Class Of Fractional-order Neural Networks Research Articles

Synchronization for fractional-order neural networks with unbounded delays

This paper deals with synchronization analysis problem for a class of fractional-order neural networks with unbounded delays. Using the Lyapunov function method combined with fractional Halanay inequality, we derive a novel sufficient condition for asymptotic stability of the error system resulting in two neural networks are synchronized. The obtained conditions are given in terms of linear matrix inequalities, which therefore can be efficiently checked. A numerical example is proposed to illustrate the effectiveness of the obtained results.

New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach

This paper deals with the problem of finite-time passivity analysis for a class of fractional-order neural networks with constant time delay. Firstly, based on the existing passivity definition, some new concepts namely, finite-time passivity, finite-time input strict passivity, finite-time output strict passivity, and finite-time strict passivity are introduced in terms of Lyapunov function for fractional-order neural networks. In this paper, for the first time, by defining an appropriate controller and by exploiting the introduced definitions, some novel delay-dependent and order-dependent sufficient conditions ensuring the passivity performances are obtained for the addressed system. In addition, the finite-time stability conditions are also presented with an explicit formula for determining the value of setting time for stability. Finally, one numerical example is given to verify the effectiveness of the obtained theoretical results and the simulation results are provided for better understanding of the proposed problem.

Event-Triggered State Estimation for Fractional-Order Neural Networks

This paper is concerned with the problem of event-triggered state estimation for a class of fractional-order neural networks. An event-triggering strategy is proposed to reduce the transmission frequency of the output measurement signals with guaranteed state estimation performance requirements. Based on the Lyapunov method and properties of fractional-order calculus, a sufficient criterion is established for deriving the Mittag–Leffler stability of the estimation error system. By making full use of the properties of Caputo operator and Mittag–Leffler function, the evolution dynamics of measured error is analyzed so as to exclude the unexpected Zeno phenomenon in the event-triggering strategy. Finally, two numerical examples and simulations are provided to show the effectiveness of the theoretical results.

Passivity analysis of fractional-order neural networks with interval parameter uncertainties via an interval matrix polytope approach

This paper investigates the passivity analysis problem of a class of fractional-order neural networks with interval parameter uncertainties (FONNs-IPUs). The previous IPU processing methods are mainly divided into three categories, i.e., directly using the maximum upper bound matrix or the minimum lower bound matrix, using the combination of these two matrices, and using the maximum norm bound matrix. These methods have some shortcomings, for example, the coupling of information between different intervals and the effect of the negative sign of connection weight are not considered. In order to better analyze the passivity of FONNs-IPUs, firstly, a novel treatment approach of IPUs called interval matrix polytope is proposed, which considers all possible boundary information matrices and the sign of IPUs. Secondly, based on the interval matrix polytope approach, the passivity criteria of FONNs-IPUs are established in linear matrix inequality forms. Finally, the effectiveness of the theoretical results is illustrated by simulation example.

New results on finite-time stability for fractional-order neural networks with proportional delay

This paper investigates the finite-time stability for a class of fractional-order neural networks with proportional delay. By some analytic techniques, a generalized Gronwall integral inequality with proportional delay is established. Based on this new inequality, a criterion is derived to guarantee the finite-time stability of systems when the fractional order is between 1 and 2. Moreover, when the fractional order is between 0 and 1, a new criterion is developed to ensure the finite-time stability of systems. This criterion is experimentally proved to be less conservative than those in the previous works. Finally, the effectiveness of our criteria is supported by some numerical examples.

Bifurcation Mechanisation of a Fractional-Order Neural Network with Unequal Delays

The theme of bifurcation for a class of fractional-order neural networks (FONNs) with unique delay has been incalculably elucidated. It exhibits that multiple delays are capable of increasing the complicacy of realistic FONNs, but this has been insufficiently probed into. This paper attempts to conduct a research on the stability and bifurcation for a FONN with two unequal delays. By intercalating one delay and taking remnant delay as a bifurcation parameter, the incongruent critical values of diverse delays-induced bifurcations are exactly gained. Eventually, confirmation experiments are offered to endorse the procured theory.

Adaptive model-free synchronization of different fractional-order neural networks with an application in cryptography

In this paper, an adaptive model-free control method is designed to synchronize a class of fractional-order neural networks which has a vast application in engineering and industry. The theoretical and analytical concepts of the method are based on the fractional-order version of the Lyapunov stability theorem and using adaptive control theory. Moreover, it is worth to mention that, because of using of boundedness property in states of chaotic systems, there is no trace of nonlinear/linear dynamic terms of the system in the control approach. Also, for the application point of view, a new crypto-system algorithm is proposed based on the designed adaptive model-free method for encryption/decryption of unmanned aerial vehicle color images. Plus, numerical simulations are created to emphasize the usability of the method and algorithm. Finally, this point should be emphasized that security analysis including key space analysis, key sensitivity analysis, histogram analysis, information entropy analysis and correlation analysis of the crypto-system are provided to confirm the results of the crypto-system.

Multiple asymptotical stability analysis for fractional-order neural networks with time delays

This paper formulates the multiple asymptotical stability for a general class of fractional-order neural networks with time delays. By exploiting the properties of upper bounded and lower bounded functions derived from the addressed fractional-order neural network model as well as the comparison principle for fractional-order calculus, a lot of sufficient conditions are obtained to guarantee the existence and multiple asymptotical stability of the equilibrium points for the fractional-order neural networks with time delays. It reveals that the results gained in this paper are applicable to analyses of both multiple asymptotical stability and global asymptotical stability. Besides, three numerical examples are presented to showcase the validity of the derived results.

