Finite-time Synchronization Research Articles

Global practical finite-time synchronization of disturbed inertial neural networks by delayed impulsive control

This paper delves into the practical finite-time synchronization (FTS) problem for inertial neural networks (INNs) with external disturbances. Firstly, based on Lyapunov theory, the local practical FTS of INNs with bounded external disturbances can be realized by effective finite time control. Then, building upon the local results, we extend the synchronization to a global practical level under delayed impulsive control. By designing appropriate hybrid controllers, the global practical FTS criteria of disturbed INNs are obtained and the corresponding settling time is estimated. In addition, for impulsive control, the maximum impulsive interval is used to describe the frequency at which the impulses occur. We optimize the maximum impulsive interval, aiming to minimize impulses occurrence, which directly translates to reduced control costs. Moreover, by comparing the global FTS results for INNs without external disturbances, it can be found that the existence of perturbations necessitates either higher impulsive intensity or denser impulses to maintain networks synchronization. Two examples are shown to demonstrate the reasonableness of designed hybrid controllers.

Finite-time synchronization of complex dynamic networks with impulsive control and actuator saturation: An LMI approach

This paper investigates the finite-time synchronization (FTS) of complex dynamic networks (CDNs) with impulsive control subject to actuator saturation. We develop a novel method that integrates the impulsive comparison principle and improved convex hull representation lemma of saturated function to derive LMI-based sufficient conditions for FTS, which are easy to verify. We also estimate the admissible set of initial values to ensure the validity of the lemma. Unlike previous work, we relax the monotonicity assumption on the Lyapunov function, which broadens our results’ applicability. Moreover, we formulate and solve an optimization problem to enlarge the admissible set under the LMI constraints, using YALMIP toolbox in MATLAB software. Finally, several numerical examples are proposed to demonstrate our results’ effectiveness and superiority.

Sliding mode control for finite-time projective synchronisation in distinct Caputo fractional-order delayed neural networks with inconsistent orders

This manuscript delves into the realm of projective synchronisation in delayed neural networks governed by Caputo fractional-order dynamics, addressing the intricate challenges of attaining finite-time synchronisation in networks with distinct structures, functions, and orders. To start, the integration of a compensation controller within the control architecture is examined, aiming to formulate the projection error dynamics. By leveraging projection error system analysis alongside output observation and sliding mode control, a meticulously crafted derivative-based sliding mode surface along with a sliding mode controller are devised, ensuring both convergence and seamless sliding motion. Afterwards, the accessibility of the surface is assessed through relevant lemmas, Caputo derivative characteristics and the Lyapunov direct approach. The subsequent stability of sliding path is corroborated, and indispensable prerequisites for achieving finite-time projective synchronisation are outlined. Furthermore, the establishment of an upper bound for synchronisation time of distinct Caputo fractional-order delayed neural networks (CFDNNs) with inconsistent orders is carried out. Ultimately, simulations on distinct CFDNNs with consistent and inconsistent orders are conducted to exemplify our approach, employing the continuous frequency distribution model.

Finite-Time Synchronization Criteria for Caputo Fractional-Order Uncertain Memristive Neural Networks with Fuzzy Operators and Transmission Delay Under Communication Feedback

Unlike existing memristive neural networks or fuzzy neural networks, this article investigates a class of Caputo fractional-order uncertain memristive neural networks (CFUMNNs) with fuzzy operators and transmission delay to realistically model complex environments. Especially, the fuzzy symbol AND and the fuzzy symbol OR as well as nonlinear activation behaviors are all concerned in the generalized master-slave networks. Based on the characteristics of the neural networks being studied, we have designed distinctive information feedback control protocols including three different functional sub-modules. Combining comparative theorems, inequality techniques, and stability theory, novel delay-independent conditions can be derived to ensure the finite-time synchronization (FTS) of fuzzy CFUMNNs. Besides, the upper bound of the settling time can be effectively evaluated based on feedback coefficients and control parameters, which makes the achievements of this study more practical for engineering applications such as signal encryption and secure communications. Ultimately, simulation experiments show the feasibility of the derived results.

