Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

THE METHOD OF SEPARATING HARMONIC SIGNALS FROM MULTIPLICATIVE AND ADDITIVE NOISES

This paper focuses on the extraction of a harmonic signal from multiplicative and additive noises. A method is proposed in two stages： （1） to square the original discrete time series, which includes both signals and noises, and form a new time series. By this means, the multiplicative noise is converted to additive noise; and （2） to filter out the noise by using existing noise removal schemes. With a large amount of simulation, experimental results demonstrated the efficiency and effectiveness of this newly developed method in terms of Signal-to-Noise Ratio （SNR） and other criteria. Prom the experiment, it is also found that： the two kinds of noises affect the SNR differently. In general, the SNR is not influenced by multiplicative Gaussian noise regardless of its variance. However, if both kinds of noise exist, the SNR decreases with the incensement of the Variance of Additive Noise to Multiplicative Noise Ratio （VAMNR）. This analysis is also supported by simulation work.

Wavelet-Based Density Estimation in Presence of Additive Noise under Various Dependence Structures

We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the β-mixing case and the ρ-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be -consistent and fast rates of convergence have been established.

MAXIMUM LIKELIHOOD SOURCE SEPARATION FOR FINITE IMPULSE RESPONSE MULTIPLE INPUT-MULTIPLE OUTPUT CHANNELS IN THE PRESENCE OF ADDITIVE NOISE

Blind identification-blind equalization for Finite Impulse Response (FIR) Multiple Input-Multiple Output (MIMO) channels can be reformulated as the problem of blind sources separation. It has been shown that blind identification via decorrelating sub-channels method could recover the input sources. The Blind Identification via Decorrelating Sub-channels(BIDS)algorithm first constructs a set of decorrelators, which decorrelate the output signals of subchannels, and then estimates the channel matrix using the transfer functions of the decorrelators and finally recovers the input signal using the estimated channel matrix. In this paper, a new approximation of the input source for FIR-MIMO channels based on the maximum likelihood source separation method is proposed. The proposed method outperforms BIDS in the presence of additive white Gaussian noise.

Adaptive Bistable Stochastic Resonance Based Weak Signal Reception in Additive Laplacian Noise

Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.

The frequency estimation of harmonic signals embedded in multiplicative and additive noise

A method to separate a harmonic signal from multiplicative and additive noises is proposed. The method is to square the signal x(t), which consists of a harmonic signal embedded in multiplicative and additive noises, to form another signal y(t) = x2(t)-E[x2(t)]. After y(t) having been gotten, the Fourier transform is imposed on it. Because the information of x(t) (especially about frequency) is included in y(t), the frequency of x(t) can be estimated from the power spectrum of y(t). According to the simulation, under the condition where frequencies divided by resolution dω are integer, the maximum relative error of estimated frequencies is less than 0.4% when the signal-to-noise ratio (SNR) is greater than -23 dB. If frequencies divided by resolution dω are not integer, the maximum relative error will be less than 2.9%. But it is still small in terms of engineering.

Exact Consensus Error for Multi-agent Systems with Additive Noises

In this paper,the consensus problem is investigated for discrete-time multi-agent systems with additive process noises.Due to the presence of additive noises in the system dynamics,consensus cannot be achieved.The main contribution of this paper is to give the exact consensus error.In particular,control gain depending on the agent dynamics and network topology is designed based on the technique dealing with the simultaneous stabilization.Finally,a numerical simulation is provided to demonstrate the effectiveness of the proposed theoretical results.

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance （SR） is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR： the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio （SNR） is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.

Passive localization of 3-D near-field sources in coexisted multiplicative noise and additive noise

By exploiting thvorable characteristics of a uniIbrm cross-array, a passive localization algorithm of narrowband sources in the spherical coordinates （azimuth, elevation and range） is proposed. Based on the properly chosen sensor outputs, we compute the third-order cyclic moment matrices, and exploit a pre-calibration technique to eliminate multiplicative noise. Then, we construct a parallel factor （PARAFAC） model, and adopt trilinear altemating least squares regression （TALS） to estimate three-dimensional （3-D） near-field parameters. The investigated algorithm is efficient in the sense that it can eliminate multiplicative noise and additive noise, provide the improved estimation accuracy, as well as avoid the parameter-pairing procedure. Simulation results are carried out to demonstrate the performance of the proposed algorithm.

