Constant Time Delay Research Articles

Stability of Markovian Jump Bidirectional Associative Memory Neural Networks Under Lévy Noise and Discrete Observation

ABSTRACTThe focus of this paper is to discuss the asymptotic stability and exponential stability problems of Markovian jump bidirectional associative memory neural networks with Lévy noise based on the discrete observation. Compared with the existing literature, this paper gives a weaker assumption regarding Lévy noise intensity functions. Furthermore, for the sake of solving difficulties caused by the discrete observation and Lévy noise, this paper designs a new Lyapunov‐Krasovskii functional which not only depends on the discrete observation interval, but also intensity measures. In virtue of the M‐matrix theory, three theorems are obtained ensuring the mean‐square asymptotic stability and mean‐square exponential stability of the trivial solution. Our theorems can not only deal with the discrete observation, but also with constant delays and variable time delays. Ultimately, two numerical examples are presented to illustrate the correctness of our theory findings.

The Effectiveness of Augmented Reality Offered with Constant Time Delay Procedure in Teaching the Functions of Organs to Students with Intellectual Disabilities

Introduction: Science course allows student to follow scientific developments, understand and interpret the events that occur around them, and develop scientific process skills. Different methods are employed in teaching science to student childeren with intellectual disabilities. There has been a recent increase in technology-supported methods. One of the technology-supported methods is Augmented Reality. For this reason, the effectiveness of the augmented reality provided with the constant time delay procedure in teaching the functions of the organs to childeren with intellectual disabilities was investigated in the present study. The study was conducted in the individual education setting of a private special education and rehabilitation center. Method: Three students who had intellectual disabilities participated in the study. The multiple probe design with probe conditions. Phases across behaviors, which is one of the single-case research designs, was used in the study. Findings: According to the study results, it was found that all participants acquired the target behaviors successfully and the participants retained the behaviors they acquired after the teaching of organs and their functions ended and they were able to generalize the behaviors they acquired to different materials. Discussion: Based on the results of the study, it can be argued that the Augmented Reality offered with the Constant Time Delay Procedure is effective in teaching science subjects to childeren with intellectual disabilities. It can also be argued that the permanence of the acquired behaviors is high when students who have mental disabilities are taught science subjects by using Augmented Reality along with the Constant Time Delay Procedure. To generalize the results obtained in the present study, it may be suggested that the same practice be performed with other experimenters and different age groups. For the social validity of the study, the teachers of the participants expressed positive opinions about the Augmented Reality offered with target behaviors and Constant Time Delay Procedure.

Effectiveness of a Three-Step Decoding Strategy with Constant Time-Delay to Teach Word Reading to Students with Mild and Moderate Intellectual Disability

The purpose of this study was to examine the effects of a three-step decoding strategy with constant time delay on teaching and acquisition of decoding and word reading skills to four students with mild and moderate intellectual disability and to measure the generalization of those skills to untaught words. A multiple probe design across participants was used to examine the percentage of sounds correctly decoded and words correctly read. The results indicate that all four participants learned to decode and read words using the two strategies. Furthermore, all participants showed an increased learning efficiency in decoding and reading when teaching the second set of similar words. Generalization data showed that only two participants were able to decode and read some of the new words before teaching them, while all participants' ability to decode the letters of the new words was improved. Keywords: Reading, Phonics, Three-step decoding, Time delay, Intellectual disability

Adaptive output feedback command filter control based on extreme learning machine for nonaffine time delay systems with input saturation

This paper is concerned with the tracking control problem of nonlinear time delay systems. For time delay systems, we consider nonaffine pure-feedback structure. Additionally, the case where the time delay systems are subject to input saturation and unknown states is also taken into account. To begin with, a mean value theorem and an implicit function theorem are exploited to transform the systems into an affine form. Afterwards, a state observer is developed to estimate the unknown state variables and an extreme learning machine (ELM) is used to approximate the unknown functions. The output of the command filter replaces the virtual control signal'derivative, thereby circumventing the problem of ‘explosion of complexity’. Meanwhile, compensation signals are introduced to eliminate the filtering errors in a dynamic surface control (DSC). A Lyapunov–Krasovskii functional is designed to mitigate the unknown constant state time delay. During the controller design process, combining a prescribed performance control (PPC) with a command filter control, the tracking error can converge to a predetermined bound. Additionally, the effect of input saturation is eliminated with the aid of an auxiliary system. Finally, the effectiveness of such controller is further proved by taking an electromechanical system as an application object.