Observer-based impulsive control for finite-time synchronization of delayed neural networks on time scales

Observer-based impulsive control for finite-time synchronization of delayed neural networks on time scales

Finite-time synchronization for a fully complex-valued BAM inertial neural network with proportional delays via non-reduced order and non-separation approach

This paper focuses on finite-time synchronization (FinTS) for fully complex-valued bidirectional associative memory inertial neural networks (FCV-BAM-INNs) with proportional delays via non-reduced order and non-separation approach. Firstly, a model of the FCV-BAM-INNs with proportional delays is established. Secondly, by using the non-reduced order transformation method of inertial neural networks (INNs) and the non-separation method of complex-valued neural networks (CVNNs), an adjustable complex feedback control law with memory is designed to reach the FinTS of the drive–response FCV-BAM-INNs with proportional delays. Thirdly, some new delay-independent algebraic sufficient criteria are formed to guarantee FinTS of FCV-BAM-INNs with proportional delays by applying non smooth theory and inequalities in the complex domain, which are flexible and adjustable and easy to implement in applications. Moreover, the settling time of FinTS theoretically is calculated. Finally, some numerical simulations and an application on image encryption and decryption as evidences of the validity and availability of the results.

Finite-time passivity of multi-weighted coupled neural networks with directed topologies and time-varying delay

In this paper, the finite-time passivity (FTP) problem for multi-weighted coupled neural networks (MWCNNs) with directed topologies and time-varying delay is discussed. Firstly, by designing a new state feedback controller, several FTP criteria are given for the considered network. Then, some finite-time synchronization (FTS) criteria are established by employing the FTP results. Secondly, a hybrid impulsive and state feedback controller is first designed, under which different FTP and FTS criteria are presented and the synchronization time is successfully shortened compared to the non-hybrid controller without impulses. Finally, numerical simulations are given to show the effectiveness and superiority of the obtained results.

Finite-time synchronization of proportional delay memristive competitive neural networks

The finite-time synchronization (FTS) is considered for proportional delay memristive competitive neural networks (PDMCNNs). By utilizing Lyapunov functional method and differential inclusion theory, two new criteria ensuring the FTS of PDMCNNs are established. These criteria with algebraic inequality forms are less complicated and easier to verify than the matrix inequality forms. In addition, the corresponding settling times have been estimated. Eventually, the effectiveness of the presented criteria and controllers is confirmed through two numerical examples, and one application about image encryption is provided.

Finite-time quasi-projective synchronization of fractional-order reaction-diffusion delayed neural networks

This paper investigates the finite-time quasi-projective synchronization (FTQPS) issue of fractional-order reaction-diffusion neural networks (FORDNNs). To the best of our knowledge, this paper introduces the concept of FTQPS for the first time. First, an integral-type Lyapunov function is constructed relying on the characterization of the reaction-diffusion term and some inequality methods. Subsequently, the nonlinear feedback control strategy is designed to achieve the FTQPS goal and some sufficient conditions are obtained to guarantee FTQPS of FORDNNs. Further, the system's synchronization speed is measured by estimating the settling time. It should be noted that the above control strategy is also applicable to conventional integer-order reaction-diffusion neural networks with time delays. Finally, a numerical example is used to illustrate the validity of the theoretical analysis presented.

Finite-time funnel synchronization control based on distributed observer for multi-motor driving systems with input saturation

In this article, the finite-time synchronization control problem is developed for multi-motor driving systems with input saturation. A radial basis function (RBF) neural network is utilized to estimate the unknown uncertainties and the disturbances. In contrast to current control strategies, this study proposes a new approach that utilizes a finite-time distributed observer to estimate the reference signal and then uses the estimated signal to design a synchronization controller, which effectively separates the tracking problem from the synchronous controller design. Furthermore, a funnel function is constructed to actualize the state constraints and confine the synchronization error within a specified boundary. Then, a finite-time funnel control protocol is proposed to ensure that each motor follows the estimated reference signal. Eventually, we illustrate the effectiveness of the proposed method through a numerical example.

