Synchronization Error Research Articles

A matrix-separation-based integral inequality for aperiodic sampled-data synchronization of delayed neural networks considering communication delay

This paper achieves the synchronization of delayed neural networks (DNNs) considering aperiodic sampled-data control and communication delay. First of all, based on the master-slave DNNs with aperiodic sampling synchronization controller, a synchronization error system is constructed. Then, an augmented functional containing both the error state and its derivative is constructed. Compared with the existing researches, the augmented functional introduces more cross information of error states to the criterion. Next, an integral inequality based on the separation of internal integral variable and matrix is developed. Compared to the inequalities that treat the internal variable and the matrix as unified ones, the developed inequality provides a tighter estimate of the derivative of the augmented functional. On this basis, a criterion with less conservative is developed for the aperiodic sampled-data synchronization of DNNs considering communication delay. Finally, to indicate the superiority of the developed method on improving the acceptable sampling upper bound of synchronization, three numerical examples are provided.

Synchronization of high-dimensional Kuramoto-oscillator networks with variable-gain impulsive coupling on the unit sphere

Kuramoto models (KMs) in scalar or high-dimensional form can describe the synchronization phenomenon for large populations of coupled oscillators in networks of dynamical systems such as power grids, satellite mobile sensing networks, etc. However, these models are developed based on continuous-time coupling among oscillators, which is not applicable to networks where the coupling between oscillators occurs only at impulsive instants. Herein, we propose for the first time a generalized high-dimensional Kuramoto oscillator network (HDKON) with variable-gain impulsive coupling on the unit sphere. The proposed HDKON can be reduced to a scalar form comprising a sinusoidal function, thereby generalizing the scalar KM in both temporal and spatial domains. Furthermore, we provide some variation coefficients of the synchronization errors for the oscillator pairs at impulsive instants, and derive a sufficient condition for the exponential synchronization of the HDKON with identical natural frequency. Moreover, we consider an HDKON with a central oscillator and demonstrate that peripheral oscillators almost globally exponentially synchronize to the central oscillator under a sufficient condition. Finally, numerical simulations are performed to verify the main theoretical results.

Synchronous Tracking Control Strategy of Dual-Actuator Excited Shaking Table

The electro-hydraulic shaking table in the laboratory is specifically designed to replicate the desired earthquake ground motion for engineering structure, requiring precise synchronization of its dual exciters and accurate tracking of the target signal. The system faces challenges such as control errors and actuator asynchronization due to the nonlinear effects of the shaking table system and the structural model. To address the issues of inadequate tracking and synchronization accuracy, this study introduces a novel strategy for synchronizing the motion of the exciters and establishes a fuzzy logic controller (FLC) for the shaking table to minimize synchronization errors of dual exciters. Furthermore, an adaptive inverse controller (AIC) is developed for the exciters to enhance tracking accuracy. By combining FLC and AIC, this approach leverages the strengths of both control techniques to achieve superior control performance. The proposed control is implemented through MATLAB\Simulink, and numerical analyses are conducted under various conditions. The numerical results demonstrate the effectiveness and feasibility of the proposed control strategy.

A cooperative timestamp-free clock synchronization scheme based on fast unscented Kalman filtering for time-sensitive networking

Clock synchronization, built on the classical two-way message exchange scheme, is the key prerequisite for the normal operation of time-sensitive networking (TSN). In practical TSN, the imperfect oscillator caused by environmental changes leads to clock parameters drift. Moreover, synchronization errors accumulate in multi-hop networks, making it difficult for nodes at the edge of the network to achieve precise synchronization performance. Additionally, in some industrial and vehicular scenarios, the energy consumption and complexity of clock synchronization are important factors that need to be considered. To address these problems, this paper proposes a cooperative synchronization clock offset and clock skew joint tracking algorithm based on fast Unscented Kalman filter (FUKF). To further reduce the computation and energy consumption caused by clock synchronization, we introduce randomized singular value decomposition and timestamp-free exchange. The former uses small sub-matrices approximations to replace extremely high-dimensional matrices, reducing computational time in the update stage of the UKF. The latter reduces energy consumption by setting response intervals at the receiving end, eliminating the need for timestamp exchange during the synchronization process. Therefore, this algorithm can achieve long-term synchronization without requiring excessive computational and communication overhead. The results show that the proposed method, while maintaining accuracy unchanged, reduced the running time by 20% to 90% as the number of observations increased, thus verifying the effectiveness of the algorithm.

