Time Delay Information Research Articles

Exponential Stability of Mixed Time-Delay Neural Networks Based on Switching Approaches.

Neural networks (NNs) have been deeply studied due to their wide applicability. Since time delays are unavoidable in reality, it is basic and crucial for all applications based on NNs to guarantee system stability under the influence of mixed time delays. To better exploit the variation information of time delay, we introduce the switching idea and approaches into mixed time-delay NNs to solve the stability problem. First, the considered mixed time-delay NNs are modeled as the switched NNs by dividing the two classes of time delays, discrete and distributed time delays, into some variable intervals and combining these intervals as new switching modes. With the help of mode-dependent average dwell-time switching, Lyapunov theory, and mathematical techniques, several exponential stability criteria on the modeled switched systems containing different modes are obtained. Moreover, via introducing the mathematical condition of the unstable subsystem in the switching system, a less conservativeness condition on the exponential stability of the modeled NNs is proposed. We perform three examples for testifying the validity of the proposed methods over existing ones.

Dynamic output feedback control for nonlinear networked control systems with a two-terminal event-triggered mechanism

This paper is mainly concerned with the stabilization problem for nonlinear networked control systems (NCSs) with a two-terminal event-triggered mechanism. Firstly, Takagi–Sugeno (T–S) fuzzy models are introduced as the presentation of the nonlinear object. A two-terminal event-triggered mechanism, which adopts the relative event-triggered conditions as the communication mode of data transmission, is distributed in the controller-to-actuator link besides sensor-to-controller link in order to reduce congestion on network servers. By taking different membership function information from the T–S fuzzy model into account, the dynamic output feedback controller is designed under imperfect premise matching to construct closed-loop model. Secondly, to ensure the asymptotic stability of NCSs, valuable theorems are derived by defining Lyapunov functions which involve time-delay information. Thirdly, using boundary information of membership functions, LMI-based membership-function-dependent stability conditions are developed to reduce the conservativeness of the imperfect premise matching, from which the explicit form of controller gain matrices is obtained. Finally, one practical example illustrates the reliability of derived results.

Extended lens reconstructions with grale: exploiting time-domain, substructural, and weak lensing information

ABSTRACT The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to ‘overfocusing’ the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspired by previous reconstructions of the cluster of galaxies MACS J1149.6+2223, where a multiply imaged background galaxy contained a supernova, SN Refsdal, of which four additional images were produced by the presence of a smaller cluster galaxy. The inversion for the cluster as a whole was not able to recover sufficient detail interior to this quad. We show how constraints on such different scales, from the entire cluster to a single member galaxy, can now be used, allowing such small-scale substructures to be resolved. Finally, the addition of weak lensing information to this method is investigated. While this clearly helps recover the environment around the strong lensing region, the mass sheet degeneracy may make a full strong and weak inversion difficult, depending on the quality of the ellipticity information at hand. We encounter ring-like structure at the boundary of the two regimes, argued to be the result of combining strong and weak lensing constraints, possibly affected by degeneracies.

Direct Position Determination for Wideband Sources Using Fast Approximation

In this correspondence paper, we address the direct position determination (DPD) problem for wideband stationary sources using time-delayed and Doppler-stretched signals collected by multiple moving receivers. The source signals are assumed to be zero-mean, stationary, and Gaussian distributed, which is reasonable in most passive sonar and acoustics scenarios. A scaled formulation is used for wideband signals to elaborate the Doppler effect, as significant biases will be introduced if such signals are approximated with narrowband models directly. In this paper, wideband signals are decomposed into a small number of low-dimensional components with high accuracy, and a computationally efficient DPD method is proposed by jointly utilizing the time delay and scaling information of received signals. In order to evaluate the performance of the proposed DPD method, the Cramer Rao lower bound for source localization in the considered scenario is derived. Numerical results validate the approximation of wideband signals and demonstrate the performance of the proposed method.

Mixed-delay-dependent L2-L∞ Filtering for Neutral Stochastic Systems with Time-varying Delays

This paper studies the issue on mixed-delay-dependent $$\mathcal{L}_2-\mathcal{L}_\infty$$ filter design for a class of neutral stochastic system with time-varying delays. By making full use of the information and interrelationship of time-delays, an augmented Lyapunov-Krasovskii functional (LKF) is constructed for the filtering error system. In the derivation process, some Writinger-based integral inequalities and an extend reciprocal convex technique (ERCT) are utilized to estimate the lower bound of $$\mathcal{L}_2-\mathcal{L}_\infty$$ disturbance attention level. Based on the derived stability criteria, two sufficient conditions on the existence of full-order $$\mathcal{L}_2-\mathcal{L}_\infty$$ filter are presented in terms of linear matrix inequalities (LMIs), which can be easily tested and less conservative. Finally, two cases in an example are given to demonstrate the effectiveness of the proposed approach.