Finite-time H∞ synchronization of semi-Markov jump neural networks with two delay components with stochastic sampled-data control

This article investigates the finite-time H∞ synchronization for semi-Markov jump neural networks with two delay components based on stochastic sampled data control. Additionally, the parametric uncertainties are randomly varying which follows the Bernoulli distributed sequences. In the stochastic sampled data control, the sampling interval ′m′ is supposed to be two different values in the time-varying component with given probability conditions. By constructing triple and quadruple integral term in the Lyapunov-Krasovskii functional (LKF) a new integral inequality technique is addressed to derive the main results. Dissimilar from previous literature, involving the new integral inequality, a delay dependent finite-time H∞ synchronization requirements are acquired with regard to linear matrix inequalities (LMIs). In the end, the effectiveness of the considered stochastic sampled data control finite time synchronization scheme is highlighted by numerical examples.

Finite-Time Synchronization of Fractional-Order Memristive Fuzzy Neural Networks: Event-Based Control With Linear Measurement Error.

This article develops a novel event-triggered finite-time control strategy to investigate the finite-time synchronization (F-tS) of fractional-order memristive neural networks with state-based switching fuzzy terms. A key distinction of this approach, compared with existing event-based finite-time control schemes, is the linearity of the measurement error function in the event-triggering mechanism (ETM). The advantage of linear measurement error not only simplifies computational tasks but also aids in demonstrating the exclusion of Zeno behavior for fractional-order systems (FSs). Furthermore, to derive F-tS criteria in the form of linear matrix inequalities (LMIs), a novel finite-time analytical framework for FSs is proposed. This framework includes two original inequalities and a weighted-norm-based Lyapunov function. The effectiveness and superiority of the theoretical results are demonstrated through two examples. Both theoretical and experimental results suggest that the criteria obtained using the new analytical framework are less conservative than existing results.

Mittag-Leffler Synchronization in Finite Time for Uncertain Fractional-Order Multi-Delayed Memristive Neural Networks with Time-Varying Perturbations via Information Feedback

Mittag-Leffler Synchronization in Finite Time for Uncertain Fractional-Order Multi-Delayed Memristive Neural Networks with Time-Varying Perturbations via Information Feedback

Time and energy costs for stochastic synchronisation of multi-layer complex networks with noise

This paper explores time cost (TC) and energy cost (EC) for finite-time stochastic outer synchronisation (FTSS) of multi-layer complex networks in noisy environments. A novel switching controller is designed for achieving FTSS and optimising TC and EC, linking the advantages of finite-time control technologies and linear feedback. Sufficient criteria for achieving FTSS are established, and the estimates of TC and EC are further obtained. At last, the validity of theoretical findings is checked using numerical simulations. Especially, the theoretical analysis and simulating calculation show that a reduction in TC will lead to an increase in EC, in other words, there is a tradeoff between TC and EC.

Fractional-Order Degn–Harrison Reaction–Diffusion Model: Finite-Time Dynamics of Stability and Synchronization

This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criteria, this lemma represents a significant extension of prior findings, laying the groundwork for subsequent investigations. Building upon this foundation, we proceed to develop efficient dependent linear controllers designed to orchestrate finite-time synchronization. Leveraging the power of a Lyapunov function, we derive new, robust conditions that ensure the attainment of synchronization within a predefined time frame. This innovative approach not only enhances our understanding of finite-time synchronization, but also offers practical solutions for its realization in complex systems. To validate the efficacy and applicability of our proposed methodology, extensive numerical simulations are conducted. Through this comprehensive analysis, we aim to contribute valuable insights to the field of fractional-order reaction–diffusion systems while paving the way for practical implementations in real-world applications.

Energetic Cost for Speedy Synchronization in Non-Hermitian Quantum Dynamics.