Non-pilot based carrier frequency offset estimation and reflection coefficient optimization for RIS-assisted OFDM systems

Carrier frequency synchronization between the transmitter and receiver is challenging due to oscillator inaccuracies and Doppler shifts, which lead to inter-carrier interference. To address this synchronization error, i.e., carrier frequency offset (CFO), we introduce a novel method for estimating the CFO in reconfigurable intelligent surfaces (RIS)-assisted orthogonal frequency division multiplexing (OFDM) systems. Additionally, we present a method to optimize reflection coefficients, as adjusting the reflection coefficient of RIS can effectively manipulate signal propagation and amplitude, thereby enhancing system performance. In the proposed method, a randomized set of reflection coefficients is applied for the first OFDM symbol, and CFO is estimated using the oversampling method within that symbol over the Rayleigh fading environment. A deterministic approach is adopted to reduce grid search complexity. Simulation results demonstrate the superior performance of the proposed CFO estimation method, particularly in high signal-to-noise ratio scenarios, compared to the existing Zadoff Chu sequence-based estimator in terms of mean square error (MSE). Subsequently, the CFO is compensated in the second OFDM symbol using the estimated CFO, and the reflection coefficient is optimized by identifying the channel tap associated with the maximum channel impulse gain technique. The optimized reflection coefficient enhances system performance in terms of bit error rate (BER) for RIS-assisted OFDM systems.

An improved clock synchronization model for typical IoT applications

In today’s scenario, the Internet of Things (IoT) has transformed people’s lives by enabling data exchange among pervasive devices in various applications. However, clock synchronization is essential to ensure seamless transmission and synchronization among IoT entities involved in processing and communication. This paper proposes a clock synchronization algorithm based on linear-quadratic regression (LQR) to address synchronization-errors in IoT applications. The algorithm uses a linear model of skew and offsets to estimate clock parameters, and performance is evaluated in terms of R-square error (RSE) and Root Mean Square Error (RMSE). Our proposed algorithm outperformed traditional algorithms with an R-Square Error of 0.71% and RMSE of 0.379%. This paper also evaluated the stability of the proposed model using the correlation coefficient, which indicated a high correlation among the variables at 86%. The results below demonstrate the proposed algorithm’s effectiveness and goodness of fit in addressing clock synchronization errors for IoT applications.

Adaptive fuzzy quantized prescribed performance synchronization of uncertain non-strict feedback chaotic systems with time-varying actuator failure

This paper addresses an adaptive fuzzy prescribed performance synchronization for a class of uncertain non-strict feedback chaotic systems subject to input quantization and time-varying actuator faults. The proposed approach utilizes fuzzy logic systems to estimate uncertainties. In addition, multiplicative and additive faults are considered simultaneously, which may occur either separately or simultaneously. To address the challenge, based on the backstepping scheme and a filter, an intermediate controller is conducted to compensate for the interference between actuator faults and quantification, in which a damping term and a positive time-varying function are introduced. Moreover, treating the error system as a constrained system, a simplified nonlinear mapping is employed to achieve asymmetric prescribed performance synchronization. Unlike traditional methods that rely on barrier Lyapunov functions and switch functions, the proposed approach eliminates the need for a switch function and extends the action scope to cover all synchronization errors. The analysis demonstrates that even if actuator faults and input quantization coexist, all signals in the closed-loop system remain bounded, and synchronization errors remain within the prescribed performance range. Finally, synchronization simulations are conducted on a nonlinear gyroscope system and a Non-autonomous chaotic Micro-Electro-Mechanical-System to reveal the validity of the proposed scheme.

