Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays

H∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback control

This paper investigates the H∞ master-slave synchronization problem for delayed impulsive implicit hybrid neural networks based on memory-state feedback control. By developing a more holistic stochastic impulse-time-dependent Lyapunov-Krasovskii functional and dealing with the nonlinear neuron activation function, the stochastic admissibility and prescribed H∞ performance index for the synchronization error closed-loop system are achieved. In addition, the desired mode-dependent memory-state feedback synchronization controller is acquired in the form of linear matrix inequalities. The free-weighting matrix technique is adopted to remove the inherent limitation of time-varying delay derivative for the implicit delayed systems, and the derivative of time-varying delay is relaxed enough to be greater than 1. The simulation of genetic regulatory network in bio-economic system is given to verify validity of the derived results.

Asynchronous dissipative stabilization for stochastic Markov-switching neural networks with completely- and incompletely-known transition rates

The asynchronous dissipative stabilization for stochastic Markov-switching neural networks (SMSNNs) is investigated. The aim is to design an output-feedback controller with inconsistent mode switching to ensure that the SMSNN is stochastically stable with extended dissipativity. Two situations, which involve completely- and incompletely-known transition rates (TRs), are taken into account. The situation that all TRs are exactly known is considered first. By applying a mode-dependent Lyapunov-Krasovskii functional, Dynkin's formula, and several matrix inequalities, a criterion for the desired performance of the closed-loop SMSNN is derived and a design method for determining the asynchronous controller is developed. Then, the study is generalized to the situation where some TRs are allowed to be uncertain or even fully unknown. An inequality is established for judging the upper bound of the product of the TRs with the Lyapunov matrix by making full use of accessible information on the incompletely-known TRs. Based on the inequality, performance analysis and control synthesis are presented without imposing the zero-sum hypothesis of the uncertainties in the TR matrix. Finally, an example with numerical calculation and simulation is provided to verify the validity of the stabilizing approaches.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme

This paper investigates the asymptotic synchronization of memristive Cohen-Grossberg neural networks (MCGNNs) with time-varying delays under event-triggered control (ETC). First, based on the designed feedback controller, some ETC conditions are provided. It is demonstrated that ETC can significantly reduce the update times of the controller and decrease the computing cost. Next, some sufficient conditions are derived to ensure the asymptotic synchronization of MCGNNs with time-varying delays under the ETC method. Finally, a numerical example is provided to verify the correctness and effectiveness of the obtained results.

Reachable Set Estimation for Markovian Jump Neutral-Type Neural Networks With Time-Varying Delays

The reachable set estimation problem for a class of Markovian jump neutral-type neural networks (MJNTNNs) with bounded disturbances and time-varying delays is tackled in this article. With the aid of the delay partitioning method, a novel stochastic Lyapunov-Krasovskii functional containing triple integral terms is constructed in mode-dependent augmented form. To begin with, transition probabilities of the concerned Markovian jump neural networks (NNs) are considered to be completely known. By employing the integral inequality approach and reciprocally convex combination method, it is proved that all state trajectories which start from the origin by bounded inputs can be constrained by an ellipsoid-like set if a group of linear matrix inequalities (LMIs) is feasible. Then, the free-connection weighting matrix technique is utilized to handle the case of partially known transition probabilities. As byproducts, some sufficient conditions are also obtained to guarantee the stochastic stability of the concerned NNs. The validity of the theoretical analysis is confirmed by numerical simulations.

Exponential passivity of discrete-time switched neural networks with transmission delays via an event-triggered sliding mode control

This paper investigates the exponential passivity of discrete-time switched neural networks (DSNNs) with transmission delays via an event-triggered sliding mode control (SMC). Firstly, a novel discrete-time switched SMC scheme is constructed on the basis of sliding mode control method and event-triggered mechanism. Next, a state observer with transmission delays is designed to estimate the system state. Moreover, some new weighted summation inequalities are further proposed to effectively evaluate the exponential passivity criteria for the closed-loop system. Finally, the effectiveness of theoretical results is showed through a simulative analysis on a multi-area power system.

H∞ synchronization of delayed neural networks via event-triggered dynamic output control

This paper investigates H_∞ exponential synchronization (ES) of neural networks (NNs) with delay by designing an event-triggered dynamic output feedback controller (ETDOFC). The ETDOFC is flexible in practice since it is applicable to both full order and reduced order dynamic output techniques. Moreover, the event generator reduces the computational burden for the zero-order-hold (ZOH) operator and does not induce sampling delay as many existing event generators do. To obtain less conservative results, the delay-partitioning method is utilized in the Lyapunov-Krasovskii functional (LKF). Synchronization criteria formulated by linear matrix inequalities (LMIs) are established. A simple algorithm is provided to design the control gains of the ETDOFC, which overcomes the difficulty induced by different dimensions of the system parameters. One numerical example is provided to demonstrate the merits of the theoretical analysis.

