Quasi-Synchronization of Discrete-Time-Delayed Heterogeneous-Coupled Neural Networks via Hybrid Impulsive Control.

This article explores the quasi-synchronization of discrete-time-delayed heterogeneous-coupled neural networks (CNNs) via hybrid impulsive control. By introducing an exponential decay function, two non-negative regions are introduced that are named time-triggering and event-triggering regions, respectively. The hybrid impulsive control is modeled by the dynamical location of Lyapunov functional in two regions. When the Lyapunov functional locates in the time-triggering region, the isolated neuron node releases impulses to corresponding nodes in a periodical manner. Whereas, when the trajectory locates in the event-triggering region, the event-triggered mechanism (ETM) is activated, and there are no impulses. Under the proposed hybrid impulsive control algorithm, sufficient conditions are derived for quasi-synchronization with a definite error convergence level. Compared with pure time-triggered impulsive control (TTIC), the proposed hybrid impulsive control method can effectively reduce the times of impulses and save communication resources on the premise of ensuring performance. Finally, an illustrative example is given to verify the validity of the proposed method.

Periodic Event-Triggered Dynamic Feedback Synchronization Control of Discrete-Time Neural Networks.

This article investigates the event-triggered synchronization control problem of discrete-time neural networks (DNNs) in the case of periodic sampled-data. A discrete-time periodic event-triggered mechanism is adopted to evaluate the measurements, which avoids formulating the triggering function in a continuous manner and saves energy consumption. Under this framework, an event-triggered dynamic output-feedback controller is designed to achieve the goal of synchronization. A piecewise Lyapunov functional is constructed to analyze the sawtooth-like pattern of sampled-error signals. Thereafter, the synchronization criteria are formulated for the considered DNNs. The co-designed issue is further discussed for the control gains and triggering parameter. Finally, a simulation example is presented to show the effectiveness of the proposed method.

Dynamic Periodic Event-Triggered Synchronization of Complex Networks: The Discrete-Time Scenario.

This article reports the synchronization control of discrete-time complex networks using an event-triggered method. The main contributions are twofold: 1) a discrete-time scenario of the dynamic periodic event-triggered mechanism is developed to schedule the transmissions of measurements. The proposed mechanism monitors the synchronization error in a periodic manner, which is beneficial to reduce the calculation resources of sensors. Simultaneously, the proposed mechanism increases the triggering threshold so that it contributes to enlarging the average interevent interval and 2) a new Lyapunov functional is developed to deal with the periodic samplings. On the one hand, the proposed functional involves a delay-dependent term, which is convenient to formulate the synchronization criterion by the delay analysis technique. On the other hand, the functional takes the sawtooth constraint of periodic samplings into consideration by introducing a piecewise functional. Finally, a succinct criterion is derived such that the considered networks are synchronized with a predetermined error level. A simulation example is provided to show our advantages in comparison with the existing approaches.

Periodic Event-Triggered Synchronization for Discrete-Time Complex Dynamical Networks.

In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the "discontinuous" Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.

Intermittent Control for Quasisynchronization of Delayed Discrete-Time Neural Networks.

This article visits the intermittent quasisynchronization control of delayed discrete-time neural networks (DNNs). First, an event-dependent intermittent mechanism is originally designed, which is described by the Lyapunov function and three non-negative real regions. The distinctive feature is that the controller starts to work only when the trajectory of the Lyapunov function goes into the presupposed work region. The proposed method fundamentally changes the principle of the existing intermittent control schemes. Under the proposed framework of the intermittent mechanism, the work/rest time of the controller is aperiodic, unpredictable, and initial value dependent. Second, several succinct sufficient conditions in terms of linear matrix inequalities are developed to achieve the quasisynchronization of the considered DNNs. A simple optimization algorithm is established to compute the control gains and the Lyapunov matrices such that synchronization error is stabilized to the smallest convergence region. Finally, two simulation examples are provided to demonstrate the feasibility of the designed intermittent mechanism.