Robust Frequency Estimation Under Additive Mixture Noise

In many applications such as multiuser radar communications and astrophysical imaging processing,the encountered noise is usually described by the finite sum ofα-stable(1≤α<2)variables.In this paper,a new parameter estimator is developed,in the presence of this new heavy-tailed noise.Since the closed-formPDF of theα-stable variable does not exist exceptα=1 andα=2,we take the sum of the Cauchy(α=1)and Gaussian(α=2)noise as an example,namely,additive Cauchy-Gaussian(ACG)noise.The probability density function(PDF)of the mixed random variable,can be calculated by the convolution of the Cauchy’s PDF and Gaussian’s PDF.Because of the complicated integral in the PDF expression of the ACG noise,traditional estimators,e.g.,maximum likelihood,are analytically not tractable.To obtain the optimal estimates,a new robust frequency estimator is devised by employing the Metropolis-Hastings(M-H)algorithm.Meanwhile,to guarantee the fast convergence of the M-H chain,a new proposal covariance criterion is also devised,where the batch of previous samples are utilized to iteratively update the proposal covariance in each sampling process.Computer simulations are carried out to indicate the superiority of the developed scheme,when compared with several conventional estimators and the Cramér-Rao lower bound.

GEKF,GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.

AN EFFICIENT FINITE DIFFERENCE METHOD FOR STOCHASTIC LINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS DRIVEN BY ADDITIVE WHITE NOISES

In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.

The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

Coherence resonance in a noise-driven gene network regulated by small RNA

Small RNA has recently drawn more and more attention. In this paper, we concentrate on the influence of noises on gene network regulated by small RNA using chemical Langevin equation. It shows that the noise can cause oscillation when the oscillate does not occur in the corresponding deterministic system. The coherence of the noise induced oscillation reaches a maximum for an optimal intensity of noise, and the coherence resonance appears accordingly. The findings imply probably omnipresent importance of noise in the functioning process of living organism.

Recovery of Transient Signals in Noise by OptimalThresholding in Wavelet Domain

：研究用离散子波变换复原被加性高斯白噪声污染的瞬态信号．在子波域中提出了一种最佳门限方法，该方法涉及到对于波系数的假设检验，利用似然比、奈曼，皮尔逊准则和最小均方差设计该门限，计算机仿真证明，该方法在较低信噪比下复原信号的有效性．

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance （SR） in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio （SNR） is calculated according to the generalized two-state theory （shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 （1999） 136]）. We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR.

Global Synchronization of Stochastically Disturbed Memristive Neurodynamics via Discontinuous Control Laws

This paper presents the theoretical results on the master-slave (or driving-response) synchronization of two memristive neural networks in the presence of additive noise. First, a control law with a linear time-delay feedback term and a discontinuous feedback term is introduced. By utilizing the stability theory of stochastic differential equations, sufficient conditions are derived for ascertaining global synchronization in mean square using this control law. Second, an adaptive control law consisting of a linear feedback term and a discontinuous feedback term is designed to achieve global synchronization in mean square, and it does not need prior information of network parameters or random disturbances. Finally, simulation results are presented to substantiate the theoretical results. © 2014 Chinese Association of Automation.

Construction of Regular Rate-Compatible LDPC Convolutional Codes

In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.

Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise

To model wave propagation in inhomogeneous media with frequency dependent power-law attenuation,it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time.The model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative Gaussian noise and additive fractional Gaussian noise,because of the potential fluctuations of the external sources.The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation.First,the space-time multiplicative Gaussian noise and additive fractional Gaussian noise are discretized,which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense.We further present a complete regularity theory for the regularized equation.A standard finite element approximation is used for the spatial operator,and a mean-square priori estimates for the modeling error and the approximation error to the solution of the regularized problem are established.Finally,numerical experiments are performed to confirm the theoretical analysis.

SYMMETRIC INFORMATION RATE OF CPM AND OPTIMAL DETECTOR DESIGN

This paper first calculates numerically the Symmetric Information Rate (SIR) of Cotinuous Phase Modulation (CPM) schemes over Additive White Gaussian Noise (AWGN) channel, modeling CPM and channel as a Memory-less Modulator (MM) plus a Markov Finite State Channel (FSMC), then proposes an optimal detector, which is of BCJR based Decision Feedback Detector (DFD) but non-iterative. It can achieve the SIR as the sequence length approaches infinity while the complexity is extremely low. Finally, both theoretic proof and numerical simulation are performed to show the op- timality. Simulation results show that it nearly achieves the theoretic bound and outperforms the Viterbi Detector (VD) with 2dB in low Eb/N0.