Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control

Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance

Synchronization of memristive neural networks (MNNs) by using network control scheme has been widely and deeply studied. However, these researches are usually restricted to traditional continuous-time control methods for synchronization of the first-order MNNs. In this paper, we study the robust exponential synchronization of inertial memristive neural networks (IMNNs) with time-varying delays and parameter disturbance via event-triggered control (ETC) scheme. First, the delayed IMNNs with parameter disturbance are changed into first-order MNNs with parameter disturbance by constructing proper variable substitutions. Next, a kind of state feedback controller is designed to the response IMNN with parameter disturbance. Based on feedback controller, some ETC methods are provided to largely decrease the update times of controller. Then, some sufficient conditions are provided to realize robust exponential synchronization of delayed IMNNs with parameter disturbance via ETC scheme. Moreover, the Zeno behavior will not happen in all ETC conditions shown in this paper. Finally, numerical simulations are given to verify the advantages of the obtained results such as anti-interference performance and good reliability.

Dynamic Self-Triggered Impulsive Synchronization of Complex Networks With Mismatched Parameters and Distributed Delay

Synchronization of complex networks with nonlinear couplings and distributed time-varying delays is investigated in this article. Since the mismatched parameters of individual systems, a kind of leader-following quasisynchronization issues is analyzed via impulsive control. To acquire appropriate impulsive intervals, the dynamic self-triggered impulsive controller is devoted to predicting the available instants of impulsive inputs. The proposed controller ensures the control effects while reducing the control costs. In addition, the updating laws of the dynamic parameter is settled in consideration of error bounds to adapt to the quasisynchronization. With the utilization of the Lyapunov stability theorem, comparison method, and the definition of average impulsive interval, sufficient conditions for realizing the synchronization within a specific bound are derived. Moreover, with the definition of average impulsive gain, the parameter variation scheme is extended from the fixed impulsive effects case to the time-varying impulsive effects case. Finally, three numerical examples are given to show the effectiveness and the superiority of proposed mathematical deduction.

Finite-Time Synchronization of Reaction-Diffusion Inertial Memristive Neural Networks via Gain-Scheduled Pinning Control

For the considered reaction-diffusion inertial memristive neural networks (IMNNs), this article proposes a novel gain-scheduled generalized pinning control scheme, where three pinning control strategies are involved and 2ⁿ controller gains can be scheduled for different system parameters. Moreover, a time delay is considered in the controller to make it has a memory function. With the designed controller, drive-and-response systems can be synchronized within a finite-time interval. Note that the final finite-time synchronization criterion is obtained in the forms of linear matrix inequalities (LMIs) by introducing a memristor-dependent sign function into the controller and constructing a new Lyapunov-Krasovskii functional (LKF). Furthermore, by utilizing some improved integral inequality methods, the conservatism of the main results can be greatly reduced. Finally, three numerical examples are provided to illustrate the feasibility, superiority, and practicability of this article.

Finite-/Fixed-Time Synchronization of Delayed Coupled Discontinuous Neural Networks With Unified Control Schemes

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

Finite-Time and Fixed-Time Synchronization of Coupled Memristive Neural Networks With Time Delay

This article is devoted to analyzing the finite-time and fixed-time synchronization of coupled memristive neural networks with time delays. The synchronization is leaderless rather than leader-follower as the tracking targets are uncertain. By designing a proper controller and using the Lyapunov method, several sufficient conditions are obtained to achieve the finite-time and fixed-time synchronization of coupled memristive neural networks by introducing a class of special auxiliary matrices. Moreover, the settling times can be estimated for finite-time synchronization that depends on the initial values as well as fixed-time synchronization that is uniformly bounded for any initial values. Finally, two examples are presented to substantiate the effectiveness of the theoretical results.

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.

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.

Exponential Stabilization of Inertial Memristive Neural Networks With Multiple Time Delays

This article investigates the global exponential stabilization (GES) of inertial memristive neural networks with discrete and distributed time-varying delays (DIMNNs). By introducing the inertial term into memristive neural networks (MNNs), DIMNNs are formulated as the second-order differential equations with discontinuous right-hand sides. Via a variable transformation, the initial DIMNNs are rewritten as the first-order differential equations. By exploiting the theories of differential inclusion, inequality techniques, and the comparison strategy, the p th moment GES ( p ≥ 1 ) of the addressed DIMNNs is presented in terms of algebraic inequalities within the sense of Filippov, which enriches and extends some published results. In addition, the global exponential stability of MNNs is also performed in the form of an M-matrix, which contains some existing ones as special cases. Finally, two simulations are carried out to validate the correctness of the theories, and an application is developed in pseudorandom number generation.

Global Exponential Synchronization of Coupled Delayed Memristive Neural Networks With Reaction-Diffusion Terms via Distributed Pinning Controls

This article presents new theoretical results on global exponential synchronization of nonlinear coupled delayed memristive neural networks with reaction-diffusion terms and Dirichlet boundary conditions. First, a state-dependent memristive neural network model is introduced in terms of coupled partial differential equations. Next, two control schemes are introduced: distributed state feedback pinning control and distributed impulsive pinning control. A salient feature of these two pinning control schemes is that only partial information on the neighbors of pinned nodes is needed. By utilizing the Lyapunov stability theorem and Divergence theorem, sufficient criteria are derived to ascertain the global exponential synchronization of coupled neural networks via the two pining control schemes. Finally, two illustrative examples are elaborated to substantiate the theoretical results and demonstrate the advantages and disadvantages of the two control schemes.

