Synchronization Of Inertial Neural Networks Research Articles

Dynamic event-triggered synchronization for semi-Markovian switching inertial neural networks with generally uncertain transition rates in finite-time interval

This paper investigates the finite-time synchronization for inertial neural networks with stochastic switching parameters based on dynamic event-triggered protocol. Due to the complexity of network environment, semi-Markovian process is introduced into the modeling of inertial neural networks, in which the transition rates vary with the operating time. The dynamic event-triggered protocol is developed to determine whether the signal is transmitted, in which Zeno phenomenon is eliminated under limited bandwidth resources. The objective is to construct an appropriate dynamic event-triggered control law such that the drive-response system maintains finite-time synchronization under generally uncertain transition rates. Based on the Lyapunov functional theory, finite-time synchronization criterion is proposed for the related inertial neural networks. Furthermore, a dynamic event-triggered controller is constructed in a finite-time interval. A numerical example and an image encryption process are given to show the efficiency of the proposed method.

Submission to Special Issue to Explainable Representation Learning-Based Intelligent Inspection and Maintenance of Complex Systems: Synchronization of Inertial Neural Networks With Unbounded Delays via Sampled-Data Control.

This article addresses the synchronization issue for inertial neural networks (INNs) with heterogeneous time-varying delays and unbounded distributed delays, in which the state quantization is considered. First, by fully considering the delay and sampling time point information, a modified looped-functional is proposed for the synchronization error system. Compared with the existing Lyapunov-Krasovskii functional (LKF), the proposed functional contains the sawtooth structure term V8(t) and the time-varying terms ex(t-βħ (t)) and ey(t-βħ (t)) . Then, the obtained constraints may be further relaxed. Based on the functional and integral inequality, less conservative synchronization criteria are derived as the basis of controller design. In addition, the required quantized sampled-data controller is proposed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness and superiority of the proposed scheme in this article.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization.

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Protocol-Based Synchronization of Stochastic Jumping Inertial Neural Networks Under Image Encryption Application.

This work investigates the protocol-based synchronization of inertial neural networks (INNs) with stochastic semi-Markovian jumping parameters and image encryption application. The semi-Markovian jumping process is adopted to characterize INNs under sudden complex changes. To conserve the limited available network bandwidth, an adaptive event-driven protocol (AEDP) is developed in the corresponding semi-Markovian jumping INNs (S-MJINNs), which not only reduces the amount of data transmission but also avoids the Zeno phenomenon. The objective is to construct an adaptive event-driven controller so that the drive and response systems maintain synchronous relationships. Based on the appropriate Lyapunov functional, integral inequality, and free weighting matrix, novel criteria are derived to realize the synchronization. Moreover, the desired adaptive event-driven controller is designed under a semi-Markovian jumping process. The proposed method is demonstrated through a numerical example and an image encryption process.

Saturated and asymmetric saturated control for projective synchronization of inertial neural networks with delays and discontinuous activations through matrix measure method

The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.

Direct approach on fixed-time stabilization and projective synchronization of inertial neural networks with mixed delays

This article mainly addresses the problems of fixed-time stabilization(FTS) and fixed-time projective synchronization(FTPS) for the chaotic inertial neural networks(INNs) with mixed delays. Unlike the previous works, the results of FTS and FTPS are constructed for the chaotic INNs by means of direct approach instead of reduced-order way, which are more intuitive and concise. Furthermore, by designing effective Lyapunov functionals and novel feedback controllers, we obtain sufficient condition to respectively ensure FTS and FTPS of the delayed chaotic INNs, which settling times of FTS and FTPS do not depend on any initial values of the investigated systems. Until now, very few works are reported on FTS and FTPS for the delayed chaotic INNs via non-reduced-order way. In addition, the proposed FTPS are more generalized than the conventional synchronization and anti-synchronization. At last, some simulation results and applications are listed to expound the correctness of the derived criteria.

Saturated and asymmetric saturated impulsive control synchronization of coupled delayed inertial neural networks with time-varying delays

This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings.

Event-triggered impulsive control design for synchronization of inertial neural networks with time delays

This paper investigates the synchronization problem of inertial neural networks (INNs) with time delays by virtue of event-triggered (E-T) impulsive control, in which a Lyapunov function based E-T mechanism is used to determine impulsive instants. The synchronization analysis of INNs through E-T impulsive control technique unlike time-triggered impulsive control, which would be activated when certain well-designed conditions exist, E-T impulsive control is only allowed when certain well-defined events occur. Besides that, control input is only required at triggered instants and also no control input is required for two triggered instants in a sequence. Considering the E-T mechanism, the synchronization analysis of the INNs is discussed by reduced and non-reduced order approaches and constructing the suitable Lyapunov functionals. Finally, two simulation results are provided to illustrate the efficacy of the theoretical results.

Exponential synchronization of inertial neural network with mixed delays via intermittent pinning control

AbstractThis article considers the problem of exponential synchronization of inertial neural networks (INNs) with mixed delays via a novel hybrid control scheme consisting of pinning and periodic intermittent control. Both the discrete delay and distributed delay are taken into account in the network model. Through the proper variable substitution, the original system is transferred into a simply formed differential equation. Meantime, some new sufficient conditions are derived by the Lyapunov stability theory for the exponential synchronization of INNs. Eventually, numerical simulations are given to present the effectiveness of the theoretical method.

Intermittent Control Based Exponential Synchronization of Inertial Neural Networks with Mixed Delays

Intermittent Control Based Exponential Synchronization of Inertial Neural Networks with Mixed Delays

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.

