heat kernel PageRank provides a quantitative ranking of nodes, and a local cluster can be efficiently found by performing a sweep over the heat kernel PageRank vector. But computing an exact heat kernel PageRank vector may be expensive, and approximate algorithms are often used instead. Most approximate algorithms compute the heat kernel PageRank vector on the whole graph, and thus are dependent on global structures. In this paper, we present an algorithm for approximating the heat kernel PageRank on a local subgraph. Moreover, we show that the number of computations required by the proposed algorithm is sublinear in terms of the expected size of the local cluster of interest, and that it provides a good approximation of the heat kernel PageRank, with approximation errors bounded by a probabilistic guarantee. Numerical experiments verify that the local clustering algorithm using our approximate heat kernel PageRank achieves state-of-the-art performance.

A pseudo-softmax function for hardware-based high speed image classification

In this work a novel architecture, named pseudo-softmax, to compute an approximated form of the softmax function is presented. This architecture can be fruitfully used in the last layer of Neural Networks and Convolutional Neural Networks for classification tasks, and in Reinforcement Learning hardware accelerators to compute the Boltzmann action-selection policy. The proposed pseudo-softmax design, intended for efficient hardware implementation, exploits the typical integer quantization of hardware-based Neural Networks obtaining an accurate approximation of the result. In the paper, a detailed description of the architecture is given and an extensive analysis of the approximation error is performed by using both custom stimuli and real-world Convolutional Neural Networks inputs. The implementation results, based on CMOS standard-cell technology, compared to state-of-the-art architectures show reduced approximation errors.

Hamiltonian simulation in the low-energy subspace

We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H. This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H. We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.

SOFTWARE PACKAGE FOR CONSTRUCTING LINEAR REGRESSION models USING THE MIXED ESTIMATION METHOD

В статье описывается программный комплекс, обеспечивающий возможность оценивания параметров линейного регрессионного уравнения методами смешанного оценивания (МСО), наименьших квадратов (МНК) и модулей (МНМ), а также антиробастного оценивания (МАО). Разработанный программный комплекс применен для моделирования объема погрузки основных видов грузов железнодорожным транспортом, в качестве независимых переменных определены объемы погрузки конкурирующими видами транспорта. Это такие факторы, как перевозки автомобильным, морским, трубопроводным и внутренним водным транспортом. Проведён анализ полученных моделей, оценены значения критериев смещения, относительных ошибок аппроксимации, согласованности поведения. The article considers a software package that provides the ability to estimate the parameters of a linear regression equation using mixed estimation (MSO), least squares (OLS) and modules (MCM), as well as anti-blast estimation (MAO). The developed software package was used to model the volume of loading of the main types of cargo by rail, and the competing types of transportation in relation to rail transportation were selected as independent variables. These are such factors as transportation by road, transportation by sea, transportation by pipeline, transportation by inland water transport. The analysis of the obtained models is carried out, the bias criteria, the relative approximation errors, and the generalized behavior consistency criterion (RSPC) are evaluated.