New Results on Robust Finite-Time Passivity for Fractional-Order Neural Networks with Uncertainties

In this paper, the robust finite-time passivity for a class of fractional-order neural networks with uncertainties is considered. Firstly, the definition of finite-time passivity of fractional-order neural networks is introduced. Then, by using finite-time stability theory and linear matrix inequality approach, new sufficient conditions that ensure the finite-time passivity of the fractional-order neural network systems are derived via linear matrix inequalities which can be effectively solved by various computational tools. Finally, three numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.

Multiple Mittag-Leffler stability and locally asymptotical ω-periodicity for fractional-order neural networks

Abstract Fractional calculus is a generalization of the conventional calculus. To describe the characteristic of the neural activity more veritably, fractional calculus is applied increasingly widely in the engineering fields. This paper presents theoretical results on the multiple Mittag-Leffler stability and locally S-asymptotical ω-periodicity for a general class of fractional-order neural networks. Several conditions are obtained to guarantee the invariance and boundedness of the solutions for this class of neural networks. By constructing appropriate Lyapunov functions, the multiple Mittag-Leffler stability is addressed. Furthermore, locally S-asymptotical ω-periodicity is discussed by reduction to absurdity and the final-value theorem. Some numerical examples with simulations are elaborated to showcase the effectiveness and validity of the obtained criteria.

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic Neural Networks with Backlash-Like Hysteresis

An adaptive fuzzy synchronization controller is designed for a class of fractional-order neural networks (FONNs) subject to backlash-like hysteresis input. Fuzzy logic systems are used to approximate the system uncertainties as well as the unknown terms of the backlash-like hysteresis. An adaptive fuzzy controller, which can guarantee the synchronization errors tend to an arbitrary small region, is given. The stability of the closed-loop system is rigorously analyzed based on fractional Lyapunov stability criterion. Fractional adaptation laws are established to update the fuzzy parameters. Finally, some simulation examples are provided to indicate the effectiveness and the robust of the proposed control method.

Observer-based sliding mode synchronization for a class of fractional-order chaotic neural networks

Observer design for nonlinear systems is very important in state-based stabilization, fault detection, chaos synchronization and secret communication. This paper deals with synchronization problem of a class of fractional-order neural networks (FONNs) based on system observer. Two sufficient conditions are given for the FONNs with known constant parameters and unknown time-varying parameters, respectively. Based on the fractional Lyapunov stability criterion, the proposed sliding mode observer can guarantee that the synchronization error between two identical FONNs converges to zero asymptotically, and all involved signals keep bounded. Finally, some simulation examples are provided to indicate the effectiveness of the proposed method.

Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

This paper studies the synchronization of fractional-order neural networks with multiple time delays. Based on an inequality of fractional-order and comparison principles of linear fractional equation with multiple time delays, some sufficient conditions for synchronization of master-slave systems are obtained. Example and related simulations are given to demonstrate the feasibility of the theoretical results.

Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty.

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Adaptive fuzzy synchronization for a class of fractional-order neural networks**Project supported by the National Natural Science Foundation of China (Grant Nos. 11401243 and 61403157), the Foundation for Distinguished Young Talents in Higher Education of Anhui Province, China (Grant No. GXYQZD2016257), the Fundamental Research Funds for the Central Universities of China (Grant No. GK201504002), the Natural Science Foundation for the Higher

In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors, are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters, fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.

Centralized Data-Sampling Approach for GlobalOt-αSynchronization of Fractional-Order Neural Networks with Time Delays

In this paper, the globalO(t-α)synchronization problem is investigated for a class of fractional-order neural networks with time delays. Taking into account both better control performance and energy saving, we make the first attempt to introduce centralized data-sampling approach to characterize theO(t-α)synchronization design strategy. A sufficient criterion is given under which the drive-response-based coupled neural networks can achieve globalO(t-α)synchronization. It is worth noting that, by using centralized data-sampling principle, fractional-order Lyapunov-like technique, and fractional-order Leibniz rule, the designed controller performs very well. Two numerical examples are presented to illustrate the efficiency of the proposed centralized data-sampling scheme.

Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments

Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results.

Global dissipativity of fractional-order neural networks with time delays and discontinuous activations

In this paper, we investigate global dissipativity of a class of fractional-order neural networks (FNNs) with time delays and discontinuous activations. The relevant results are in the sense of Caputo׳s fractional derivation. The existence of global solutions in Filippov׳s sense can be guaranteed by using nonsmooth analysis, differential inclusion theory and the properties of fractional calculus. Based on comparison theorem and stability theorem for a class of fractional-order systems with time delays, some new sufficient conditions are derived to ensure dissipativity of solutions, meanwhile, the globally attractive set is given. The obtained results enrich and enhance the earlier reports. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.

Stability Analysis and Synchronization for a Class of Fractional-Order Neural Networks

Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall–Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second method and linear feedback control, the synchronization problem between two fractional-order chaotic neural networks is investigated. Finally, several numerical examples are presented to justify the feasibility of the proposed methods.

Global Mittag-Leffler synchronization of fractional-order neural networks with discontinuous activations

This paper is concerned with the global Mittag-Leffler synchronization for a class of fractional-order neural networks with discontinuous activations (FNNDAs). We give the concept of Filippov solution for FNNDAs in the sense of Caputo’s fractional derivation. By using a singular Gronwall inequality and the properties of fractional calculus, the existence of global solution under the framework of Filippov for FNNDAs is proved. Based on the nonsmooth analysis and control theory, some sufficient criteria for the global Mittag-Leffler synchronization of FNNDAs are derived by designing a suitable controller. The proposed results enrich and enhance the previous reports. Finally, one numerical example is given to demonstrate the effectiveness of the theoretical results.