Finite-time funnel synchronization control based on distributed observer for multi-motor driving systems with input saturation

In this article, the finite-time synchronization control problem is developed for multi-motor driving systems with input saturation. A radial basis function (RBF) neural network is utilized to estimate the unknown uncertainties and the disturbances. In contrast to current control strategies, this study proposes a new approach that utilizes a finite-time distributed observer to estimate the reference signal and then uses the estimated signal to design a synchronization controller, which effectively separates the tracking problem from the synchronous controller design. Furthermore, a funnel function is constructed to actualize the state constraints and confine the synchronization error within a specified boundary. Then, a finite-time funnel control protocol is proposed to ensure that each motor follows the estimated reference signal. Eventually, we illustrate the effectiveness of the proposed method through a numerical example.

A modified dispersed frequency and phase consensus algorithm based on differential evolution and credibility weighting matrix

In distributed antenna array systems, accurate synchronization of the frequency and phase of the transmission signals among subarrays is a premise for beamforming. To solve this problem, a modified dispersed frequency and phase consensus (MDFPC) algorithm, which is based on differential evolution (DE) and the credibility weighting matrix, is proposed in this paper. DE algorithm is adopted to optimize the mixing matrix of MDFPC algorithm, and the convergence speed of consensus algorithm can be improved. Moreover, Lanczos method is adopted to calculate the fitness of individuals during optimization, thus the computation amount of the eigenvalue decomposition of the large-scale, sparse and symmetric mixing matrix can be effectively reduced. In addition, the influence of the transmission distance between subarrays on the received Signal-to-Noise Ratio (SNR) is considered, and the credibility weighting matrix can be obtained. Then the contribution of low-credible frequency and phase messages to the iterative updated values can be decreased by the credibility weighting matrix, thus more accurate frequency and phase updated values can be obtained in each iteration. It is shown from simulation results that the proposed algorithm can further reduce the phase synchronization error by at least 8% and achieve at least 18% convergence speed improvement compared to dispersed frequency and phase consensus (DFPC) algorithm.

Application of Fractional-Order Multi-Wing Chaotic System to Weak Signal Detection

This work investigates a fractional-order multi-wing chaotic system for detecting weak signals. The influence of the order of fractional calculus on chaotic systems’ dynamical behavior is examined using phase diagrams, bifurcation diagrams, and SE complexity diagrams. Then, the principles and methods for determining the frequencies and amplitudes of weak signals are examined utilizing fractional-order multi-wing chaotic systems. The findings indicate that the lowest order at which this kind of fractional-order multi-wing chaotic system appears chaotic is 2.625 at a=4, b=8, and c=1, and that this value decreases as the driving force increases. The four-wing and double-wing change dynamics phenomenon will manifest in a fractional-order chaotic system when the order exceeds the lowest order. This phenomenon can be utilized to detect weak signal amplitudes and frequencies because the system parameters control it. A detection array is built to determine the amplitude using the noise-resistant properties of both four-wing and double-wing chaotic states. Deep learning images are then used to identify the change in the array’s wing count, which can be used to determine the test signal’s amplitude. When frequencies detection is required, the MUSIC method estimates the frequencies using chaotic synchronization to transform the weak signal’s frequencies to the synchronization error’s frequencies. This solution adds to the contact between fractional-order calculus and chaos theory. It offers suggestions for practically implementing the chaotic weak signal detection theory in conjunction with deep learning.