Sediment Corrections for Distributed Acoustic Sensing

AbstractOn continental margins, sediments cause significant and spatially variable delays in seismic phase arrival times. The strong impedance contrast of the sediment‐bedrock interface causes P‐wave splitting that is clearly seen on distributed acoustic sensing recordings of earthquakes, resulting in additional phase arrivals that must be picked separately. We introduce sediment corrections to correctly account for those additional phases in the hypocenter localization procedure. Conceptually, the sediment correction method differs from the commonly‐used station corrections; instead of introducing a mathematically optimal constant time delay for each station and each phase, the corrections are derived from a physical, first‐order modeling of the wave propagation in the sediments. To calibrate the sediment corrections, a two‐step procedure is adopted: (a) the delay between the P‐phase and the converted Ps‐phase is taken as a proxy of the sediment thickness; (b) the P‐ and S‐wave speeds are determined through inversion. We show that sediment corrections are able to account for most of the observed bias while considerably reducing the number of free parameters compared to classical station correction. Moreover, the observed local delays are almost fully explained by the presence of the sedimentary layer, rather than by the 3D velocity variations of the bedrock. We retrieve and values that are compatible with values commonly found for sediments. Given the simplicity and physical foundation of the proposed method, we recommend the use of sediment corrections over station corrections whenever significant P‐wave splitting can be observed.

Positivity and semi-global polynomial stability of high-order Cohen–Grossberg BAM neural networks with multiple proportional delays

In this paper, we study positivity and semi-global polynomial stability (PS) of higher-order Cohen-Grossberg BAM neural networks with multiple proportional time delays. The proportional delays considered here are unbounded and time-varying, differing from constant, bounded, and distributional time delays. The system model cannot be represented using vector and matrices, making certain approaches within the vector-matrix framework unsuitable for applying. To address this limitation, a direct method based on the solution of the system is proposed to provide sufficient conditions guaranteeing the positivity and semi-global polynomial stability (PS) of the model under consideration. Furthermore, the direct method is applied to establish global PS conditions for BAM neural networks with multiple proportional delays. The obtained conditions contain only a few simple linear scalar inequalities that are easily solved. The applicability of the obtained PS conditions is verified by two numerical examples, and the solution of a linear programming problem is also obtained based on these theoretical results. Notably, this method can be applied to many system models with proportional delays after minor modifications.

Adaptive control of bilateral teleoperators with convergent parameter estimation and guaranteed compliance

Although adaptive control has been studied for teleoperation systems in the past decades, the convergence of parameter estimation is generally difficult to claim in the existing methods, and thus only specific scenarios (e.g., free motion) and partial operation performance (e.g., synchronization) have been addressed. In this paper, we found that the convergence of parameter estimation is crucial for bilateral teleoperation systems to retain the guaranteed operation performances, including compliance in the tracking motion and transparency in the contact motion. Accordingly, this paper suggests an alternative adaptive control for bilateral teleoperation systems, where a new adaptive law with the estimation errors as leakage terms is developed to obtain finite-time convergence of the parameter estimation. This convergent property allows to compensate for the undesired dynamics (e.g., gravity) in the closed-loop system so as to achieve ideal compliance and transparency. The control system’s stability and performances under constant time delays are analyzed for three scenarios: free motion, tracking motion, and contact motion. The quantitative relationship between the joint velocities and the human torques in the tracking motion is also studied, and the transparency is addressed in the contact motion. Simulations and experiments on a Baxter robot all showcase the effectiveness and superiority of the developed approach.

Using Constant Time Delay to Teach Sight Words to Students Identified as Deafblind

Using Constant Time Delay to Teach Sight Words to Students Identified as Deafblind

A delay differential equation model on covid-19 with vaccination strategy

In this paper, we have extended SEIR model of COVID-19. The model incorporates two vital aspects in the form of vaccine compartment and constant time delay. The vaccination and time delay provide the information about immune protection and actual existence of the infection among the individuals, respectively. The model is analysed numerically and numerical simulation are executed for three different initial histories and constant time delays which affirm the biological relevance of the system. The analysis includes disease-free equilibrium (DFE), endemic equilibrium, and the basic reproduction number. The stability analysis is performed which reveal the asymptotic stability of the DFE when the basic reproduction number R0 < 1. The study addresses the boundedness and positivity of the solution as the time delay approaches zero. In addition, sensitivity analysis and contour plots for R0 with different parameters offer deeper insights into the model. The impact of vaccination and vaccine inefficacy on the model dynamics is explored.