Saturated impulsive control for synchronization of coupled delayed neural networks

The paper focuses on the synchronization problem for a class of coupled neural networks with impulsive control, where the saturation structure of impulse action is fully considered. The coupled neural networks under consideration are subject to mixed delays including transmission delay and coupled delay. The sector condition in virtue of a new constraint of set inclusion is given for a addressed network, based on which a sufficient condition for exponential synchronization problem is obtained by replacing saturation nonlinearity with a dead-zone function. In the framework of saturated impulses, our results relying on the domain of attraction can still achieve the synchronization of coupled delayed neural networks. In addition, the estimating domain of attraction is proposed as large as possible by solving an optimization problem. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed results.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters

This paper deals with the anti-synchronization issue for stochastic delayed reaction-diffusion neural networks subject to semi-Markov jump parameters. A resilient fault-tolerant controller is utilized to ensure the anti-synchronization in the presence of actuator failures as well as gain perturbations, simultaneously. Firstly, by means of the Lyapunov functional and stochastic analysis methods, a mean-square exponential stability criterion is derived for the resulting error system. It is shown the obtained criterion improves a previously reported result. Then, based on the present analysis result and using several decoupling techniques, a strategy for designing the desired resilient fault-tolerant controller is proposed. At last, two numerical examples are given to illustrate the superiority of the present stability analysis method and the applicability of the proposed resilient fault-tolerant anti-synchronization control strategy, respectively.

Finite-time nonfragile time-varying proportional retarded synchronization for Markovian Inertial Memristive NNs with reaction-diffusion items

The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction-diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported.

Synchronization of Nonlinearly and Stochastically Coupled Markovian Switching Networks via Event-Triggered Sampling

This paper studies the exponential synchronization problem for a new array of nonlinearly and stochastically coupled networks via events-triggered sampling (ETS) by self-adaptive learning. The networks include the following features: 1) a Bernoulli stochastic variable is introduced to describe the random structural coupling; 2) a stochastic variable with positive mean is used to model the coupling strength; and 3) a continuous time homogeneous Markov chain is employed to characterize the dynamical switching of the coupling structure and pinned node sets. The proposed network model is capable to capture various stochastic effect of an external environment during the network operations. In order to reduce networks' workload, different ETS strategies for network self-adaptive learning are proposed under continuous and discrete monitoring, respectively. Based on these ETS approaches, several sufficient conditions for synchronization are derived by employing stochastic Lyapunov-Krasovskii functions, the properties of stochastic processes, and some linear matrix inequalities. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results and the superiority of the proposed ETS approach.

Protocol-based state estimation for delayed Markovian jumping neural networks

This paper is concerned with the state estimation problem for a class of Markovian jumping neural networks (MJNNs) with sensor nonlinearities, mode-dependent time delays and stochastic disturbances subject to the Round-Robin (RR) scheduling mechanism. The system parameters experience switches among finite modes according to a Markov chain. As an equal allocation scheme, the RR communication protocol is introduced for efficient usage of limited bandwidth and energy saving. The update matrix method is adopted to deal with the periodic time-delays resulting from the RR protocol. The objective of the addressed problem is to construct a state estimator for the MJNNs such that the dynamics of the estimation error is exponentially ultimately bounded in the mean square with a certain upper bound. Sufficient conditions are established for the existence of the desired state estimator by resorting to a combination of the Lyapunov stability theory and the stochastic analysis technique. Furthermore, the estimator gain matrices are characterized in terms of the solution to a convex optimization problem. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design strategy.

Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: An event-triggered communication scheme

This study examines the problem of robust reliable control for Takagi-Sugeno (T-S) fuzzy Markovian jumping delayed neural networks with probabilistic actuator faults and leakage terms. An event-triggered communication scheme. First, the randomly occurring actuator faults and their failures rates are governed by two sets of unrelated random variables satisfying certain probabilistic failures of every actuator, new type of distribution based event triggered fault model is proposed, which utilize the effect of transmission delay. Second, Takagi-Sugeno (T-S) fuzzy model is adopted for the neural networks and the randomness of actuators failures is modeled in a Markov jump model framework. Third, to guarantee the considered closed-loop system is exponential mean square stable with a prescribed reliable control performance, a Markov jump event-triggered scheme is designed in this paper, which is the main purpose of our study. Fourth, by constructing appropriate Lyapunov-Krasovskii functional, employing Newton-Leibniz formulation and integral inequalities, several delay-dependent criteria for the solvability of the addressed problem are derived. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones, among them one example was supported by real-life application of the benchmark problem.

Event-triggered H∞ filtering for delayed neural networks via sampled-data

This paper is concerned with event-triggered H_∞ filtering for delayed neural networks via sampled data. A novel event-triggered scheme is proposed, which can lead to a significant reduction of the information communication burden in the network; the feature of this scheme is that whether or not the sampled data should be transmitted is determined by the current sampled data and the error between the current sampled data and the latest transmitted data. By constructing a proper Lyapunov-Krasovskii functional, utilizing the reciprocally convex combination technique and Jensen's inequality sufficient conditions are derived to ensure that the resultant filtering error system is asymptotically stable. Based on the derived H_∞ performance analysis results, the H_∞ filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, the proposed stability conditions are demonstrated with numerical example.