Interference-enhanced micro-vision-based single-shot imaging of five degrees-of-freedom error motions for ultra-precision rotary axes

The measurement of five degrees-of-freedom (5-DOF) error motions, including radial, axial, and tilt motions, is crucial for ultra-precision rotary axes, which are key components of ultra-precision machine tools and instrumentation. In this study, we propose an interference-enhanced micro-vision technique to concurrently derive the 5-DOF error motions from a single-shot two-dimensional image, which was captured by a standard industrial camera equipped with an interference objective lens. By consolidating the essential features into a single optical path, the interference-enhanced micro-vision technique ingeniously merges machine micro-vision and modified white-light interference to detect in-plane and out-of-plane motions. Numerical simulations demonstrated, the basic principle for deriving the 5-DOF error motions, and the magnification of objective lens had inconsistent effects on the measurement accuracy for the radial and tilt motions, i.e. higher magnification led to higher radial accuracy but lower tilt accuracy. As practical application, the error motion detection capability was demonstrated by simultaneously measuring the 5-DOF synchronous and asynchronous error motions for a typical air bearing spindle at rotation speeds of 8.33, 108.33, and 308.33 rpm. The synchronous errors were nearly identical at various spindle speeds. However, because of system dynamics, increased vibrations were observed to be superimposed on the basic tilt error motions as the spindle speeds increased, which were verified by the vibration marks imprinted on the turned surfaces. For the 5-DOF motion measurements, the least-square fitting using large-volume edge and greyscale data of the captured image enabled super-high resolutions, despite using a camera with a relatively large pixel size and low bit depth. These results demonstrate that the proposed interference-enhanced micro-vision technique is a simple and effective tool for measuring spatial error motions in ultra-precision rotary axes.

Admissible and dissipative synchronisation of fractional order singular systems with time delay using event-triggered feedback control

The purpose of this work is to study the admissible and dissipative synchronisation of fractional order singular systems with time delay. The key goal is to use as few network resources as possible while retaining the desired closed-loop performance. An event-triggered control method is used to accomplish this. The Lyapunov function method, linear matrix inequality approach, and mathematical techniques are used to develop new synchronisation criteria that assure the synchronisation error system is Mittag–Leffler stable. Because fractional order differential equations have memory characteristics, which are very different from ordinary differential equations, leading to difficulties in preventing Zeno behaviour related to the event-triggered mechanism of fractional order systems, especially of delayed fractional order singular systems. To solve this issue, we propose a new theoretical framework and a new condition to preclude Zeno behaviours. This derived conditions use inequality techniques and take advantage of a number of fundamental aspects of fractional order calculus. Furthermore, the dissipative synchronous problem of delayed fractional order singular systems is also solved for the first time using the suggested stable criterion in conjunction with some auxiliary characteristics of fractional calculus. Two numerical examples are provided to demonstrate the usefulness of the proposed strategy.

A noise‐tolerant fuzzy‐type zeroing neural network for robust synchronization of chaotic systems

SummaryAs a significant research issue in control and science field, chaos synchronization has attracted wide attention in recent years. However, it is difficult for traditional control methods to realize synchronization in predefined time and resist external interference effectively. Inspired by the excellent performance of zeroing neural network (ZNN) and the wide application of fuzzy logic system (FLS), a noise‐tolerant fuzzy‐type zeroing neural network (NTFTZNN) with fuzzy time‐varying convergent parameter is proposed for the synchronization of chaotic systems in this paper. Notably the fuzzy parameter generated from FLS combined with traditional convergent parameter embedded into this NTFTZNN can adjust the convergence rate according to the synchronization errors. For the sake of emphasizing the advantages of NTFTZNN model, other three sets of contrast models (FTZNN, VPZNN, and PTZNN) are constructed for the purpose of comparison. Besides, the predefined‐time convergence and noise‐tolerant ability of NTFTZNN model are distinctly demonstrated by detailed theoretical analysis. Furthermore, synchronization simulation experiments including two chaotic systems with different dimensions are provided to verify the related mathematical theories. Finally, the schematic of NTFTZNN model for chaos synchronization is accomplished completely through Simulink, further accentuating its effectiveness and potentials in practical applications.