Enhanced [formula omitted]–[formula omitted] state estimation design for delayed neural networks including leakage term via quadratic-type generalized free-matrix-based integral inequality

The issue of L2–L∞ state estimation design for delayed neural networks (NNs) has been considered in this proposal under the leakage delay effects. By utilizing time-delay information sufficiently together with a suitable Lyapunov–Krasovskii functionals (LKFs), and estimating their derivative via quadratic generalized free-matrix-based integral inequality (QGFMBII) to access a stronger upper bound of the integral term. As a result, a new L2–L∞ state estimation criterion has been launched in term of linear matrix inequalities (LMIs), which includes both the time-varying delay function is differentiable and non-differentiable cases. It is amazing that the leakage delay has a disrupting effect on the state estimation performance of NNs and they cannot be avoided. At the end, this was demonstrated to facilitate the effectiveness and applicability of the designed state estimation technique using well-studied numerical examples together with a four-tank system model as a practical example in terms of the NN model. Also, the illustrative simulation results confirm that the developed state estimation technique performs well and is successful in this proposal where existing techniques fail.

Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays

In this paper, the robust stability problem for a class of uncertain stochastic complex-valued neural networks (USCVNNs) with additive time-varying delays (ATDs) is discussed. By constructing a suitable Lyapunov–Krasovskii functional (LKF), more time delay information is considered. By employing integral inequalities, some delay-dependent stability criteria are derived by converting USCVNNs into an equivalent real-valued uncertain stochastic neural networks. The obtained stability criterion is presented in the form of linear matrix inequalities (LMIs), which can be calculated through MATLAB LMI toolbox. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.

Exponential Consensus Analysis for Multiagent Networks Based on Time-Delay Impulsive Systems

In this paper, some consensus problems are considered for time-delay multiagent networks with directed topologies. Since agents are driven by not only long-term but instant contact with their neighbors, dynamic behaviors of agents can be described by impulsive differential equations. A period of non time-delay and time-delay information and instantaneous information are adopted in the proposed algorithms. Moreover, robust problems with the corresponding ${H_{\infty }}$ performance are investigated for multiagent networks with external disturbances. Sufficient conditions are obtained such that consensus can be exponentially reached for multiagent networks with/without external disturbances. Numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

State estimation for neural networks with two additive time-varying delay components using delay-product-type augmented Lyapunov–Krasovskii functionals

This paper focuses on the state estimation issue of neural networks with two additive time-varying delay components. By constructing a suitable augmented Lyapunov–Krasovskii functional, more time delay information is considered. Using the recently developed reciprocally convex inequality, some reciprocally convex combinations can be estimated more closely. The design conditions of state estimators are expressed as linear matrix inequalities (LMIs). The delay-product-type Lyapunov–Krasovskii functional is used to further reduce the conservativeness. With the help of state estimation method, the stability conditions of neural networks with two additive time-varying delay components are also developed. Finally, two numerical examples widely used in the literature show the effectiveness of the proposed method.

Distributed acoustic sensor based on improved minimum control recursive average algorithm

Abstract An optical fiber acoustic sensor based on the combination of generalized cross-correlation and improved minimum control recursive average algorithms is proposed. The sensing system consists of a double Sagnac interference structure that picks up acoustic signals along the sensing fiber. The improved minimum control recursive average algorithm is used to preprocess the acquired signal to improve the signal-to-noise ratio, then the time-delay information is obtained through the correlation operation on the processed signal, and the acoustic source is located through the time delay information. Experiments show that under the condition of high signal-to-noise ratio of the acquired signal, the accuracy of acoustic source localization can be improved.

New Results on Stability Analysis for Delayed Markovian Generalized Neural Networks With Partly Unknown Transition Rates.

The stability of delayed Markovian generalized neural networks is studied where the transition rates of the modes are partly unknown. The partly unknown transition rates generalize the traditional works that are with all known transition rates. Then, a Lyapunov-Krasovskii functional (LKF) with a delay-product-type (DPT) term is constructed. The DPT term is not only simple but also fully utilizes the information of time delay. Based on the new DPT LKF, stability criteria are presented, which are with lower computational complexity and less conservative. In the end, the validity and superiorities of the analytical results are verified by several examples.

