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1.
《Journal of The Franklin Institute》2022,359(18):10653-10675
Without considering identical systems, this paper investigates the finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks (FDMNN) by designing a novel fractional sliding mode controller (SMC). Due to the existence of memristor, the research is under the framework of Filippov solution. We firstly construct a fractional integral sliding mode surface (SMS). Based on sliding mode control theory and Lyapunov stability theorem, a novel fractional SMC is proposed to realize the lag projective synchronization of nonidentical FDMNN in finite time, and the synchronization setting time is less conservative than the existing results. As the special cases, some sufficient conditions are extended to projective synchronization, lag synchronization, anti-lag synchronization of nonidentical FDMNN in finite time, which improve and enrich some existing results. At last, a simulation example is given to prove the validity of the conclusions.  相似文献   

2.
Based on the idea of tracking control and stability theory of fractional-order systems, a novel synchronization approach for fractional order chaotic systems is proposed. We prove that the synchronization between drive system and response system with different fractional order q can be achieved, and the synchronization between different fractional-order chaotic systems with different fractional order q can be achieved. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.  相似文献   

3.
Projective synchronization is a type of chaos synchronization where the response system states are scaled replicas of the drive system states. This paper deals with the propagation of projective synchronization in a series connection of N chaotic discrete-time drive systems and N response systems. By exploiting an observer-based approach, the paper demonstrates that dead-beat projective synchronization (i.e., exact synchronization in finite time for any scaling factor) is achieved between the nth drive and nth response systems. In particular, it is shown that projective synchronization starts from the innermost (Nth) drive-response system pair and propagates toward the outermost (first) drive-response system pair. Only a single scalar synchronizing signal connects the cascaded drive and response systems. Finally, an example illustrates the propagation of different types of chaos synchronization in a series connection consisting of a Gingerbreadman map, a third order hyperchaotic Henon map and a Lozi map.  相似文献   

4.
Finite-time inter-layer projective synchronization (FIPS) of Caputo fractional-order two-layer networks (FTN) based on sliding mode control (SMC) technique is investigated in this article. Firstly, in order to realize the FIPS of FTN, a fractional-order integral sliding mode surface (SMS) is established. Then, through the theory of SMC, we design a sliding mode controller (SMCr) to ensure the appearance of sliding mode motion. According to the fractional Lyapunov direct method, the trajectories of the system are driven to the proposed SMS, and some novel sufficient conditions for FIPS of FTN are derived. Furthermore, as two special cases of FIPS, finite-time inter-layer synchronization and finite-time inter-layer anti-synchronization for the FTN are studied. Finally, this paper takes the fractional-order chaotic Lü’s system and the fractional-order chaotic Chen’s system as the isolated node of the first layer system and the second layer system, respectively. And the numerical simulations are given to demonstrate the feasibility and validity of the proposed theoretical results.  相似文献   

5.
This paper deals with the function projective synchronization problem of two different chaotic systems with unknown and perturbed parameters. The parameter perturbations are assumed to appear in both drive and response systems, which perturbed about the nominal parameter values. A new robust function projective synchronization method is proposed, which is able to overcome random uncertainties of all model parameters. Corresponding numerical simulations are performed to verify and illustrate the analytical results.  相似文献   

6.
The computational complexity of the numerical simulation of fractional chaotic system and its synchronization control is O(N2) compared with O(N) for integer chaotic system, where N is step number and O is the computational complexity. In this paper, we propose optimizing methods to solve fractional chaotic systems, including equal-weight memory principle, improved equal-weight memory principle, chaotic combination and fractional chaotic precomputing operator. Numerical examples show that the combination of these algorithms can simulate fractional chaotic system and synchronize the fractional master and slave systems accurately. The presented algorithms for simulation and synchronization of fractional chaotic system are up to 1.82 and 1.75 times faster than the original implementation respectively.  相似文献   

7.
This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker.  相似文献   

8.
The chaotic behaviors in the fractional order unified system are numerically investigated. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional order unified system with order less than 3. The lowest order we found to have chaos in this system is 2.76. Chaos synchronization of the fractional order unified system is theoretically and numerically studied using the one-way coupling method. The suitable conditions for achieving synchronization of the fractional order differential system are derived by using the Laplace transform theory. It is noticed that the time required for achieving synchronization of the drive system and the response system and the synchronization effect sensitively depend on the coupling strength. Numerical simulations are performed to verify the theoretical analysis.  相似文献   

9.
This article aims to study fixed-time projective lag synchronization(FXPLS) and preassigned-time projective lag synchronization(PTPLS) of hybrid inertial neural networks(HINNs) with state-switched and discontinuous activation functions(DAFs). By constructing new hybrid fixed-time control and based on theory of non-smooth analysis, we achieve novel results on FXPLS for such HINNs. Through designing novel hybrid preassigned-time control, new criteria on PTPLS of the HINNs is also taken into account. And as distinct from recent works, the FXPLS and PTPLS results are established via non-variable substitution and in a more generalized framework than common synchronization, which also has more extensive practical applications. Finally, example simulations are displayed to set forth the validity of the acquired FXPLS and PTPLS.  相似文献   

10.
This paper investigates the problem of complete synchronization of chaotic systems with unknown parameters. An adaptive control scheme based on a feedback passivity approach is proposed. The convergence of the synchronization error is guaranteed. The unified chaotic and hyperchaotic Lü systems are taken as illustrative examples. The feasibility and effectiveness of the proposed scheme are demonstrated through numerical simulations.  相似文献   