Investigation on the biaxial tensile testing method for metal foil using cruciform specimen

The assessment of mechanical properties of metal foil under complicated stress states poses a considerable challenge, requiring the development of new testing methods and the optimization of new specimen geometry. In this research, the biaxial tensile method and specimen shape were designed and optimized by using simulation and experiment. It is determined that the strain measurement area can be suggested as the central area of 0.6 to 0.8 times the arm width. The influence of different parameters on the tensile results of cruciform specimens was comprehensively evaluated by finite element method and multi-factor analysis. The results indicate that the number of slits markedly impacts the stress–strain uniformity and shear stress in the central region, followed by the slit length. The effect of the arm width and the slit width is comparable, more influential than the corner radius. According to the analyzed results and application requirements, a four-axis independently driven biaxial tensile test machine for small scale samples was fabricated. During the biaxial tension, the center point offset of the specimen remains within ±0.01 mm. The displacement and load synchronization errors do not exceed 0.01 mm and 50 N, respectively, facilitating the precise control of four-axis synchronization. Conclusively, cruciform specimens featuring diverse geometric characteristics were designed for industrial pure titanium, 304 stainless steel, and Inconel 718 superalloy with thickness of less than 0.3 mm. The biaxial tensile tests were performed to delineate the yield loci, revealing notable anisotropy and size effect. The validation confirms the suitability of the testing method and optimized cruciform specimens for conducting biaxial tensile mechanical properties testing on metal foils characterized by diverse types and thicknesses.

Emergent order in adaptively rewired networks.

We explore adaptive link change strategies that can lead a system to network configurations that yield ordered dynamical states. We propose two adaptive strategies based on feedback from the global synchronization error. In the first strategy, the connectivity matrix changes if the instantaneous synchronization error is larger than a prescribed threshold. In the second strategy, the probability of a link changing at any instant of time is proportional to the magnitude of the instantaneous synchronization error. We demonstrate that both these strategies are capable of guiding networks to chaos suppression within a prescribed tolerance, in two prototypical systems of coupled chaotic maps. So, the adaptation works effectively as an efficient search in the vast space of connectivities for a configuration that serves to yield a targeted pattern. The mean synchronization error shows the presence of a sharply defined transition to very low values after a critical coupling strength, in all cases. For the first strategy, the total time during which a network undergoes link adaptation also exhibits a distinct transition to a small value under increasing coupling strength. Analogously, for the second strategy, the mean fraction of links that change in the network over time, after transience, drops to nearly zero, after a critical coupling strength, implying that the network reaches a static link configuration that yields the desired dynamics. These ideas can then potentially help us to devise control methods for extended interactive systems, as well as suggest natural mechanisms capable of regularizing complex networks.

WITHDRAWN: Adaptive fuzzy fixed-time bipartite consensus control for stochastic nonlinear multi-agent systems with performance constraints

This paper investigates the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) with performance constraints. A constraint scaling function is proposed to model the performance constraints with user-predefined steady-state accuracy and settling time without relying on the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable using the constraint scaling function and an error transformation function before being used to design the controller. To achieve fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to guarantee the prescribed performance. Then, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and one adaptive parameter needs to be estimated online. It is shown that the closed-loop system has practical fixed-time stability in probability, and the antagonistic network’s consensus error evolves within user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.

Development of calibration device for on-load tap changer tester of transformer

Abstract More and more transformer on load tap changers are being tested using the AC method, which is closer to the actual operating status of the transformer on load tap changers. From the analysis of the switch operating status, the test results are closer to the actual value. However, the existing calibration devices for transformer on load tap changer testers are all aimed at DC testers, and traditional calibration methods are difficult to achieve synchronous calibration of transition resistance, transition time, and synchronization under AC test signals. Therefore, this article designs a three channel variable AC resistor module based on FPGA controlled DAC to simulate different resistors. The variable resistor module can achieve fast switching of resistors through frequency compensation, and achieve synchronous verification of analog conversion resistance, conversion time, and synchronization. After testing, the maximum allowable error of the calibration device for simulating transition resistance is ± (0.3% RD+5 m Ω), and the absolute error of transition time and synchronization is less than 20us, which fully meets the needs of laboratory calibration and solves the calibration problem of the transformer on load tap changer tester.