The combined Lyapunov functionals method for stability analysis of neutral Cohen–Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen–Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Variable-step [formula omitted] method combined with time two-grid algorithm for multi-singularity problems arising from two-dimensional nonlinear delay fractional equations

In this paper, we focus on the numerical simulation for two-dimensional nonlinear fractional sub-diffusion equations in the presence of time delay. Firstly, we investigate the existence, uniqueness and regularity of the solution for such problems. The theoretical result implies that the solution at τ+ is smoother than that at 0+, where τ is a constant time delay, and this is an improvement for the work (Tan et al., 2022). Secondly, a high-order difference scheme based on L1 method is constructed. For the sake of repairing the convergence order in temporal direction and improving the computational efficiency, an efficient time two-grid algorithm based on nonuniform meshes is first developed. The convergence order of the two-grid scheme reaches O(NF−min{rα,2−α}+NC−min{2rα,4−2α}+h12+h22), where NF and NC represent the number of the fine and coarse grids respectively, while h1 and h2 are the space-step sizes. Furthermore, stability and convergence analysis of the proposed scheme are carefully verified by energy method. Finally, numerical experiments are carried out to show the validity of theoretical statements.

Energy-dependent intrinsic time delay of gamma-ray bursts on testing Lorentz invariance violation

High-energy photons of gamma-ray bursts (GRBs) might be emitted at different intrinsic times with energy dependence at the source. In this letter, we expand the model from previous works on testing the Lorentz Invariance Violation (LV) with the observed GRB data from the Fermi Gamma-ray Space Telescope. We reanalyze the previous data with the full Bayesian parameter estimation method and get consistent results by assuming that the time delays are due to an LV term and a constant intrinsic time delay term. Subsequently, we neglect the LV effect and only consider the intrinsic time delay effect. We assume a common intrinsic time delay term along with a source energy correlated time delay of high-energy photons. We find that the energy-dependent emission times can also explain the observed GRB data of high-energy photon events. Finally, we integrate these two physical mechanisms into a unified model to distinguish and evaluate their respective contributions using the observed GRB data.

Synchronization of Coupled Neural Networks With Constant Time-Delay Using Sampled-Data Information.

In this article, a synchronization control method is studied for coupled neural networks (CNNs) with constant time delay using sampled-data information. A distributed control protocol relying on the sampled-data information of neighboring nodes is proposed. Lyapunov functional is constructed to analyze the synchronization of CNNs with constant time delay. Using Park's integral inequality and improved free-weight matrix integral inequality, sufficient conditions are provided for CNNs to achieve synchronization with less conservatism. In addition, the maximum sampling interval is determined by transforming the sufficient conditions into an optimization problem, and an aperiodic sampling control technique is implemented to reduce the communication energy load. Finally, numerical simulations are provided to demonstrate that the proposed method is capable of achieving synchronization.

Adaptive Iterative Learning Tracking Control for Nonlinear Teleoperators with Input Saturation

Addressing input saturation, external disturbances, and uncertain system parameters, this paper investigates the position tracking control problem for bilateral teleoperation systems with a time delay communication channel. Based on a composite energy function, we propose an adaptive iterative learning control (AILC) method to achieve the objective of position tracking under the alignment condition. This extends the existing research on the control of nonlinear teleoperation systems with time delay. The saturation constraint property of the Softsign function ensures that no state of the system exceeds its constraints. The controller learns to simultaneously deal with the uncertainty of system parameters online, reject external disturbances, and eliminate positional errors along the time and iteration axes. All signals in the system for any constant time delay are proved to be bounded. Ultimately, the performance of the proposed controller is further verified through numerical simulations.

Hypergolic Ignition by Off-Center Binary Collision of Monoethanolamine-NaBH4 and Hydrogen Peroxide Droplets

Hypergolic ignition of H2O2 and MEA-NaBH4 by off-center collision of their droplets was experimentally studied, focusing on the characteristics and mechanism of droplet mixing, droplet heating and evaporation, and gas-phase ignition. The whole collision ignition process was divided into five stages, which were compared, respectively, with that of head-on collision. Under the condition of a slightly off-center collision (for cases where B < 0.35), H2O2 droplets penetrate MEA-NaBH4 droplets after the collision and coalesce with it, but the internal H2O2 drop inside the MEA-NaBH4 droplet does not form a stable sphere. Instead, it rotates and expands inside the mixed droplet. With B increasing to 0.59, the droplets no longer coalesce after collision but separate away, forming satellite droplets. In such cases, multi-ignition mode is observed. When B increases to a certain extent, specifically, 0.85, a grazing collision is observed such that no mass transfer exists during the interaction of droplets, which leads to ignition failure. A theoretical model quantifying droplet swelling rate was established to calculate the volume change of the droplet. It was found that the swelling can be attributed to the flash boiling of superheated internal H2O2 fluid. Meanwhile, the ignition delay time was found to linearly decrease with B at various Wes until the extent where the chemical reaction takes over control, leading to an almost constant time delay defined as RDT. Additionally, the regime of ignition modes corresponding to different droplet mixing features is summarized in the We-B parametric space.