Sliding mode control-based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays

In this article, we are interested in the fixed-time stabilization (FTSt) and fixed-time synchronization (FTSy) of a class of inertial neural networks with time-varying and distributed delays. To obtain FTSt and FTSy, sliding mode controllers are developed based on sliding mode control techniques and by using sliding variables. Two polynomial feedback control laws are exploited to achieve the FTSt and the FTSy but they are singular. To get rid of the singularities, the saturation function is used into the design of the controllers and the almost FTSt and almost FTSy are proved. Finally, numerical examples are presented to show the effectiveness of the theoretical results.

Finite-time lag synchronization of inertial neural networks with mixed infinite time-varying delays and state-dependent switching

In this article, we design a new control scheme to investigate the finite-time lag synchronization (FTLS) of inertial neural networks (INNs) with mixed infinite time-varying delays and state-dependent switching. Several novel and easily verified conditions are gained guaranteeing the FTLS of INNs via the finite-time stability theory and nonsmooth analysis. Moreover, it is worth emphasizing that here we directly analyze INNs without using variable substitution, which is different from the reduced-order approach used in correspondingly previous works. At last, a numerical example and an application in image encryption are given to verify the correctness and practicability of the obtained results.

Finite-Time and Fixed-Time Synchronization of Inertial Neural Networks with Mixed Delays

This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays (mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities, some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.

Synchronization of Inertial Neural Networks With Time-Varying Delays via Quantized Sampled-Data Control.

This article addresses the quantized sampled-data (QSD) synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays, in which the sampled-data control and state quantization effect have been considered. By utilizing a proper variable substitution to transform the original system into a first-order differential system, choosing a new Lyapunov-Krasovskii functional (LKF) containing both the continuous terms and the discontinuous terms, and applying Jensen inequality and an improved reciprocally convex inequality to estimate the derivative of the LKF, the sufficient conditions for QSD synchronization for INNs are newly obtained in terms of linear matrix inequalities (LMIs), and the desired QSD controllers are designed by solving a set of LMIs. Finally, three numerical examples are provided to validate the effectiveness and benefit of the proposed results.

Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay

Based on the framework of Filippov solutions, this paper considers synchronization of inertial neural networks (INNs) with discontinuous activation functions and proportional delay. By designing several non-chattering controllers, both finite-time and fixed-time synchronization are studied. The designed controllers are simple to be implemented and can overcome the effects of both nonidentical uncertainties of Filippov solutions and the proportional delay without inducing any chattering. By designing new Lyapunov functionals and utilizing 1-norm methods, several sufficient conditions are obtained to ensure that the INNs achieve drive-response synchronization in finite time and fixed time, respectively. Moreover, the settling time is estimated for the two types of synchronization. Simulations are provided to illustrate the effectiveness of theoretical analysis.

Exponential Synchronization in Inertial Neural Networks with Time Delays

In this paper, exponential synchronization for inertial neural networks with time delays is investigated. First, by introducing a directive Lyapunov functional, a sufficient condition is derived to ascertain the global exponential synchronization of the drive and response systems based on feedback control. Second, by introducing a variable substitution, the second-order differential equation is transformed into a first-order differential equation. As such, a new Lyapunov functional is constructed to formulate a novel global exponential synchronization for the systems under study. The two obtained sufficient conditions complement each other and are suitable to be applied in different cases. Finally, two numerical examples are given to illustrated the effectiveness of the proposed theoretical results.

Exponential synchronization of inertial neural networks with mixed time-varying delays via periodically intermittent control

This paper is concerned with the problem on the exponential synchronization of inertial neural networks with discrete and finite distributed time-varying delays using intermittent control. Two kinds of time varying delays are considered: one is whose derivatives are strictly smaller than one and the other is without any restriction on the delay derivatives. Based on Lyapunov–Krasovskii functional method and applying inequality techniques, some new delay-dependent criteria are obtained to ensure the global exponential synchronization for the discussed networks, which are very simple to implement in practice and reduce the computational burden. Moreover, the exponential synchronization convergence rates depend on the norm, the transformation parameters, the control parameters and the width index of the control. Finally, some numerical examples are presented to demonstrate the validity of our results.

Quantized Sampled-Data Control for Synchronization of Inertial Neural Networks With Heterogeneous Time-Varying Delays.

This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control. The control scheme, which takes the communication limitations of quantization and variable sampling into account, is first employed for tackling the synchronization of INNs. A novel Lyapunov-Krasovskii functional (LKF) is constructed for synchronizing an error system. Compared with existing LKFs by the largest upper bound of all HTVDs, the proposed LKF is superior, since it can make full use of the information on the lower and upper bounds of each HTVD. Based on the LKF and a new integral inequality technique, less conservative synchronization criteria are derived. The desired quantized sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and conservatism reduction of the proposed results.

Exponential synchronization of inertial neural networks with mixed delays via quantized pinning control

Abstract In this paper, exponential synchronization of coupled inertial neural networks (CINNs) with bounded time-varying discrete delay and infinite-time distributed delay (mixed delays) is considered by designing quantized pinning controllers. By designing novel Lyapunov–Krasovskii functionals and using new weighted integral inequalities, delay-dependent criteria formulated by linear matrix inequality (LMI) are obtained. Different from existing ones, the designed Lyapunov–Krasovskii functionals include negative terms, which lead to less conservative results. Numerical simulations verify the effectiveness of the theoretical results.