Adaptive Finite-time Synchronization Research Articles

Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Adaptive finite-time passivity and synchronization of coupled fractional-order memristive neural networks with multi-state couplings

In this article, the adaptive finite-time passivity (FTP) and finite-time synchronization (FTS) of coupled fractional-order memristive neural networks with multi-state couplings (CFMNNMCs) are investigated. Firstly, a sufficient condition for guaranteeing the FTP of CFMNNMCs is obtained by developing an edge-based adaptive strategy and a state-feedback controller. Furthermore, a node-based adaptive controller is designed to ensure the FTP of CFMNNMCs. Additionally, with the help of properties of Gamma function and some inequality techniques, the adaptive FTS problem for the considered network model is addressed. Finally, two numerical examples are given to demonstrate the validity of the adaptive FTP and FTS criteria.

Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations.

Adaptive Finite-time Synchronization of Stochastic Complex Networks with Mixed Delays via Aperiodically Intermittent Control

Adaptive Finite-time Synchronization of Stochastic Complex Networks with Mixed Delays via Aperiodically Intermittent Control

Adaptive finite-time synchronization of fractional-order delayed fuzzy cellular neural networks

The adaptive finite-time synchronization problems are investigated for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs). First, with the aid of the properties of the Mittag-Leffler function and the Laplace transform with the parameter, some novel fractional-order differential inequalities are established to provide new perspective to explore finite-time synchronization of fractional-order systems. Second, based on these inequalities and the designed adaptive controller, some novel sufficient conditions are given to guarantee the adaptive finite-time synchronization of FODFCNNs. Finally, the effectiveness of the results is demonstrated by a numerical example.

Adaptive finite-time synchronization of fractional-order memristor chaotic system based on sliding-mode control

Adaptive finite-time synchronization of fractional-order memristor chaotic system based on sliding-mode control

Finite-time adaptive synchronization of coupled uncertain neural networks via intermittent control

This paper considers the finite-time synchronization (FTS) of coupled neural networks (CNNs) with parameter uncertainties. Based on the adaptive periodically intermittent control method and the finite-time stability theory, some sufficient conditions are derived to achieve synchronization within a finite time. Both the models of CNNs with/without delays are considered and the corresponding upper-bounds of synchronization time are estimated as well. Finally, two illustrative examples are presented to demonstrate the effectiveness and applicability of the theoretical results.

Finite-Time Synchronization Control for Bilateral Teleoperation Systems With Asymmetric Time-Varying Delay and Input Dead Zone

In this article, the synchronization control problem of bilateral teleoperation systems with time-varying delays and input dead zones is addressed. A novel radial basis function network (RBFN)-based adaptive finite-time synchronization control scheme is proposed, where system uncertainties, asymmetric time-varying delays, and dead-zone phenomena are considered simultaneously. Specifically, an RBFN is designed to approximate system uncertainties and unknown nonlinearities. The approximation error as well as the time-associated uncertainty and the nonlinear margin of the dead zone is compensated by an adaptive compensator. Using a Lyapunov-Krasovskii function and the finite-time stability criteria, the system is proved to be semiglobally practically finite-time stable. The theoretical analysis is given to prove the stability of the closed-loop system. The tracking performance of the designed controller is demonstrated by comparative simulation studies and experiment results.

Dynamic modeling and aperiodically intermittent strategy for adaptive finite-time synchronization control of the multi-weighted complex transportation networks with multiple delays* *Project supported by the National Natural Science Foundation of China (Grant No. 61803275), Liaoning Provincial Department of Education Scientific Research Fund Project, China (Grant Nos. lnjc202018 and lnzd202007), Liaoning BaiQianWan Talents Program (Grant No. 2017076), and Liaoning Province Doctor Starting

The idea of network splitting according to time delay and weight is introduced. Based on the cyber physical systems (CPS), a class of multi-weighted complex transportation networks with multiple delays is modeled. The finite-time synchronization of the proposed complex transportation networks model is studied systematically. On the basis of the theory of stability, the technique of adaptive control, aperiodically intermittent control and finite-time control, the aperiodically intermittent adaptive finite-time synchronization controller is designed. The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays. In addition, the conditions for the existence of finite time synchronization have been discussed in detail. And the specific value of the settling finite time for synchronization is obtained. Moreover, the outer coupling configuration matrices are not required to be irreducible or symmetric. Finally, simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.

