Event-Triggered Exponential Synchronization of the Switched Neural Networks With Frequent Asynchronism

The synchronization for a class of switched uncertain neural networks (NNs) with frequent asynchronism based on event-triggered control is researched in this article. Compared with existing works that require one switching during an inter-event interval, frequent switching is allowed in this article. By employing controller-mode-dependent Lyapunov-Krasovskii functionals (LKFs), we devise the control strategy to guarantee that the switched NNs can be synchronized. The proposed LKFs can make full use of system information. Using an improved integral inequality, some sufficient stability conditions formed by linear matrix inequalities (LMIs) are derived for the synchronization of switched uncertain NNs. Average dwell time (ADT) is obtained in the form of inequality that includes the maximum inter-event interval. In addition, the existence of lower bound of inter-event interval is discussed to avoid Zeno behavior. At last, the feasibility of the proposed method is proven by a numerical example.

H∞ state estimation of continuous-time neural networks with uncertainties

[Formula: see text] state estimation is addressed for continuous-time neural networks in the paper. The norm-bounded uncertainties are considered in communication neural networks. For the considered neural networks with uncertainties, a reduced-order [Formula: see text] state estimator is designed, which makes that the error dynamics is exponentially stable and has weighted [Formula: see text] performance index by Lyapunov function method. Moreover, it is also given the devised method of the reduced-order [Formula: see text] state estimator. Then, considering that sampling the output y(t) of the neural network at every moment will result in waste of excess resources, the event-triggered sampling strategy is used to solve the oversampling problem. In addition, a devised method is also given for the event-triggered reduced-order [Formula: see text] state estimator. Finally, by the well-known Tunnel Diode Circuit example, it shows that a lower order state estimator can be designed under the premise of maintaining the same weighted [Formula: see text] performance index, and using the event-triggered sampling method can reduce the computational and time costs and save communication resources.

Delay-Dependent Switching Approaches for Stability Analysis of Two Additive Time-Varying Delay Neural Networks

This article analyzes the exponentially stable problem of neural networks (NNs) with two additive time-varying delay components. Disparate from the previous solutions on this similar model, switching ideas, that divide the time-varying delay intervals and treat the small intervals as switching signals, are introduced to transfer the studied problem into a switching problem. Besides, delay-dependent switching adjustment indicators are proposed to construct a novel set of augmented multiple Lyapunov-Krasovskii functionals (LKFs) that not only satisfy the switching condition but also make the suitable delay-dependent integral items be in the each corresponding LKF based on each switching mode. Combined with some switching techniques, some less conservativeness stability criteria with different numbers of switching modes are obtained. In the end, two simulation examples are performed to demonstrate the effectiveness and efficiency of the presented methods comparing other available ones.

Finite-Time H∞ Estimator Design for Switched Discrete-Time Delayed Neural Networks With Event-Triggered Strategy

This article is concerned with the event-triggered finite-time H_∞ estimator design for a class of discrete-time switched neural networks (SNNs) with mixed time delays and packet dropouts. To further reduce the data transmission, both the measured information of system outputs and switching signal of the SNNs are only allowed to be accessible for the constructed estimator at the certain triggering time instants. Under this consideration, the simultaneous presence of the switching and triggering actions also leads to the asynchronism between the indices of the SNNs and the designed estimator. Unlike the existing event-triggered strategies for the general switched linear systems, the proposed event-triggered mechanism not only allows the occurrence of multiple switches in one triggering interval but also removes the minimum dwell-time constraint on the switched signal. In light of the piecewise Lyapunov-Krasovskii functional theory, sufficient conditions are developed for the estimation error system to be stochastically finite-time bounded with a finite-time specified H_∞ performance. Finally, the effectiveness and applicability of the theoretical results are verified by a switched Hopfield neural network.

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.

Stability Analysis of Continuous-Time Switched Neural Networks With Time-Varying Delay Based on Admissible Edge-Dependent Average Dwell Time

This article investigates the stability of the switched neural networks (SNNs) with a time-varying delay. To effectively guarantee the stability of the considered system with unstable subsystems and reduce conservatism of the stability criteria, admissible edge-dependent average dwell time (AED-ADT) is first utilized to restrict switching signals for the continuous-time SNNs, and multiple Lyapunov-Kravosikii functionals (LKFs) combining relaxed integral inequalities are employed to develop two novel less-conservative stability conditions. Finally, the numeral examples clearly indicate that the proposed criteria can reduce conservatism and ensure the stability of continuous-time SNNs.

