Event-Triggered Stabilization of Neural Networks With Time-Varying Switching Gains and Input Saturation

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Fully Distributed Event-Triggered Anti-Windup Consensus of Heterogeneous Systems With Input Saturation and an Active Leader

This article addresses the event-based fully distributed consensus problem for linear heterogeneous multiagent systems (MASs) subject to input saturation. A leader with unknown but bounded control input is also considered. Based on an adaptive dynamic event-triggered protocol, all the agents can reach output consensus without knowing any global knowledge. Moreover, by applying a multiple-level saturation technique, the input-constrained leader-following consensus control is achieved. The given event-triggered algorithm can be utilized for the directed graph containing a spanning tree with the leader as the root. One distinct feature compared with previous works is that the proposed protocol can achieve saturated control without any a priori condition, instead, the local information is needed. Finally, the numerical simulations are illustrated to verify the performance of the proposed protocol.

Dual periodic event-triggered control for multi-agent systems with input saturation

This paper is concerned with the periodic event-triggered consensus of multi-agent systems subject to input saturation. Due to the nonlinearity caused by the input saturation constraint, the accuracy of the event-triggered mechanism to screen data will be reduced. To deal with this problem, a novel dual periodic event-triggered mechanism is first proposed, in which a saturation-assisted periodic event-trigger and a complemental periodic event-trigger work synergistically to screen data more efficiently under the input saturation constraint. In addition, considering the various disturbances in the environment, a more general mixed H_∞ and passive performance is introduced to describe the disturbance attenuation level. Based on the Lyapunov-Krasovskii functional, some less conservative consensus criteria are obtained for the multi-agent systems. In addition, under different input saturation constraints, the relationship between the disturbance attenuation level and the data transmission rate is explored. After that, a particle swarm optimization algorithm is a first attempt to estimate and enlarge the region of asymptotic consensus. Finally, an example is given to verify the effectiveness and superiority of our proposed method.

Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks

This article focuses on the resilient fixed-time stabilization of switched neural networks (SNNs) under impulsive deception attacks. A novel theorem for the fixed-time stability of impulsive systems is established by virtue of the comparison principle. Existing fixed-time stability theorems for impulsive systems assume that the impulsive strength is not greater than 1, while the proposed theorem removes this assumption. SNNs subjected to impulsive deception attacks are modeled as impulsive systems. Some sufficient criteria are derived to ensure the stabilization of SNNs in fixed time. The estimation of the upper bound for the settling time is also given. The influence of impulsive attacks on the convergence time is discussed. A numerical example and an application to Chua's circuit system are given to demonstrate the effectiveness of the theoretical results.

A Switched Integral-Based Event-Triggered Control of Uncertain Nonlinear Time-Delay System With Actuator Saturation

This article explores the asymptotic stabilization criteria of the uncertain nonlinear time-delay system subject to actuator saturation. A switched integral-based event-triggered scheme (IETS) is established to reduce the redundant data transmission over the networks. The switched IETS condition uses the integration of system states over a time period in the past. A fixed waiting time is included to avoid the Zeno behavior. In order to estimate a larger domain of attraction, a delay-dependent polytopic representation method is presented to deal with the effects of actuator saturation in the proposed model. A new series of less conservative linear matrix inequalities (LMIs) is proposed on the basis of delay-dependent Lyapunov-Krasovskii functional (LKF) to ensure the stability of nonlinear time-delay system subject to actuator saturation using the proposed IETS. Numerical examples are used to confirm the effectiveness and advantages of the proposed IETS approach.

Quasisynchronization of Memristive Neural Networks With Communication Delays via Event-Triggered Impulsive Control

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.

