New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes

Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.

Quasi-synchronization of drive-response systems with parameter mismatch via event-triggered impulsive control

In this paper, an event-triggered impulsive control method is proposed to investigate the quasi-synchronization of drive-response systems with parameter mismatch, which integrates the event-triggered control and impulsive control together. The impulsive instants are event-triggered and determined by a certain state-dependent triggering law. Sufficient conditions for achieving quasi-synchronization are achieved. The synchronization error is shown to be no more than a nonzero bound. Furthermore, Zeno-behavior of impulsive instants is excluded. Finally, a numerical example is presented to verify the validity of the theoretical results.

Bounded synchronization for uncertain master-slave neural networks: An adaptive impulsive control approach

This paper investigates the bounded synchronization of the discrete-time master-slave neural networks (MSNNs) with uncertainty. To deal with the unknown parameter in the MSNNs, a parameter adaptive law combined with the impulsive mechanism is proposed to improve the estimation efficiency. Meanwhile, the impulsive method also is applied to the controller design for saving the energy. In addition, a novel time-varying Lyapunov functional candidate is employed to depict the impulsive dynamical characteristic of the MSNNs, wherein a convex function related to the impulsive interval is used to obtain a sufficient condition for bounded synchronization of the MSNNs. Based on the above condition, the controller gain is calculated utilizing an unitary matrix. An algorithm is proposed to reduce the boundary of the synchronization error by optimizing its parameters. Finally, a numerical example is provided to illustrate the correctness and the superiority of the developed results.

Adaptive Synchronization for Delayed Chaotic Memristor-Based Neural Networks

This article considers the adaptive synchronization problem of delayed chaotic memristor-based neural networks (MNNs). Note that MNNs are modeled as continuous systems in the flux-voltage-time (ϕ,x,t) domain where memristors are viewed as continuous systems based on HP memristors. New adaptive controllers of MNNs are proposed, where controllers are both on memristors in the flux-time (ϕ,t) domain and neurons in the voltage-time (x,t) domain. Based on the Lyapunov method, Barbalat's lemma, differential mean value Theorem, and other inequality techniques, completed synchronization criteria for delayed chaotic MNNs are derived. In the end, two examples are given to demonstrate the validity of the derived results.

Multistability of Switched Neural Networks With Gaussian Activation Functions Under State-Dependent Switching

This article presents theoretical results on the multistability of switched neural networks with Gaussian activation functions under state-dependent switching. It is shown herein that the number and location of the equilibrium points of the switched neural networks can be characterized by making use of the geometrical properties of Gaussian functions and local linearization based on the Brouwer fixed-point theorem. Four sets of sufficient conditions are derived to ascertain the existence of 7^p₁5^p₂3^p₃ equilibrium points, and 4^p₁3^p₂2^p₃ of them are locally stable, wherein p₁ , p₂ , and p₃ are nonnegative integers satisfying 0 ≤ p₁+p₂+p₃ ≤ n and n is the number of neurons. It implies that there exist up to 7ⁿ equilibria, and up to 4ⁿ of them are locally stable when p₁=n . It also implies that properly selecting p₁ , p₂ , and p₃ can engender a desirable number of stable equilibria. Two numerical examples are elaborated to substantiate the theoretical results.

Extended Robust Exponential Stability of Fuzzy Switched Memristive Inertial Neural Networks With Time-Varying Delays on Mode-Dependent Destabilizing Impulsive Control Protocol

This article investigates the problem of robust exponential stability of fuzzy switched memristive inertial neural networks (FSMINNs) with time-varying delays on mode-dependent destabilizing impulsive control protocol. The memristive model presented here is treated as a switched system rather than employing the theory of differential inclusion and set-value map. To optimize the robust exponentially stable process and reduce the cost of time, hybrid mode-dependent destabilizing impulsive and adaptive feedback controllers are simultaneously applied to stabilize FSMINNs. In the new model, the multiple impulsive effects exist between two switched modes, and the multiple switched effects may also occur between two impulsive instants. Based on switched analysis techniques, the Takagi-Sugeno (T-S) fuzzy method, and the average dwell time, extended robust exponential stability conditions are derived. Finally, simulation is provided to illustrate the effectiveness of the results.

Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control

In this study, we consider the fixed-time synchronization problem for stochastic memristor-based neural networks (MNNs) via two different controllers. First, a new stochastic differential equation is established using differential inclusions and set-valued maps. Next, two kinds of control protocols are designed, including a nonlinear delayed state feedback control scheme and a novel adaptive control strategy, by which fixed-time synchronization of MNNs can be achieved. Then based on stochastic analysis techniques and a Lyapunov function, some sufficient criteria are obtained to ensure that stochastic MNNs achieve stochastic fixed-time synchronization in probability. In addition, the upper bound of the settling time is estimated. Finally, simulation results are provided to demonstrate the validity of the proposed schemes.

Adaptive Synchronization of Reaction-Diffusion Neural Networks and Its Application to Secure Communication

This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks.

The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control

In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.

Adaptive Antisynchronization of Multilayer Reaction-Diffusion Neural Networks

In this paper, an antisynchronization problem is considered for an array of linearly coupled reaction-diffusion neural networks with cooperative-competitive interactions and time-varying coupling delays. The interaction topology among the neural nodes is modeled by a multilayer signed graph. The state evolution of a neuron in each layer of the coupled neural network is described by a reaction-diffusion equation (RDE) with Dirichlet boundary conditions. Then, the collective dynamics of the multilayer neural network are modeled by coupled RDEs with both spatial diffusion coupling and state coupling. An edge-based adaptive antisynchronization strategy is proposed for each neural node to achieve antisynchronization by using only local information of neighboring nodes. Furthermore, when the activation functions of the neural nodes are unknown, a linearly parameterized adaptive antisynchronization strategy is also proposed. The convergence of the antisynchronization errors of the nodes is analyzed by using a Lyapunov-Krasovskii functional method and a structural balance condition. Finally, some numerical simulations are presented to demonstrate the effectiveness of the proposed antisynchronization strategies.

O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations

This paper investigates O(t^-α)-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t^-α)-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays.

Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales

The existed results of Lagrange stability and finite-time synchronization for memristive recurrent neural networks (MRNNs) are scale-free on time evolvement, and some restrictions appear naturally. In this paper, two novel scale-limited comparison principles are established by means of inequality techniques and induction principle on time scales. Then the results concerning Lagrange stability and global finite-time synchronization of MRNNs on time scales are obtained. Scaled-limited Lagrange stability criteria are derived, in detail, via nonsmooth analysis and theory of time scales. Moreover, novel criteria for achieving the global finite-time synchronization are acquired. In addition, the derived method can also be used to study global finite-time stabilization. The proposed results extend or improve the existed ones in the literatures. Two numerical examples are chosen to show the effectiveness of the obtained results.

Synchronization Control of Neural Networks With State-Dependent Coefficient Matrices

This brief is concerned with synchronization control of a class of neural networks with state-dependent coefficient matrices. Being different from the existing drive-response neural networks in the literature, a novel model of drive-response neural networks is established. The concepts of uniformly ultimately bounded (UUB) synchronization and convex hull Lyapunov function are introduced. Then, by using the convex hull Lyapunov function approach, the UUB synchronization design of the drive-response neural networks is proposed, and a delay-independent control law guaranteeing the bounded synchronization of the neural networks is constructed. All present conditions are formulated in terms of bilinear matrix inequalities. By comparison, it is shown that the neural networks obtained in this brief are less conservative than those ones in the literature, and the bounded synchronization is suitable for the novel drive-response neural networks. Finally, an illustrative example is given to verify the validity of the obtained results.

Passivity of memristor-based BAM neural networks with different memductance and uncertain delays

This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov-Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Function projective synchronization of memristor-based Cohen-Grossberg neural networks with time-varying delays

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen-Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.