Anti-Synchronization of Delayed State-Based Switched Inertial Neural Networks

In this article, global anti-synchronization control for a class of state-based switched inertial neural networks (SBSINNs) with time-varying delays is considered. Based on the hybrid control strategies and Lyapunov stability theory, several criteria are obtained to ensure global anti-synchronization of the underlying SBSINNs. Furthermore, we consider the global asymptotic anti-synchronization directly from the SBSINNs themselves with a nonreduced-order method. Finally, a numerical simulation is given to illustrate the effectiveness of the results.

Sampled-Data-Based H∞ Synchronization of Switched Coupled Neural Networks

This paper investigates the sampled-data-based H_∞ synchronization problem for a class of switched coupled neural networks subject to exogenous perturbations. Different from the existing results on the nonswitched and continuous-time control cases, the unmatched phenomena between the switching of the system models and that of the controllers will occur, when the resulting error system switches within a sampling interval. In the framework of time-dependent switching mechanism, sufficient conditions for the existence of the sampled-data controllers are derived under the variable sampling and asynchronous switching. We prove that the proposed method not only renders the synchronization error system exponentially stable but also constrains the influence of the exogenous perturbations on the synchronization performance at a specified level. Finally, a switched coupled cellular neural network and a switched coupled Hopfield neural network are provided to illustrate the applicability and validity of the developed results.

Energy-to-Peak State Estimation for Switched Neutral-Type Neural Networks With Sector Condition via Sampled-Data Information

In this article, the energy-to-peak state estimation problem is investigated for a class of switched neutral neural networks subject to the external perturbations with bounded energy. Both the values of the measurement outputs and switching signal of the subsystems are only available for the controllers at the discrete sampling instants. Unlike the results for nonswitched neural networks, the coexistence of the switching and sampling actions directly causes the asynchronous phenomena between the indexes of subsystems and their corresponding controllers. To address this situation, the piecewise time-dependent Lyapunov-Krasovskii functional and slow switching mechanism are introduced. Under the developed theorem conditions, we prove that the designed state estimator exponentially tracks the true value of the neural state with the accessible sampled-data information. Also, the influence of the exogenous perturbations on the peak value of the estimation error is constrained at a prescribed level. Finally, a neutral cellular neural network with switching parameters is employed to substantiate the effectiveness and applicability of the theoretical results.

Finite-Horizon H∞ State Estimation for Stochastic Coupled Networks With Random Inner Couplings Using Round-Robin Protocol

This article is concerned with the problem of finite-horizon H_∞ state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors' measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon H_∞ state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.

Design of State-Dependent Switching Laws for Stability of Switched Stochastic Neural Networks With Time-Delays

We study the stability properties of switched stochastic neural networks (SSNNs) with time-varying delays whose subsystem is not necessarily stable. We introduce state-dependent switching (SDS) as a tool for stability analysis. Some SDS laws for asymptotic stability and p th moment exponentially stable are designed by employing Lyapunov-Krasovskii (L-K) functional and Lyapunov-Razumikhin (L-R) method, respectively. It is shown that the stability of SSNNs with time-varying delays composed of unstable subsystems can be achieved by using SDS law. The control gains in the designed SDS laws can be derived by solving the LMIs in derived stability criteria. Two numerical examples are provided to demonstrate the effectiveness of the proposed SDS laws.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Neural Network-Based Distributed Cooperative Learning Control for Multiagent Systems via Event-Triggered Communication

In this paper, an event-based distributed cooperative learning (DCL) law is proposed for a group of adaptive neural control systems. The plants to be controlled have identical structures, but reference signals for each plant are different. During control process, each agent intermittently broadcasts its neural network (NN) weight estimation to its neighboring agents under an event-triggered condition that is only based on its own estimated NN weights. If communication topology is connected and undirected, the NN weights of all neural control systems can converge to a small neighborhood of their optimal values. The generalization ability of NNs is guaranteed in the event-triggered context, that is, the approximation domain of each NN is the union of all system trajectories. Furthermore, a strictly positive lower bound on the interevent intervals is also guaranteed to avoid the Zeno behavior. Finally, a numerical example is given to illustrate the effectiveness of the proposed learning law.