Lagrange Stability and Finite-Time Stabilization of Fuzzy Memristive Neural Networks With Hybrid Time-Varying Delays

This paper focuses on Lagrange exponential stability and finite-time stabilization of Takagi-Sugeno (T-S) fuzzy memristive neural networks with discrete and distributed time-varying delays (DFMNNs). By resorting to theories of differential inclusions and the comparison strategy, an algebraic condition is developed to confirm Lagrange exponential stability of the underlying DFMNNs in Filippov's sense, and the exponentially attractive set is estimated. When external input is not considered, global exponential stability of DFMNNs is derived directly, which includes some existing ones as special cases. Furthermore, finite-time stabilization of the addressed DFMNNs is analyzed by exploiting inequality techniques and the comparison approach via designing a nonlinear state feedback controller. The boundedness assumption of activation functions is removed herein. Finally, two simulations are presented to demonstrate the validness of the outcomes, and an application is performed in pseudorandom number generation.

Novel results on finite-time stabilization of state-based switched chaotic inertial neural networks with distributed delays

The p-norm finite-time stabilization (FTS) issue of a class of state-based switched inertial chaotic neural networks (SBSCINNs) with distributed time-varying delays is investigated. By using a suitable variable transformation, such second-order SBSCINNs are turned into the first-order differential equations. Then some novel criteria are obtained to stabilize SBSCINNs in a finite time based on the theory of finite-time control and non-smooth analysis together with designing two proper delay-dependent feedback controllers. Besides, the settling time of FTS is also estimated and discussed. Finally, the validity and practicability of the deduced theoretical results are verified by examples and applications.

Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method

In this paper, we propose a novel analysis method to investigate the finite-time synchronization (FTS) control problem of the drive-response inertial memristive neural networks (IMNNs) with mixed time-varying delays (MTVDs). Firstly, an improved control scheme is proposed under the delay-independent conditions, which can work even when the past state cannot be measured or the specific time delay function is unknown. Secondly, based on the assumption of bounded activation functions, we establish a new Lemma, which can effectively deal with the difficulties caused by memristive connection weights and MTVDs. Thirdly, by constructing a suitable Lyapunov functions and using a new inequality method, novel sufficient conditions to ensure the FTS for the discussed IMNNs are obtained. Compared with the existing results, our results obtained in a more general framework are more practical. Finally, some numerical simulations are given to substantiate the effectiveness of the theoretical results.

An improved result on synchronization control for memristive neural networks with inertial terms and reaction-diffusion items

This paper investigates the synchronization issue of the memristive neural networks (MNNs) with inertial terms and reaction-diffusion items. In order to smoothly derive the controller gains and obtain an excellent control effect, the desired controller that contains a discontinuous function is proposed. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining the inequality techniques, several sufficient conditions in terms of algebraic inequalities are obtained to guarantee the synchronization of the proposed drive and response systems. Finally, three numerical simulations are exploited to support the acquired theoretical results.

Global exponential stabilization and lag synchronization control of inertial neural networks with time delays

The global exponential stabilization and lag synchronization control of delayed inertial neural networks (INNs) are investigated. By constructing nonnegative function and employing inequality techniques, several new results about exponential stabilization and exponential lag synchronization are derived via adaptive control. And the theoretical outcomes are developed directly from the INNs themselves without variable substitution. In addition, the synchronization results are also applied to image encryption and decryption. Finally, an example is presented to illustrate the validity of the derived results.

Stabilization of Second-Order Memristive Neural Networks With Mixed Time Delays via Nonreduced Order

In this brief, we investigate a class of second-order memristive neural networks (SMNNs) with mixed time-varying delays. Based on nonsmooth analysis, the Lyapunov stability theory, and adaptive control theory, several new results ensuring global stabilization of the SMNNs are obtained. In addition, compared with the reduced-order method used in the existing research studies, we consider the global stabilization directly from the SMNNs themselves without the reduced-order method. Finally, we give some numerical simulations to show the effectiveness of the results.

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.

Novel Finite-Time Synchronization Criteria for Inertial Neural Networks With Time Delays via Integral Inequality Method

In this paper, we are concerned with the finite-time synchronization of a class of inertial neural networks with time delays. Without applying some finite-time stability theorems, which are widely applied to studying the finite-time synchronization for neural networks, by constructing two Lyapunov functions and using integral inequality method, two sufficient conditions on the finite-time synchronization for a class of inertial neural networks with time delays are derived. Considering that the method and research results of the finite-time synchronization are different from some existing works, this paper extends the works on the finite-time synchronization of neural networks.

Finite-Time Stabilization for Stochastic Interval Systems with Time Delay and Application to Energy-Storing Electrical Circuits

In this paper, the problem of stochastic finite-time stabilization is investigated for stochastic delay interval systems. A nonlinear state feedback controller with input-to-state delay is introduced. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions on stochastic finite-time stabilization are derived for closed-loop stochastic delay interval systems using the I t o ^ ’s differential formula. Suitable nonlinear state feedback controllers can be designed in terms of linear matrix inequalities. The obtained results are finally applied to an energy-storing electrical circuit to illustrate the effectiveness of the proposed method.