Research on optical security based on simulated noise induced encryption scheme

The security of a noise-induced optical encryption scheme with two dimensional keys is examined by a series of statistical analysis. We introduce the cross correlation function (CCF) and mutual information (MI) approach to estimate the time-delay information, which is considered as the most important physical key in the secure strategy. Subsequently, the other key can be cracked by using the independent component analysis (ICA) method. Meanwhile, the plaintext can be extracted with a small deviation.

Experimental investigation on delay time phenomenon in rotating detonation engine

This study explored the phenomenon of the detonation formation delay time in an RDE with an annular combustion chamber with an array of holes fueled with hydrogen. It was determined that the delay time increased when the combustor prefilling time increased. Due to the explosion, the interaction of the shock wave and the pressure wave in the combustor leads to an increase in pressure near the inlet wall surface, thereby impeding the gas feeding. The wavelet transformation was used to analyze the pressure time signal associated with the detonation wave, which was found to be better than the fast Fourier transform typically used. Moreover, the phenomenon of single–double–single wave transformation was observed, of which the underlying mechanism can be explained by an interactive-adjusting process. Also, the experiment captured the reinitiation phenomenon of detonations after a long period of time (around 300 ms) of extinction.

H∞ Consensus Control for Heterogeneous Multi-Agent via Output under Markov Switching Topologies

The paper investigates H ∞ consensus problem of heterogeneous multi-agent systems including agents with first- and second-order integrators in the presence of disturbance and communication time delays under Markov switching topologies. Based on current messages, outdated information stored in memory and communication time delay information from neighbors, a more general kind of distributed consensus algorithm is proposed, which is faster consensus convergence. By applying stochastic stability analysis, model transformation techniques and graph theory, sufficient conditions of mean square consensus and H ∞ consensus are obtained, respectively. Finally, simulation examples are given to illustrate the effectiveness of obtained theoretical results.

Hybrid-delay-dependent approach to synchronization in distributed delay neutral neural networks

This paper is concerned with the master-slave synchronization in a class of neutral neural networks with both leakage and distributed delays. Firstly, based on state feedback controller, the closed-loop error system can be obtained. Then by fully utilizing the information and internal relationship of time-delays, three augmented Lyapunov–Krasovskii functionals (LKFs) are constructed, in which infinite distributed delay and finite one are respectively studied. Especially, some Wirtinger-based inequalities are exploited and an extended reciprocal combination technique (ERCT) is proposed, which can reconsider the previously ignored information. Sufficient conditions are formulated in terms of linear matrix inequalities (LMIs) and can be easily tested. Finally, three numerical examples are given to illustrate the designed schemes.

Efficient Synapse Memory Structure for Reconfigurable Digital Neuromorphic Hardware.

Spiking Neural Networks (SNNs) have high potential to process information efficiently with binary spikes and time delay information. Recently, dedicated SNN hardware accelerators with on-chip synapse memory array are gaining interest in overcoming the limitations of running software-based SNN in conventional Von Neumann machines. In this paper, we proposed an efficient synapse memory structure to reduce the amount of hardware resource usage while maintaining performance and network size. In the proposed design, synapse memory size can be reduced by applying presynaptic weight scaling. In addition, axonal/neuronal offsets are applied to implement multiple layers on a single memory array. Finally, a transposable memory addressing scheme is presented for faster operation of spike-timing-dependent plasticity (STDP) learning. We implemented a SNN ASIC chip based on the proposed scheme with 65 nm CMOS technology. Chip measurement results showed that the proposed design provided up to 200X speedup over CPU while consuming 53 mW at 100 MHz with the energy efficiency of 15.2 pJ/SOP.

A multi-term, multi-harmonic Boltzmann equation model for kinetic behavior in intense microwave and terahertz excited low temperature plasmas