Analysis of Phase-Locked Loop Filter Delay on Transient Stability of Grid-Following Converters

To ensure precise phase estimation within the q-axis of the phase-locked loop (PLL), integrating a filter into the q-axis loop is essential to mitigate grid-voltage harmonics. Nevertheless, the intrinsic delay characteristics of this filter impede PLL synchronization during significant grid disturbances. This study begins by developing mathematical models for three types of filters—moving-average filter (MAF) for eliminating odd harmonic components, dq-frame cascaded delayed signal cancellation (dqCDSC) filter, and notch filter (NF). Following the reduction in filter orders, a third-order nonlinear large-signal model of the PLL, incorporating an additional q-axis internal filter, is formulated. Using phase plane analysis, this study investigates the transient synchronism of the grid-following converter (GFL) and explores the influence of delay time constants from the three PLL filters on its behavior while delineating the boundaries of their basins of attraction. Theoretical findings indicate that, relative to the traditional SRF-PLL, incorporating an internal filter into the PLL compromises the transient synchronous stability of GFL. Specifically, greater filter delay time constants exacerbate the GFL’s vulnerability to transient instability amid substantial grid disturbances. Hence, careful consideration is essential when using MAF-PLL and NF-PLL in situations demanding high synchronization stability. The theoretical analyses are validated using Matlab/Simulink to verify their accuracy.

Paraprofessionals’ Implementation of Constant Time Delay Procedures With Elementary Students With High-Intensity Behavioral Support Needs

Paraprofessionals play a significant role in the education system. However, they often need more training on specific instructional strategies to use with the students they work with. In this study, we trained two paraprofessionals working in a self-contained elementary classroom for students with high-intensity behavioral support needs. Each paraprofessional used constant time delay to support students’ learning to read grade-level sight and science words. Paraprofessionals also gathered maintenance and generalization sessions using individualized social stories created by the classroom teacher. Not only did the four student participants meet mastery of their personalized word sets but paraprofessionals also implemented all phases with high fidelity. We discuss limitations, implications for practice, and recommendations for future research.

Reconstruction of self-oscillating systems with delay time modulation

The aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. The possibility of estimating the parameters of systems with delay time modulation from their time series is considered using the known method for reconstructing systems with constant delay time, which is based on statistical analysis of time intervals between all possible pairs of extrema in time series. A new method for estimating the parameters of systems with variable delay time is proposed, based on statistical analysis of time intervals between two successive extrema in time series. Results. It is shown that in some cases the known methods for reconstructing systems with constant delay time are also effective for reconstructing systems with varying delay time. With their help, one can estimate the mean delay time and recove the nonlinear function of the system. The proposed method, aimed at application to time-delay systems with delay time modulation, allows one to estimate the frequency and amplitude of delay time modulation. Conclusion. The obtained results are of interest to various scientific disciplines that study systems with variable delay times based on their time series.

RESEARCH AND DEVELOPMENT OF THE DRYING TECHNOLOGY

Static and dynamic characteristics of the drying process as an object of automation are experimentally determined in the work. It was established that the drying object can be represented as two linked "air" – "drying object" and has interconnected input and output parameters. A mathematical description of the static and dynamic characteristics of the drying process as an object of automatic regulation has been researched and carried out. With the help of mathematical processing of experimental data, mathematical dependences on the studied regulation channels were obtained as the transfer functions, differential equations, and acceleration curve equations. The obtained experimental time characteristics of the drying object on different control channels are approximated with an error of less than 3% by differential equations of the 1st order with a delay. The object is characterized by variable constant time and delay time values for different drying phases.

Apparent simplicity and emergent robustness in the control of the Escherichia coli cell cycle

To examine how bacteria achieve robust cell proliferation across diverse conditions, we developed a method that quantifies 77 cell morphological, cell cycle, and growth phenotypes of a fluorescently labeled Escherichia coli strain and >800 gene deletion derivatives under multiple nutrient conditions. This approach revealed extensive phenotypic plasticity and deviating mutant phenotypes were often nutrient dependent. From this broad phenotypic landscape emerged simple and robust unifying rules (laws) that connect DNA replication initiation, nucleoid segregation, FtsZ ring formation, and cell constriction to specific aspects of cell size (volume, length, or added length) at the population level. Furthermore, completion of cell division followed the initiation of cell constriction after a constant time delay across strains and nutrient conditions, identifying cell constriction as a key control point for cell size determination. Our work provides a population-level description of the governing principles by which E.coli integrates cell cycle processes and growth rate with cell size to achieve its robust proliferative capability. A record of this paper's transparent peer review process is included in the supplemental information.