Quantum synchronization is crucial for understanding complex dynamics and holds potential applications in quantum computing and communication. Therefore, assessing the thermodynamic resources required for finite-time synchronization in continuous-variable systems is a critical challenge. In the present work, we find these resources to be extensive for large systems. We also bound the speed of quantum and classical synchronization in coupled damped oscillators with non-Hermitian anti-PT-symmetric interactions, and show that the speed of synchronization is limited by the interaction strength relative to the damping. Compared to the classical limit, we find that quantum synchronization is slowed by the noncommutativity of the Hermitian and anti-Hermitian terms. Our general results could be tested experimentally, and we suggest an implementation in photonic systems.

Finite-time synchronization of fractional-order uncertain quaternion-valued neural networks via slide mode control

This paper investigates finite-time synchronization of fractional-order quaternion-valued neural networks (F-QV-NNs), involving uncertainties in the system parameters. We adopt a combined approach of sliding mode control (SMC) and a non-separation strategy to achieve finite-time synchronization. Based on SMC theory, we construct a specific sliding surface and design a controller to ensure the occurrence of sliding motion. To achieve the desired sliding motion, we apply the fractional Lyapunov direct method to guide the system's states to the designed sliding surface. Moreover, the derived sufficient conditions ensure finite-time synchronization within the models. Lastly, we give a numerical example to validate the effectiveness of the acquired results.

Novel Caputo fractional differential approach and hybrid control scheme for finite‐time synchronization of nonidentical delayed reaction–diffusion neural networks

AbstractThis work focuses on the finite‐time synchronization (F‐TS) for nonidentical delayed neural networks (DNNs) including Caputo fractional partial differential operator and reaction–diffusion terms. A novel F‐TS lemma is proposed by constructing a new Caputo differential inequality. Applying the new lemma and designing two hybrid controllers with time delay and the sign function, the F‐TS criteria on the introduced Caputo reaction–diffusion nonidentical DNNs under the Neumann boundary condition are derived by making use of the Filippov differential inclusion, Green's theorem, and fractional Razumikhin theorem. The conditions are expressed through the algebraic inequality which can greatly decrease the computation in checking the F‐TS performance. Moreover, the validity and correctness of the F‐TS results are illustrated by selecting various orders, spatial positions, and diffusion parameters.

Finite-time synchronization criteria on delayed FOCVNNs with uncertain parameters and difference operator

This article analyzes the finite-time synchronization (FTS) issues of delayed complex-valued neural networks (CVNNs) with uncertain parameters and fractional difference operator. Firstly, a significant lemma is derived based on discrete fractional calculus. The proposed lemma can help us reach FTS and estimate the setting time. Next, two controllers with delay terms are established, respectively. The designed control strategies can effectively remove delay terms. By utilizing the proposed lemma, control strategies and inequality techniques, the conditions for FTS are derived. The setting time has also been estimated. Finally, we present two examples to demonstrate the theoretical results.

Adaptive finite-time synchronization of quaternion-valued inertial neural networks with mixed delays under quantized event-triggered impulsive strategy

By incorporating inertial terms, quaternions, and time-varying discrete and distributed delays into traditional neural networks (NNs), this paper establishes a category of drive-response quaternion-valued inertial neural networks (QVINNs) with mixed delays. The issue of adaptive finite-time synchronization (FTS) of the QVINNs with mixed delays is explored. To do this, a fresh and low-cost adaptive controller is devised by combining event-triggered impulsive control (ETIC) with quantized control to greatly lower the amount of communication and economic costs. In virtue of the variable substitution, the Lyapunov method, the comparison principle, the inequality technique, and the concept of average impulsive interval (AII), the novel criteria that the QVINNs can accomplish FTS are derived. Meanwhile, it is possible to determine that Zeno-behavior and chattering are absent, and the settling time is predicted. Ultimately, by performing the numerical instance, the efficiency and accuracy of the theoretical results are confirmed.