Event-Triggered Fault Detection Filter Design for Discrete-Time Memristive Neural Networks With Time Delays

In this article, the fault detection (FD) filter design problem is addressed for discrete-time memristive neural networks with time delays. When constructing the system model, an event-triggered communication mechanism is investigated to reduce the communication burden and a fault weighting matrix function is adopted to improve the accuracy of the FD filter. Then, based on the Lyapunov functional theory, an augmented Lyapunov functional is constructed. By utilizing the summation inequality approach and the improved reciprocally convex combination method, an FD filter that guarantees the asymptotic stability and the prescribed H_∞ performance level of the residual system is designed. Finally, numerical simulations are provided to illustrate the effectiveness of the presented results.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Observer-Based Dissipativity Control for T-S Fuzzy Neural Networks With Distributed Time-Varying Delays

An observer-based dissipativity control for Takagi-Sugeno (T-S) fuzzy neural networks with distributed time-varying delays is studied in this article. First, the network channel delays are modeled as a distributed delay with its kernel. To make full use of kernels of the distributed delay, a Lyapunov-Krasovskii functional (LKF) is established with the kernel of the distributed delay. It is noted that the novel LKF and delay-dependent reciprocally convex inequality plays an important role in dealing with global asymptotical stability and strict (Q, S,R) - α -dissipativity of the T-S fuzzy delayed model. Through the constructed LKF, a new set of less conservative linear matrix inequality (LMI) conditions is presented to obtain an observer-based controller for the T-S fuzzy delayed model. This proposed observer-based controller ensures that the state of the closed-loop system is globally asymptotically stable and strictly (Q, S,R) - α -dissipative. Finally, the effectiveness of the proposed results is shown in numerical simulations.

Extended Dissipativity Analysis for Markovian Jump Neural Networks via Double-Integral-Based Delay-Product-Type Lyapunov Functional

This brief studies the problem of extended dissipativity analysis for the Markovian jump neural networks (MJNNs) with time-varying delay. A double-integral-based delay-product-type (DIDPT) Lyapunov functional is first constructed in this brief, which makes full use of the information of time delay. Moreover, some unnecessary constraints on the system structure are removed, which leads to more general results. A numerical example is employed to illustrate the advantages of the proposed method.

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.

Memory-Event-Triggered H∞ Output Control of Neural Networks With Mixed Delays

This article investigates the problem of memory-event-triggered H∞ output feedback control for neural networks with mixed delays (discrete and distributed delays). The probability density of the communication delay among neurons is modeled as the kernel of the distributed delay. To reduce network communication burden, a novel memory-event-triggered scheme (METS) using the historical system output is introduced to choose which data should be sent to the controller. Based on a constructed Lyapunov-Krasovskii functional (LKF) with the distributed delay kernel and a generalized integral inequality, new sufficient conditions are formed by linear matrix inequalities (LMIs) for designing an event-triggered H∞ controller. Finally, experiments based on a computer and a real wireless network are executed to confirm the validity of the developed method.

Neural-Network-Based Event-Triggered Adaptive Control of Nonaffine Nonlinear Multiagent Systems With Dynamic Uncertainties

This article addresses the adaptive event-triggered neural control problem for nonaffine pure-feedback nonlinear multiagent systems with dynamic disturbance, unmodeled dynamics, and dead-zone input. Radial basis function neural networks are applied to approximate the unknown nonlinear function. A dynamic signal is constructed to deal with the design difficulties in the unmodeled dynamics. Moreover, to reduce the communication burden, we propose an event-triggered strategy with a varying threshold. Based on the Lyapunov function method and adaptive neural control approach, a novel event-triggered control protocol is constructed, which realizes that the outputs of all followers converge to a neighborhood of the leader's output and ensures that all signals are bounded in the closed-loop system. An illustrative simulation example is applied to verify the usefulness of the proposed algorithms.

Master-Slave Synchronization of Delayed Neural Networks With Time-Varying Control

This brief investigates the master-slave synchronization problem of delayed neural networks with general time-varying control. Assuming a linear feedback controller with time-varying control gain, the synchronization problem is recast into the stability problem of a delayed system with a time-varying coefficient. The main theorem is established in terms of the time average of the control gain by using the Lyapunov-Razumikhin theorem. Moreover, the proposed framework encompasses some general intermittent control schemes, such as the switched control gain with external disturbance and intermittent control with pulse-modulated gain function, while some useful corollaries are consequently deduced. Interestingly, our theorem also provides a solution for regaining stability under control failure. The validity of the theorem and corollaries is further demonstrated with numerical examples.

Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control

This paper considers the drive-response synchronization of memristive neural networks (MNNs) with unknown parameters, where the unbounded discrete and bounded distributed time-varying delays are involved. Aiming at the unknown parameters of MNNs, the updating law of weight in response system and the gain of adaptive controller are proposed to realize the synchronization of delayed MNNs. In view of the limited communication and bandwidth, the event-triggered mechanism is introduced to adaptive control, which not only decreases the times of controller update and the amount of data sending out but also enables synchronization when parameters of MNNs are unknown. In addition, a relative threshold strategy, which is relative to fixed threshold strategy, is proposed to increase the inter-execution intervals and to improve the control effect. When the parameters of MNNs are known, the algebraic criteria of synchronization are established via event-triggered state feedback control by exploiting inequality techniques and calculus theorems. Finally, one simulation is presented to validate the effectiveness of the proposed results.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

Adaptive Neural Quantized Control for a Class of MIMO Switched Nonlinear Systems With Asymmetric Actuator Dead-Zone

This paper concentrates on the adaptive state-feedback quantized control problem for a class of multiple-input-multiple-output (MIMO) switched nonlinear systems with unknown asymmetric actuator dead-zone. In this study, we employ different quantizers for different subsystem inputs. The main challenge of this study is to deal with the coupling between the quantizers and the dead-zone nonlinearities. To solve this problem, a novel approximation model for the coupling between quantizer and dead-zone is proposed. Then, the corresponding robust adaptive law is designed to eliminate this nonlinear term asymptotically. A direct neural control scheme is employed to reduce the number of adaptive laws significantly. The backstepping-based adaptive control scheme is also presented to guarantee the system performance. Finally, two simulation examples are presented to show the effectiveness of our control scheme.

A Novel Sliding Mode Control for a Class of Stochastic Polynomial Fuzzy Systems Based on SOS Method

In this paper, a novel robust controller for continuous stochastic polynomial fuzzy systems is investigated. The aim of the proposed method is to eliminate the restrictive assumptions that the local input matrix B_i must be uniform and the sliding mode surface proposed did not consider the stochastic perturbations, which are required in most existing results. At the same time, the proposed method could handle the system with matched external disturbances. First, a novel vector integral sliding mode surface (VISMS) is constructed according to the basis matrix [Formula: see text]. The sliding mode surface parameter matrix [Formula: see text] can be obtained through the provided sum of squares conditions. Second, by using an improved Lyapunov method and a new proposed lemma, a novel sliding mode control law is designed to keep the state of the closed-loop systems on the VISMS approximately since the initial time. Third, a practical example and a numerical one are provided to illustrate the validity of the proposed approach.

Event-triggered synchronization of discrete-time neural networks: A switching approach

This paper investigates the event-triggered synchronization control of discrete-time neural networks. The main highlights are threefold: (1) a new event-triggered mechanism (ETM) is presented, which can be regarded as a switching between the discrete-time periodic sampled-data control and a continuous ETM; (2) a saturating controller which is equipped with two switching gains is designed to match the switching property of the proposed ETM; (3) a dedicated switching Lyapunov-Krasovskii functional is constructed, which takes the sawtooth constraints of control input into account. Based on these ingredients, the synchronization criteria are derived such that the considered error systems are locally stable. Whereafter, two co-design problems are discussed to maximize the set of admissible initial conditions and the triggering threshold, respectively. Finally, the effectiveness and advantages of the proposed method are validated by two numerical examples.

Quasi-Synchronization of Delayed Memristive Neural Networks via Region-Partitioning-Dependent Intermittent Control

This paper aims at investigating the master-slave quasi-synchronization of delayed memristive neural networks (MNNs) by proposing a region-partitioning-dependent intermittent control. The proposed method is described by three partitions of non-negative real region and an auxiliary positive definite function. Whether the control input is imposed on the slave system or not is decided by the dynamical relationships among the three subregions and the auxiliary function. From these ingredients, several succinct criteria with the associated co-design procedure are presented such that the synchronization error converges to a predetermined level. The proposed intermittent control scheme is also applied to the event-triggered control, and an intermittent event-triggered mechanism is devised to investigate the quasi-synchronization of MNNs correspondingly. Such mechanism eliminates the events in rest time, and then it reduces the amount of samplings. Finally, two illustrative examples are presented to verify the effectiveness of our theoretical results.