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.

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

This paper investigates the event-triggered stabilization of neural networks (NNs) subject to input saturation. The main core lies in the design of a novel controller with time-varying switching gains and the associated switching event-triggered condition (ETC). The ETC is essentially a switching between the aperiodic sampling and continuous event trigger. The control gains of the designed controller are composed of an exponentially decaying term and two gain matrices. The two gain matrices are required to be switched when the switching between the aperiodic sampling and continuous event trigger is met. By employing the generalized sector condition and switching Lyapunov function, several sufficient conditions that ensure the local exponential stability of the NNs are formulated in terms of linear matrix inequalities (LMIs). Both the exponentially decaying term and switching gains improve the feasible region of LMIs, and then they are helpful to enlarge the set of admissible initial conditions, the threshold in ETC, and the average waiting time. Together with several optimization problems, two numerical examples are employed to validate the effectiveness of our results.

Dissipativity Analysis for Stochastic Memristive Neural Networks With Time-Varying Delays: A Discrete-Time Case.

In this paper, the dissipativity problem of discrete-time memristive neural networks (DMNNs) with time-varying delays and stochastic perturbation is investigated. A class of logical switched functions are put forward to reflect the memristor-based switched property of connection weights, and the DMNNs are then recast into a tractable model. Based on the tractable model, the robust analysis method and Refined Jensen-based inequalities are applied to establish some sufficient conditions that ensure the of DMNNs. Two numerical examples are presented to illustrate the effectiveness of the obtained results.

Exponential Stabilization of Memristive Neural Networks via Saturating Sampled-Data Control.

This paper is concerned with the exponential stabilization of memristive neural networks (MNNs) by taking into account the sampled-data control and actuator saturation. On the one hand, the MNNs are converted into a tractable model by defining a class of logical switched functions. Based on this model, the connection weights of MNNs are dealt with by a robust analysis method. On the other hand, a saturating sampled-data controller containing an exponentially decaying term is designed. With the help of generalized sector condition and the Lyapunov stability theory, a novel sufficient condition ensuring the local exponential stability of the closed-loop systems is formulated in terms of linear matrix inequalities. In addition, three optimization problems are given to design the control gain with the aims of enlarging the sampling interval, expanding the estimation of the domain of attraction, and minimizing the size of actuators, while preserving the stability of the closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

Stability of Recurrent Neural Networks With Time-Varying Delay via Flexible Terminal Method.

This brief is concerned with the stability criteria for recurrent neural networks with time-varying delay. First, based on convex combination technique, a delay interval with fixed terminals is changed into the one with flexible terminals, which is called flexible terminal method (FTM). Second, based on the FTM, a novel Lyapunov-Krasovskii functional is constructed, in which the integral interval associated with delayed variables is not fixed. Thus, the FTM can achieve the same effect as that of delay-partitioning method, while their implementary ways are different. Guided by FTM, Wirtinger-based integral inequality and free-weight matrix method are employed to develop several stability criteria, respectively. Finally, the feasibility and the effectiveness of the proposed results are tested by two numerical examples.

H∞ state estimation for memristive neural networks with time-varying delays: The discrete-time case.

This paper investigates the H∞ state estimation problem for a class of discrete-time memristive neural networks (DMNNs) with time-varying delays. For the sake of coping with the switched weight matrices, the DMNNs are recast into a tractable model by defining a series of state-dependent switched signals. Based on the tractable model, the robust analysis method and Lyapunov stability theory are developed to devise a sufficient condition which ensures the global asymptotical stability of the estimation error system with a prescribed H∞ performance. The desired state estimator gain matrix and optimal performance index can be accomplished via solving a convex optimization problem subject to several linear matrix inequalities (LMIs). Finally, one numerical example is presented to check the effectiveness of the theoretical results.

Exponential Stability and Stabilization of Delayed Memristive Neural Networks Based on Quadratic Convex Combination Method.

This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.