Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

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

The problem of passivity analysis is investigated 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 belongs to a given interval,which means that the lower and upper bounds of interval time-varying delays are available.By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique,new delay-dependent passivity conditions are derived in terms of linear matrix inequalities（LMIs）.Finally,numerical examples are given to show the less conservatism of the proposed conditions.

Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays

This paper deals with H∞ state estimation problem of neural networks with discrete and distributed time-varying delays. A novel delay-dependent concept of H∞ state estimation is proposed to estimate the H∞ performance and global asymptotic stability of the concerned neural networks. By constructing the Lyapunov-Krasovskii functional and using the linear matrix inequality technique, sufficient conditions for delay-dependent H∞ performances are obtained, which can be easily solved by some standard numerical algorithms. Finally, numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

Adaptive NN stabilization for stochastic systems with discrete and distributed time-varying delays

A new adaptive neural network（NN） output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.

DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS

In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.

Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays

Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks （RNNs） with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.

Global stability of Cohen-Grossberg neural networks with time-varying and distributed delays

In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descriptor form of the considered system, several delay-dependent sufficient conditions are obtained to guarantee the asymptotic stability of the addressed systems. These conditions are dependent on both time-varying and distributed delays and presented in terms of LMIs and therefore, the stability criteria of such systems can be checked readily by resorting to the Matlab LMI toolbox. Finally, an example is given to show the effectiveness and less conservatism of the proposed methods.

Delay-dependent Robust Stabilization and H_∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno （T-S） fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities （LMIs） and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.

Distributed Synchronization of Stochastic Complex Networks with Time-Varying Delays via Randomly Occurring Control

This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed adaptive controller and the update of the control gain designed in this paper all happen randomly. Based on the Lyapunov stability theory, LaSalle invariance principle, combined with the use of the properties of the matrix Kronecker product, stochastic differential equation theory and other related tools, by constructing the appropriate Lyapunov functional, the criterion for the distributed synchronization of this type of stochastic complex networks in mean square is obtained.

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

Event-Triggered Zero-Gradient-Sum Distributed Algorithm for Convex Optimization with Time-Varying Communication Delays and Switching Directed Topologies

Nowadays, distributed optimization algorithms are widely used in various complex networks. In order to expand the theory of distributed optimization algorithms in the direction of directed graph, the distributed convex optimization problem with time-varying delays and switching topologies in the case of directed graph topology is studied. The event-triggered communication mechanism is adopted, that is, the communication between agents is determined by the trigger conditions, and the information exchange is carried out only when the conditions are met. Compared with continuous communication, this greatly saves network resources and reduces communication cost. Using Lyapunov-Krasovskii function method and inequality analysis, a new sufficient condition is proposed to ensure that the agent state finally reaches the optimal state. The upper bound of the maximum allowable delay is given. In addition, Zeno behavior will be proved not to exist during the operation of the algorithm. Finally, a simulation example is given to illustrate the correctness of the results in this paper.

Exponential stability criteria on neural networks with continuously distributed delays

The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.

Position Measurement Based Slave Torque Feedback Control for Teleoperation Systems With Time-Varying Communication Delays

Bilateral teleoperation system is referred to as a promising technology to extend human actions and intelligence to manipulating objects remotely.For the tracking control of teleoperation systems,velocity measurements are necessary to provide feedback information.However,due to hardware technology and cost constraints,the velocity measurements are not always available.In addition,the time-varying communication delay makes it challenging to achieve tracking task.This paper provides a solution to the issue of real-time tracking for teleoperation systems,subjected to unavailable velocity signals and time-varying communication delays.In order to estimate the velocity information,immersion and invariance(I&I)technique is employed to develop an exponential stability velocity observer.For the proposed velocity observer,a linear relationship between position and observation state is constructed,through which the need of solving partial differential and certain integral equations can be avoided.Meanwhile,the mean value theorem is exploited to separate the observation error terms,and hence,all functions in our observer can be analytically expressed.With the estimated velocity information,a slave-torque feedback control law is presented.A novel Lyapunov-Krasovskii functional is constructed to establish asymptotic tracking conditions.In particular,the relationship between the controller design parameters and the allowable maximum delay values is provided.Finally,simulation and experimental results reveal that the proposed velocity observer and controller can guarantee that the observation errors and tracking error converge to zero.

Neural Dynamics for Distributed Collaborative Control of Manipulators With Time Delays

Time-delay phenomena extensively exist in practical systems,e.g.,multi-agent systems,bringing negative impacts on their stabilities.This work analyzes a collaborative control problem of redundant manipulators with time delays and proposes a time-delayed and distributed neural dynamics scheme.Under assumptions that the network topology is fixed and connected and the existing maximal time delay is no more than a threshold value,it is proved that all manipulators in the distributed network are able to reach a desired motion.The proposed distributed scheme with time delays considered is converted into a time-variant optimization problem,and a neural dynamics solver is designed to solve it online.Then,the proposed neural dynamics solver is proved to be stable,convergent and robust.Additionally,the allowable threshold value of time delay that ensures the proposed scheme’s stability is calculated.Illustrative examples and comparisons are provided to intuitively prove the validity of the proposed neural dynamics scheme and solver.

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

Stability analysis of Markovian jumping stochastic Cohen Grossberg neural networks with discrete and distributed time varying delays

In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays （MJSCGNNs） is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.

ADMM-based Distributed Algorithm for Economic Dispatch in Power Systems With Both Packet Drops and Communication Delays

By virtue of alternating direction method of multipliers(ADMM), Newton-Raphson method, ratio consensus approach and running sum method, two distributed iterative strategies are presented in this paper to address the economic dispatch problem(EDP) in power systems. Different from most of the existing distributed ED approaches which neglect the effects of packet drops or/and time delays, this paper takes into account both packet drops and time delays which frequently occur in communication networks. Moreover, directed and possibly unbalanced graphs are considered in our algorithms, over which many distributed approaches fail to converge. Furthermore, the proposed schemes can address the EDP with local constraints of generators and nonquadratic convex cost functions, not just quadratic ones required in some existing ED approaches. Both theoretical analyses and simulation studies are provided to demonstrate the effectiveness of the proposed schemes.

Delay-dependent stability of linear multistep methods for differential systems with distributed delays

This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.

GLOBAL STABILITY IN HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED TIME DELAYS

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.