A New Settling-time Estimation Protocol to Finite-time Synchronization of Impulsive Memristor-Based Neural Networks.

In this article, the issues of finite-time synchronization and finite-time adaptive synchronization for the impulsive memristive neural networks (IMNNs) with discontinuous activation functions (DAFs) and hybrid impulsive effects are probed into and elaborated on, where the stabilizing impulses (SIs), inactive impulses (IIs), and destabilizing impulses (DIs) are taken into account, respectively. Not resembling several earlier works, a more extensive range of impulses in the context of impulsive effects has been analyzed without using the known average impulsive interval strategy (AIIS). In light of the theories of differential inclusions and set-valued map, as well as impulsive control, new sufficient criteria with respect to the estimated settling time for synchronization of the related IMNNs are established using two types of switching control approaches, which sufficiently utilize information from not only the SIs, DIs, and DAFs but also the impulse sequences. Two simulation experiments are presented to the efficiency of the proposed results.

A New Robust Finite-Time Synchronization and Anti-Synchronization Method for Uncertain Chaotic Systems by Using Adaptive Estimator and Terminal Sliding Mode Approaches

In this paper, a new robust adaptive finite-time synchronization method has been proposed for chaotic systems by considering model uncertainties and external disturbances. The finite-time synchronization between master and slave systems is achieved under terminal sliding mode control method. The most important innovation of this paper is designing of an adaptive law to estimate the unknown upper bound of the disturbance and uncertainty. To handle the disturbances/uncertainties with unknown upper bounds and get finite-time synchronization, the adaptive law is combined with terminal sliding mode control method. Numerical simulation results and comparative studies show the effectiveness of proposed method.

Adaptive finite-time synchronization of stochastic mixed time-varying delayed memristor-based neural networks

This paper focuses on the finite-time synchronization of stochastic memristor-based neural networks with time-varying discrete and distributed delays and discontinuous nonlinear functions via the adaptive state-feedback controller. Based on the theories of set-valued mappings and stochastic differential inclusions, the finite-time synchronization of the drive neural network and response neural network is transformed into the finite-time stabilization problem of the corresponding error stochastic neural network. By choosing an appropriate Lyapunov function and employing the theory of stochastic finite-time stability, we present a method to design the control gain parameters. Finally, an example verifies the validity of the proposed method.

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.

Adaptive finite-time synchronization control for fractional-order complex-valued dynamical networks with multiple weights

In this paper, finite-time synchronization issue of fractional-order complex-valued dynamical networks with multiple weights is addressed. Multiple weights are pulled into consideration, which makes our model more practical and general than single-weight one. Combining Lyapunov method with graph-theoretic method and making use of the theory of complex functions, finite-time synchronization criteria for fractional-order complex-valued dynamical networks with multiple weights are established by using feedback control and adaptive control, respectively. Furthermore, the settling time of synchronization is effectively estimated, which is connected with the order of fractional derivative, the parameters of control and topological structure of networks. Eventually, numerical simulations are exhibited to demonstrate the validity of theoretical results and analyse the relationship between the settling time of synchronization and the order of fractional derivative with the parameters of control.

Finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays

This paper is concerned with the issue of the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays. For synchronizing the drive-response memristive neural networks in finite time, an adaptive state-feedback controller and a state-feedback controller are proposed, respectively. Then by using the theories of differential inclusions and set-valued map, the synchronization issue of drive-response memristive neural networks with discontinuous activation functions and mixed time-varying delays is transformed into the stabilization issue of the error system. Moreover, based on the stability theory, Forti Lemma and Hardy inequality, some novel algebraic synchronization criteria are deduced to ensure the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays under the adaptive state-feedback controller and the state-feedback controller. And the settling times for finite-time adaptive synchronization and finite-time synchronization are given. Furthermore, it is hard to estimate the initial conditions for a large system, so the settling times in this paper are not dependent on initial conditions of system. Finally, an example is provided to demonstrate the effectiveness of the obtained results.

