State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.     

State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates

This Letter is concerned with the robust state estimation problem for uncertain time-delay Markovian jumping genetic regulatory networks (GRNs) with SUM logic, where the uncertainties enter into both the network parameters and the mode transition rate. The nonlinear functions describing the feedback regulation are assumed to satisfy the sector-like conditions. The main purpose of the problem addressed is to design a linear estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. By resorting to the Lyapunov functional method and some stochastic analysis tools, it is shown that if a set of linear matrix inequalities (LMIs) is feasible, the desired state estimator, that can ensure the estimation error dynamics to be globally robustly asymptotically stable in the mean square, exists. The obtained LMI conditions are dependent on both the lower and the upper bounds of the delays. An illustrative example is presented to demonstrate the feasibility of the proposed estimation schemes.     

Exponential synchronization of complex networks with Markovian jump and mixed delays

In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.     

Robust H∞state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks

We investigate the dynamic event-triggered state estimation for uncertain complex networks with hybrid delays suffering from both deception attacks and denial-of-service attacks.Firstly,the effects of time-varying delays and finitedistributed delays are considered during data transmission between nodes.Secondly,a dynamic event-triggered scheme(ETS)is introduced to reduce the frequency of data transmission between sensors and estimators.Thirdly,by considering the discussed plant,dynamic ETS,state estimator,and hybrid attacks into a unified framework,this framework is transferred into a novel dynamical model.Furthermore,with the help of Lyapunov stability theory and linear matrix inequality techniques,sufficient condition to ensure that the system is exponentially stable and satisfies H∞performance constraints is obtained,and the design algorithm for estimator gains is given.Finally,two numerical examples verify the effectiveness of the proposed method.     

State estimation for neural neutral-type networks with mixed time-varying delays and Markovian jumping parameters

This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed timevarying delays and Markovian jumping parameters.The addressed neural networks have a finite number of modes,and the modes may jump from one to another according to a Markov process.By construction of a suitable Lyapunov-Krasovskii functional,a delay-dependent condition is developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable in a mean square.The criterion is formulated in terms of a set of linear matrix inequalities(LMIs),which can be checked efficiently by use of some standard numerical packages.     

Optimal Estimation of Qubit States with Continuous Time Measurements

We propose an adaptive, two step strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given n identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size n ^−1/2 of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions. We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits. The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large n, the statistical model described by n identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator. The term ‘local’ refers to a shrinking neighborhood around a fixed state ρ ₀. An essential result is that the neighborhood radius can be chosen arbitrarily close to n ^−1/4. This allows us to use a two step procedure by which we first localize the state within a smaller neighborhood of radius n ^−1/2+ϵ, and then use LAN to perform optimal estimation.     

Synchronization control of stochastic delayed neural networks

In this paper, synchronization control of stochastic neural networks with time-varying delays has been considered. A novel control method is given using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several sufficient conditions have been derived to ensure the global asymptotical stability in mean square for the error system, and thus the drive system synchronize with the response system. Also, the estimation gains can be obtained. With these new and effective methods, synchronization can be achieved. Simulation results are given to verify the theoretical analysis in this paper.     

Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.     

Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This Letter is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI) and by introducing some free-weighting matrices. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Consensus in noisy environments with switching topology and time-varying delays

In this paper, the leader-following consensus problem of noise perturbed multi-agent systems with time-varying delays is investigated. We analyze two different cases of coupling topologies: fixed topology and switching topology. Based on the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, it is analytically proved that the consensus could be achieved almost surely with the perturbation of noise and communication time delays. Furthermore, numerical examples are provided to illustrate the effectiveness of the theoretical results. The simulation results show that the speed of convergence in environments with relatively strong noise intensity is lower than that in environments with relatively weak noise intensity.     

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs). Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov–Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.     

Event-based state estimation for a class of complex networks with time-varying delays: A comparison principle approach

The paper is concerned with the state estimation problem for a class of time-delayed complex networks with event-triggering communication protocol. A novel event generator function, which is dependent not only on the measurement output but also on a predefined positive constant, is proposed with hope to reduce the communication burden. A new concept of exponentially ultimate boundedness is provided to quantify the estimation performance. By means of the comparison principle, some sufficient conditions are obtained to guarantee that the estimation error is exponentially ultimately bounded, and then the estimator gains are obtained in terms of the solution of certain matrix inequalities. Furthermore, a rigorous proof is proposed to show that the designed triggering condition is free of the Zeno behavior. Finally, a numerical example is given to illustrate the effectiveness of the proposed event-based estimator.     

Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes

This paper deals with the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delays and time-varying delays in the dynamical nodes.We control a part of the nodes of the complex networks by using adaptive feedback controllers and adjusting the time-varying coupling strengths.Based on the Lyapunov-Krasovskii stability theory for functional differential equations and a linear matrix inequality(LMI),some sufficient conditions for the synchronization are derived.A numerical simulation example is also provided to verify the correctness and the effectiveness of the proposed scheme.     

Receiver structure and estimation of the modulation index for tamed frequency modulated (TFM) signals

Tamed frequency modulation (TFM) is a spectrally efficient constant amplitude continuous phase modulation (CPM) scheme which can be simply realized by using a frequency modulator (FM). In the implementation the modulation index of TFM is calibrated to have a nominal value of 0.5, but due to temperature variations it can drift causing time varying phase jitter. In this paper we present novel algorithms and performance results to measure and control the modulation index in a coherent receiver based on the joint reduced state sequence detector (RSSD) and per-survivor processing (PSP) carrier phase estimation. The modulation index estimator measures phase transitions in the receiver and derives estimates by comparing the result to the coding rule of the TFM signal. The estimator has acquisition and tracking ability, and the current estimate can be used to replace the nominal index value. Our simulation results show that the proposed coherent receiver with the novel modulation index estimator has less than 1 dB performance degradation compared to around 4.5 dB exploiting only the PSP carrier phase estimation.     

Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease.     

Exponentially convergent state estimation for delayed switched recurrent neural networks

This paper deals with the delay-dependent exponentially convergent state estimation problem for delayed switched neural networks. A set of delay-dependent criteria is derived under which the resulting estimation error system is exponentially stable. It is shown that the gain matrix of the proposed state estimator is characterised in terms of the solution to a set of linear matrix inequalities (LMIs), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.     

Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays

In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.