Reduced precision of motor and perceptual rhythmic timing in autistic adults

Recent results suggest that autistic individuals exhibit reduced accuracy compared to non-autistic peers in temporally coordinating their actions with predictable external cues, e.g., synchronizing finger taps to an auditory metronome. However, it is not yet clear whether these difficulties are driven primarily by motor differences or extend into perceptual rhythmic timing tasks. We recruited autistic and non-autistic participants for an online study testing both finger tapping synchronization and continuation as well as rhythmic time perception (anisochrony detection). We fractionated each participant's synchronization results into parameters representing error correction, motor noise, and internal time-keeper noise, and also investigated error-correcting responses to small metronome timing perturbations. Contrary to previous work, we did not find strong evidence for reduced synchronization error correction. However, we found compelling evidence for noisier internal rhythmic timekeeping in the synchronization, continuation, and perceptual components of the experiment. These results suggest that noisier internal rhythmic timing processes underlie some sensorimotor coordination challenges in autism.

SPACE TECHNOLOGIES AND DEVOPS: INTEGRATING POSITIONING AND TIMING SYSTEMS FOR RELIABLE SOFTWARE DEPLOYMENT IN AEROSPACE APPLICATIONS

The specific topic of investigation in this paper is the integration of PNT technologies into the DevOps paradigm for the aerospace domain with an emphasis on improved robustness and accuracy of software releases. The paper's goal is to show how PNT systems, especially GNSS and machine learning applied to time-series data, can solve several critical issues faced in software deployment in aerospace, whether using simulation reports and real-world case study examples, areas and ways in which the PNT-enabled DevOps pipeline may be employed may be highlighted. The fact that the timing and positioning investigations improve the accuracy of the deployment also reduces synchronization errors, as evidenced by the research. Through the preceding technologies, aerospace organizations will be able to elevate the reliability of software installations, hence positively contributing to the operational and safety aspects of aerospace and space missions. This integration indicates a significant advancement in what must be done to handle DevOps processes for the critical requirements of aerospace applications.

Satellite orbit determination and time synchronization using GPS single-frequency observables in low and high solar activities

We assess the orbit accuracy and time synchronization error using the L1 and C1 observables during the different solar activities. In general, GPS single-frequency (SF) observable can be used for commercial applications in satellite industry. The accuracy of satellite orbit determination using the SF observations is dominated by solar activities. The solar activities are indexed by the F10.7 value. The different solar activities lead to the ionosphere perturbation, triggering off the occurrence probability of ionospheric irregularities. The ionospheric irregularity affects the amplitude and phase of GPS signal. The affected amplitude and phase are indexed by the S4 value. We determine the GRACE satellite orbit using the SF GPS observations and compare the resulting orbit to that derived by dual-frequency observations for the effectiveness. The SF phase data are very sensitive to the variation in electron density and indirectly affects both the orbit accuracy and the time synchronization error. This is most likely caused by the phase ambiguity disturbed by the ionosphere. However, the C1 is relatively free from such a disturbance due to the strong signal-to-noise ratio (SNR) and the phase shift keying technique. The C1 performs the consistent solution over the low and high solar activities. However, this is not the case for the L1. The L1-derived orbit solution during the high solar activities is worse than that during the low solar activities. On the other hand, the time synchronization errors derived by the L1 and C1 are also different. The L1-derived time synchronization error has a relatively large perturbation as compared to the C1-derived one, which shows a consistent solution for a long-term period. This work suggests that the C1 observable is able to produce a consistent the orbit solution and time synchronization for the commercial applications of the satellite industry.Graphical