Adaptive Finite-Time Synchronization for Complex Dynamical Network with Different Dimensions of Nodes and Time-Varying Outer Coupling Structures

In this paper, we investigate finite-time synchronization problems of complex dynamical networks with different dimensions of nodes, which contain unknown periodically coupling structures and bounded time-varying delay. Based on finite-time stability theory, the inequality techniques, and the properties of Kronecker production of matrices, some useful finite-time synchronization criteria for complex dynamical network with unknown periodical couplings have been obtained. In addition, with proper adaptive periodical learning law designed, the unknown periodical couplings have been estimated successfully. Finally, some simulation examples are performed to verify the theoretical findings.

Finite-Time Synchronization for a Class of Dynamical Complex Networks with Nonidentical Nodes and Uncertain Disturbance

This paper investigates the finite-time synchronization for a class of linearly coupled dynamical complex networks with both nonidentical nodes and uncertain disturbance. A set of controllers are designed such that the considered system can be finite-timely synchronized onto the target node. Based on the stability of the error equation, the Lyapunov function method and the linear matrix inequality technique, several sufficient conditions are derived to ensure the finite-time synchronization, and applied to the case of identical nodes and the one without uncertain disturbance. Also the adaptive finite-time synchronization is discussed. A numerical example is given to show the effectiveness of the main results obtained.

Finite-time synchronization of time-delayed neural networks with unknown parameters via adaptive control

In this paper, the problem of finite-time adaptive synchronization is investigated for two different delayed neural networks with unknown parameters. Two adaptive control approaches are designed in order to synchronize the neural networks in finite time. The first controller fully involves the information of time-varying delay and the second one is delay-independent under the case that time-varying delay is unknown. By utilizing the Lyapunov stability theory, sufficient conditions are proposed to guarantee the finite-time synchronization of the addressed neural networks. In addition, the settling time for synchronization is estimated. Finally, two numerical simulations are used to illustrate the correctness and effectiveness of the proposed methods.

Adaptive Finite-Time Synchronization Control for Teleoperation System With Varying Time Delays

In practical application, the synchronization tracking of teleoperation system requires the fast speed and strong robustness. It is the ideal control effect that the synchronization errors between master and slave robots can converge to zero in finite time. In this paper, we propose the new nonsingular terminal sliding mode and the adaptive finite-time control method for position tracking in teleoperation system. First, a novel nonsingular terminal sliding mode is designed to provide higher tracking precision and robustness. Second, the radial basis function neural networks are applied to solve dynamic uncertainties, and the adaptive laws are proposed to estimate the uncertain parameters and upper bounds of estimation. Then, the corresponding finite-time controllers of master and slave robots are designed. Third, based on the Lyapunov stability theory, synchronization performances of the closed-loop system are proved to be stable state and finite time. Finally, simulations are achieved, and some comparisons with two nonsingular terminal sliding mode control schemes and two PD methods are shown. The simulation results verify the effectiveness of the proposed control laws.

Adaptive Finite-Time Synchronization of Neutral Type Dynamical Network with Double Derivative Coupling

This paper discusses the problem of adaptive finite-time synchronization for neutral type dynamical network model with double derivative coupling. Based on the Lyapunov functional theory, inequality theorem, and adaptive control technique, some synchronization criteria of neutral type dynamical network are established by using adaptive finite-time control, which is different from the existence of finite-time synchronization of neutral type network using LMI and matrix equality constraint methods. Moreover, when the dynamics nodes of the neutral type network contain delay or no delay, the control gain of the response network are also provided. Finally, the effectiveness of the synchronization criteria proposed in this paper is verified by numerical simulations.