A multi-term (MT), multi-harmonic (MH) decomposition of the Boltzmann equation (BE) is developed to describe electron kinetic behavior in microwave and THz excited low temperature plasmas. In the decomposition of the BE, velocity distribution functions retain an arbitrary time dependence enabling the prediction of electron kinetic behavior from an arbitrary initial condition to a steady-state periodic solution. By exploiting the time-periodic nature of the electron swarm, the MTMH-BE model is not restricted to numerically resolving the electric field cycle. The MTMH-BE model is validated via the Reid ramp model gas and the ionization model gas of Lucas and Salee. Following successful validation, the MTMH-BE model is utilized to elucidate the basic electron kinetic behavior in air at atmospheric pressure. Namely, the error associated with the effective field approximation (EFA) is explored, where it is demonstrated that for atmospheric pressure air, given a microwave frequency of 1 GHz, the EFA may result in more than a factor of two errors in the time-averaged ionization rate. In the second part of this study, the MTMH-BE model is demonstrated as a basic modeling tool for low temperature plasmas. First, the MTMH-BE model is utilized to calculate electron heating profiles from a cold initial condition. The MTMH-BE model is demonstrated to be in excellent agreement with strictly time-dependent kinetic models, including a time-dependent MT-BE model and a Monte Carlo collision model. To highlight the advantage of this work, the MTMH-BE model is used to predict the formative delay time of 95 GHz high power microwave induced breakdown. In this example, the numerical time step utilized in the MTMH-BE model is approximately six orders of magnitude larger than is possible using a strictly time-dependent MT-BE model. Overall, the MTMH-BE model presents a powerful pathway to modeling temporal kinetic behavior in microwave and THz excited low temperature plasmas.

Correlations among morphology, composition, and photoelectrochemical water splitting properties of InGaN nanorods grown by molecular beam epitaxy

The mechanism underlying the effect of growth condition on the morphology evolution of InGaN nanorods (NRs) has been systematically investigated. The increased Ga flux enhances both the axial and the radial growth at the growth stage. However, the changed Ga flux influences not only the growth but also the nucleation of InGaN NRs. At the nucleation stage, the increased Ga flux shortens the delay time for NR formation, and prolongs the growth stage for a fixed total growth time. Those two aspects result in the increase of NR diameter and height with the supplied Ga flux. In addition, the continuous nucleation is ended much earlier due to the accelerated saturation of substrate area with the increased Ga flux, resulting in a decreased final NR density. In addition to the morphology evolution with the Ga flux, the composition characteristic of InGaN NRs has been also studied. The In distribution of InGaN NRs depends critically on the NR diameter along the NR growth direction, and the NRs show a morphology-dependent In incorporation. Interestingly, the InGaN NRs discussed here show a radial Stark effect induced by the pinned Fermi level. The radial Stark effect shifts the absorption edge of the InGaN NRs toward longer wavelengths, makes the InGaN NRs attractive for photoelectrochemical water splitting applications. The photoelectrochemical measurements present a significant increase in the photocurrent with the increased total surface area of the InGaN NRs, which is due to the enhanced light absorption effects and the enlarged interfacial area of the semiconductor/electrolyte.

On the formation history of Galactic double neutron stars

Double neutron stars (DNSs) have been observed as Galactic radio pulsars, and the recent discovery of gravitational waves from the DNS merger GW170817 adds to the known DNS population. We perform rapid population synthesis of massive binary stars and discuss model predictions, including formation rates, mass distributions, and delay time distributions. We vary assumptions and parameters of physical processes such as mass transfer stability criteria, supernova kick distributions, remnant mass distributions and common-envelope energetics. We compute the likelihood of observing the orbital period-eccentricity distribution of the Galactic DNS population under each of our population synthesis models, allowing us to quantitatively compare the models. We find that mass transfer from a stripped post-helium-burning secondary (case BB) onto a neutron star is most likely dynamically stable. We also find that a natal kick distribution composed of both low (Maxwellian $\sigma=30\rm~km~s^{-1}$) and high ($\sigma=265\rm~km~s^{-1}$) components is preferred over a single high-kick component. We find that the observed DNS mass distribution can place strong constraints on model assumptions.

A New Approach to Stochastic Stability of Markovian Neural Networks With Generalized Transition Rates.

This paper investigates the stability problem of Markovian neural networks (MNNs) with time delay. First, to reflect more realistic behaviors, more generalized transition rates are considered for MNNs, where all transition rates of some jumping modes are completely unknown. Second, a new approach, namely time-delay-dependent-matrix (TDDM) approach, is proposed for the first time. The TDDM approach is associated with both time delay and its time derivative. Thus, the TDDM approach can fully capture the information of time delay and would play a key role in deriving less conservative results. Third, based on the TDDM approach and applying Wirtinger's inequality and improved reciprocally convex inequality, stability criteria are derived. In comparison with some existing results, our results are not only less conservative but also involve lower calculation complexity. Finally, numerical examples are provided to show the effectiveness and advantages of the proposed results.