11.
By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.  相似文献   

12.
This paper studies drive-response synchronization in fractional-order memristive neural networks (FMNNs) with switching jumps mismatch. A comparison theorem for fractional-order systems with variable order is provided first. Theories of fractional order Filippov differential inclusions are used to treat FMNNs because the parameters of FMNNs are state dependent and the FMNNs has discontinuous right hand sides. Based on Laplace transform and linear feedback control, some lag quasi-synchronization conditions are obtained with variable order α: 0?<?α?<?1 and 1?<?α?<?2. The error level is estimated and the larger synchronization regain is discussed. Finally, two numerical examples are presented to illustrate the effectiveness of our proposed theorems.  相似文献   

13.
This paper focuses on the issue of finite-time stability for a general form of nonlinear systems subject to state-dependent delayed impulsive controller. Based on the Lyapunov theory and the impulsive control theory, sufficient conditions for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained. Additionally, we apply theoretical results to finite-time synchronization of chaotic systems and design the effective state-dependent delayed impulsive controllers in terms of techniques of linear matrix inequality (LMI). Finally, we present two numerical examples of finite-time synchronization of cellular neural networks and Chua’s circuit to verify the effectiveness of our results.  相似文献   

14.
Synchronization of two identical chaotic systems with matched and mismatched perturbations by utilizing adaptive sliding mode control (ASMC) technique is presented in this paper. The sliding surface function is specially designed based on the Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. The designed tracking controller can not only suppress the mismatched perturbations when the controlled dynamics (master–slave) are in the sliding mode, but also drive the trajectories of synchronization errors into a small bounded region whose size can be adjusted through the designed parameters. Adaptive mechanisms are employed in the proposed control scheme for adapting the unknown upper bounds of the perturbations, and the stability of overall controlled synchronization systems is guaranteed. The comparison of the proposed chaotic synchronization technique with an existing generalized chaotic synchronization (GCS) method as well as application of the proposed control method to secure communications is also demonstrated in this paper.  相似文献   

15.
Because of the high sensitivity of chaotic systems to their initial conditions, synchronization of chaotic systems with uncertain parameters has been a challenging problem especially in noisy environment. Since synchronization of the transmitter and receiver systems involves recursive estimation, recursive nonlinear filters are called for and the extended Kalman (EKF) filter and unscented Kalman (UKF) filter have been applied. However, such suboptimal filters incur high synchronization errors and provide no capacity for uncertain environment, which motivated the use of the neural filter for chaotic synchronization in this paper. The neural filter, which is a recurrent neural network, can approximate the minimum-variance to any degree. Furthermore, the neural filter can adapt to a uncertain environment without online filter weight adjustment, which is computationally efficient. Numerical experiments show that the chaotic synchronization scheme based on the neural filter outperforms those based on EKF and UKF by a large margin.  相似文献   

16.
In this article, a novel synchronization scheme is proposed to achieve hybrid modified function projective synchronization (HMFPS) in two different dimensional complex nonlinear systems with fully unknown parameters. In the complex space, the response system are asymptotically synchronized up to the different order’s drive system by the state transformation with a scaling function matrix, and all of unknown parameters in both drive and response systems are achieved to be identified. Based on the Lyapunov stability theory, an adaptive controller and updated laws of parameters are developed. Respectively on the ways of increased order and reduced order, the corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.  相似文献   

17.
This paper analyses the weak projective synchronization (WPS) of the parameter mismatched memristive neural networks (MNNs) with stochastic disturbance and time delays via impulsive control. Complete synchronization cannot achieve because of the projective factor and mismatched parameters. Therefore, the WPS of practical MNNs under impulsive control strategy is studied. The augmented systems are built to utilize more information of the system and reduce the constraint conditions. Meanwhile, two types of comparison principles are used owing to the impulsive controller with and without time delays. Then, sufficient criteria for the exponential convergence of systems are obtained under the positive and negative effects of impulses. Finally, the validity of the theoretical results is verified by simulations of different conditions.  相似文献   

18.
This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.  相似文献   

19.
In this paper, we investigate the Lyapunov stability for general nonlinear systems by means of the event-triggered impulsive control (ETIC), in which the delayed impulses are greatly taken into account. On the basis of impulsive control theory, a set of Lyapunov-based sufficient conditions for uniform stability and asymptotic stability of the addressed system are obtained in the framework of event triggering, under which Zeno behavior is excluded. It is shown that our results depend on the event-triggering mechanism (ETM) and the time delays. Then the mentioned results are applied to synchronization of chaotic systems and moreover, a kind of impulsive controllers is designed in form of linear matrix inequality (LMI), where the delayed impulsive control can be activated only when events happen. In the end, to illustrate the validity of the mentioned theoretical results, we present a numerical example.  相似文献   

20.
The present study investigates the fixed-time synchronization issue for delayed complex networks under intermittent pinning control. Different from some existing semi-intermittent controllers for finite/fixed-time synchronization, our pinning controller is designed in a complete intermittent way. In order to address the encountered theoretical analysis difficulties, a new differential inequality lemma is developed, which is suitable for the fixed-time synchronization studies under periodic or aperiodic complete intermittent control. Then, by using Lyapunov theory and pinning control approach, sufficient conditions are proposed which can guarantee the aperiodically completely intermittent-controlled delayed complex networks realizing fixed-time pinning synchronization. Moreover, the settling time is explicitly estimated, which is irrelevant to the initial values of our network systems. Additionally, as a special case, the scenario of periodic complete intermittent control is also discussed. At last, some simulation examples are utilized to confirm our theoretical outcomes.  相似文献   

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