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.

Sampled-Data Synchronization of Markovian Coupled Neural Networks With Mode Delays Based on Mode-Dependent LKF

This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method.This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method.

On Stabilization of Quantized Sampled-Data Neural-Network-Based Control Systems

This paper investigates the problem of stabilization of sampled-data neural-network-based systems with state quantization. Different with previous works, the communication limitation of state quantization is considered for the first time. More specifically, it is assumed that the sampled state measurements from sensor to the controller are quantized via a quantizer. To reduce conservativeness, a novel piecewise Lyapunov-Krasovskii functional (LKF) is constructed by introducing a line-integral type Lyapunov function and some useful terms that take full advantage of the available information about the actual sampling pattern. Based on the new LKF, much less conservative stabilization conditions are derived to obtain the maximal sampling period and the minimal guaranteed cost control performance. The desired quantized sampled-data three-layer fully connected feedforward neural-network-based controllers are designed by a linear matrix inequality approach. A search algorithm is given to find the optimal values of tuning parameters. The effectiveness and advantage of proposed method are demonstrated by the numerical simulation of an inverted pendulum.

Energy-Efficient Distributed Filtering in Sensor Networks: A Unified Switched System Approach

This paper is concerned with the energy-efficient distributed filtering in sensor networks, and a unified switched system approach is proposed to achieve this goal. For the system under study, the measurement is first sampled under nonuniform sampling periods, then the local measurement elements are selected and quantized for transmission. Then, the transmission rate is further reduced to save constrained power in sensors. Based on the switched system approach, a unified model is presented to capture the nonuniform sampling, the measurement size reduction, the transmission rate reduction, the signal quantization, and the measurement missing phenomena. Sufficient conditions are obtained such that the filtering error system is exponentially stable in the mean-square sense with a prescribed H∞ performance level. Both simulation and experiment studies are given to show the effectiveness of the proposed new design technique.

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Stability analysis for uncertain switched neural networks with time-varying delay

In this paper, stability for a class of uncertain switched neural networks with time-varying delay is investigated. By exploring the mode-dependent properties of each subsystem, all the subsystems are categorized into stable and unstable ones. Based on Lyapunov-like function method and average dwell time technique, some delay-dependent sufficient conditions are derived to guarantee the exponential stability of considered uncertain switched neural networks. Compared with general results, our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being stable, thus getting less conservative criteria. Finally, two numerical examples are provided to show the validity and the advantages of the obtained results.

On Input-to-State Stability of Switched Stochastic Nonlinear Systems Under Extended Asynchronous Switching

An extended asynchronous switching model is investigated for a class of switched stochastic nonlinear retarded systems in the presence of both detection delay and false alarm, where the extended asynchronous switching is described by two independent and exponentially distributed stochastic processes, and further simplified as Markovian. Based on the Razumikhin-type theorem incorporated with average dwell-time approach, the sufficient criteria for global asymptotic stability in probability and stochastic input-to-state stability are given, whose importance and effectiveness are finally verified by numerical examples.

Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays

In this brief, the problems of the mixed H-infinity and passivity performance analysis and design are investigated for discrete time-delay neural networks with Markovian jump parameters represented by Takagi-Sugeno fuzzy model. The main purpose of this brief is to design a filter to guarantee that the augmented Markovian jump fuzzy neural networks are stable in mean-square sense and satisfy a prescribed passivity performance index by employing the Lyapunov method and the stochastic analysis technique. Applying the matrix decomposition techniques, sufficient conditions are provided for the solvability of the problems, which can be formulated in terms of linear matrix inequalities. A numerical example is also presented to illustrate the effectiveness of the proposed techniques.

Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov-Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.

Receding Horizon Stabilization and Disturbance Attenuation for Neural Networks With Time-Varying Delay

This paper is concerned with the problems of receding horizon stabilization and disturbance attenuation for neural networks with time-varying delay. New delay-dependent conditions on the terminal weighting matrices of a new finite horizon cost functional for receding horizon stabilization are established for neural networks with time-varying or time-invariant delays using single- and double-integral Wirtinger-type inequalities. Based on the results, delay-dependent sufficient conditions for the receding horizon disturbance attenuation are given to guarantee the infinite horizon H∞ performance of neural networks with time-varying or time-invariant delays. Three numerical examples are provided to illustrate the effectiveness of the proposed approach.