Region Stabilization of Switched Neural Networks With Multiple Modes and Multiple Equilibria: A Pole Assignment Method

This article investigates region stabilization issue of switched neural networks (SNNs) with multiple modes (MMs) and multiple equilibria (ME) via a pole assignment method. In such an SNN, every neuron is observed with more than one mode and unstable equilibrium point. First, SNNs with MMs and ME are modeled in terms of switched systems with unstable subsystems and ME. Second, a necessary and sufficient condition and a sufficient condition are, respectively, proposed for arbitrary switching paths pole assignment and arbitrary periodic/quasi-periodic switching paths (PSPs/QSPs) asymptotically region stabilizing pole assignment of switched linear time-invariant (LTI) systems with ME. It is shown that to stabilize a switched LTI system, some/all poles of all/some linear subsystems can be assigned to suitable locations of the right-half side of the complex plane. Third, based on the obtained pole assignment results, an asymptotical-region-stabilizing-control law observed as distributed state feedback controllers of MMs, asymptotical-region-stabilizing PSPs/QSPs, and a corresponding algorithm are all designed for asymptotical region stabilization of switched linear/nonlinear neural networks with MMs and ME. Finally, a numeral example is given to illustrate the effectiveness and practicality of the new results.

Identification and Control of Nonlinear Systems Using Neural Networks: A Singularity-Free Approach

In this paper, identification and control for a class of nonlinear systems with unknown constant or variable control gains are investigated. By reformulating the original system dynamic equation into a new form with a unit control gain and introducing a set of filtered variables, a novel neural network (NN) estimator is constructed and a new estimation error is used to update the augmented weights. Based on the identification results, two singularity-free NN indirect adaptive controllers are developed for nonlinear systems with unknown constant control gains or variable control gains, respectively. Because the singularity problem is eradicated, the proposed methods remove limitations on parameter estimates that are used to guarantee the positiveness of the estimated control gain. Consequently, a more accurate estimation result can be achieved and the system state can track the given reference signal more precisely. The effectiveness of the proposed identification and control algorithms are tested and the superiority of the proposed singularity-free approach is demonstrated by simulation results.

Event-Based Synchronization Control for Memristive Neural Networks With Time-Varying Delay

In this paper, we investigate the global synchronization control problem for memristive neural networks (MNNs) with time-varying delay. A novel event-triggered controller is introduced with the linear diffusive term and discontinuous sign term. In order to greatly reduce the computation cost of the controller under certain event-triggering condition, two event-based control schemes are proposed with static event-triggering condition and dynamic event-triggering condition. Some sufficient conditions are derived by these control schemes to ensure the response MNN to be synchronized with the driving one. Furthermore, under certain event-triggering conditions, a positive lower bound is achieved for the interexecution time to guarantee that Zeno behavior cannot be executed. Finally, numerical simulations are provided to substantiate the effectiveness of the proposed theoretical results.

Switching event-triggered control for global stabilization of delayed memristive neural networks: An exponential attenuation scheme

In this paper, an exponential-attenuation-based switching event-trigger (EABSET) scheme is designed to achieve the global stabilization of delayed memristive neural networks (MNNs). The issue is proposed for two reasons: (1) the available methods may be complicated in dealing with the state-dependent memristive connection weights; (2) the existing event-trigger mechanisms may be conservative in decreasing the amount of triggering times. To overcome these difficulties, the stabilization problem is formulated within a framework of networked control first. Then, an exponential attenuation term is introduced into the prescribed threshold function. It can enlarge the time span between two neighboring triggered events and further reduce the frequency of data packets sending out. By utilizing the input delay approach, time-dependent and piecewise Lyapunov functionals, and matrix norm inequalities, some sufficient criteria are obtained to guarantee the global stabilization of delayed MNNs and to design both the controller and the trigger parameters. Finally, some comparison simulation results demonstrate that the novel event-trigger scheme has some advantages over some existing ones.