Memristive Recurrent Neural Networks Research Articles

Event-based nonfragile state estimation for memristive recurrent neural networks with stochastic cyber-attacks and sensor saturations

Abstract This paper addresses the issue of nonfragile state estimation for memristive recurrent neural networks with proportional delay and sensor saturations. In practical engineering, numerous unnecessary signals are transmitted to the estimator through the networks, which increases the burden of communication bandwidth. A dynamic event-triggered mechanism, instead of a static event-triggered mechanism, is employed to select useful data. By constructing a meaningful Lyapunov–Krasovskii functional, a delay-dependent criterion is derived in terms of linear matrix inequalities for ensuring the global asymptotic stability of the augmented system. In the end, two numerical simulations are employed to illustrate the feasibility and validity of the proposed theoretical results.

Secure defense control for memristive recurrent neural networks under denial-of-service attacks with quantized sampled-data signals

Secure defense control for memristive recurrent neural networks under denial-of-service attacks with quantized sampled-data signals

Memristive Recurrent Neural Network Circuit for Fast Solving Equality-Constrained Quadratic Programming With Parallel Operation

Equality-constrained quadratic programming (QP) has been one of the most basic and typical problems in the Internet of Things domain. In big data scenarios, how to quickly and accurately solve the problem in hardware has not been realized. Therefore, in this article, a memristive recurrent neural circuit that can parallel solve the QP problem in real time is proposed. First, a new memristive synaptic array is designed that can simultaneously implement parallel reading and writing. On the basis of this structure, a new neural network circuit based on memristor is designed that can perform large-scale recursive operations by parallel methods. This circuit can solve the equality-constrained QP problem in different situations by using such real-time programmable memristor arrays processing in memory. The PSpice simulation results show that the problem can be solved with 99.8% precision. Based on practical verification, the neural circuit experiment on PCB is presented with 97.34% precision. Moreover, the circuit has good robustness under the interference of weight value. And, it has an advantage in processing time compared with FPGA.

Time-Delay Memristive Recurrent Neural Network and Its Complex Dynamics

This paper focuses on the hybrid effects of memristor characteristics, coupling coefficient and time-delay on the recurrent neural network. We construct a novel time-delay recurrent neural network based on a passive hyperbolic tangent memristor, whose instability condition at equilibrium points is judged according to the Routh criterion. Under the changes of the memristor internal parameter, coupling coefficient and time-delay, some complex dynamic behaviors, including chaos and various coexisting attractors, of the time-delay memristive recurrent neural network are observed in detail through the bifurcation diagram, the largest Lyapunov exponent, and the basin of attraction. Finally, the theoretical results are verified by the circuit simulation through MULTISIM.

Synchronization of fractional-order memristive recurrent neural networks via aperiodically intermittent control.

In this paper, synchronization of fractional-order memristive recurrent neural networks via aperiodically intermittent control is investigated. Considering the special properties of memristor neural network, differential inclusion theory is introduced. Similar to the aperiodically strategy of integer order, aperiodically intermittent control strategy of fractional order is proposed. Under the framework of Fillipov's solution, based on the intermittent strategy of fractional order systems and the properties Mittag-Leffler, sufficient criteria of aperiodically intermittent strategy are obtained by constructing appropriate Lyapunov functional. Some comparisons are given to demonstrate the advantages of aperiodically strategy. A simulation example is given to illustrate the derived conclusions.

Quasi-Synchronization of Fractional-Order Complex-Valued Memristive Recurrent Neural Networks with Switching Jumps Mismatch

In this paper, quasi-synchronization of fractional-order complex-valued memristive recurrent neural networks with switching jumps mismatch is investigated. Complex-valued systems are divided into two real-valued systems, which can avoid discussing the strict constraints in complex-value domain. A lemma is derived to deal with the mismatch. Under the framework of Fillipov’s solution, the sufficient conditions of quasi-synchronization are obtained by constructing suitable Lyapunov function. Besides, the error levels of quasi-synchronization are obtained. Some comparisons with existing results are given to verify the improvements. Two numerical simulations are given to demonstrate the effectiveness of the derived conditions.

Memory analysis for memristors and memristive recurrent neural networks

Traditional recurrent neural networks are composed of capacitors, inductors, resistors, and operational amplifiers. Memristive neural networks are constructed by replacing resistors with memristors. This paper focuses on the memory analysis, i.e., the initial value computation, of memristors. Firstly, we present the memory analysis for a single memristor based on memristors&#x02BC mathematical models with linear and nonlinear drift. Secondly, we present the memory analysis for two memristors in series and parallel. Thirdly, we point out the difference between traditional neural networks and those that are memristive. Based on the current and voltage relationship of memristors, we use mathematical analysis and SPICE simulations to demonstrate the validity of our methods.

Passivity and passification of memristive recurrent neural networks with multi-proportional delays and impulse

The research direction of this paper is passivity and passification of memristive recurrent neural networks (MRNNs) with multi-proportional delays and impulse. Preparing for passive analysis, the model of MRNNs is transformed into the general recurrent neural networks (RNNs) model through the way of non-smooth analysis. Utilizing the proper Lyapunov–Krasovskii functions constructed in this paper and the common matrix inequalities technique, a novel condition is derived which is sufficient to make sure that system is passive. In addition, it relaxes the condition that the symmetric matrices are all required to be positive definite. The final results are presented by linear matrix inequalities (LMIs) and its verification is easy to be carried out by the LMI toolbox. And there are several numerical examples showing the effectiveness and correctness of the derived criteria.

The Intermittent Control Synchronization of Complex-Valued Memristive Recurrent Neural Networks with Time-Delays

In this paper, the intermittent control synchronization of complex-valued memristive recurrent neural networks with time-delays is investigated. As a generalization on the real-valued memristive recurrent neural networks, complex-valued memristive recurrent neural networks own more complicated properties. In complex-valued domain, bounded and analytic complex-valued activation functions do not exist. Some assumptions about activation functions in real-valued domain cannot be applied directly to complex-valued fields. By appropriate transformation, complex-valued memristive recurrent neural networks can be divided into real parts and imaginary parts, which can avoid discussing the bounded and analytic. In the framework of differential inclusion theory and Lyapunov method, sufficient criteria of intermittent control synchronization are established. Finally, a simulation is given to verify the validity and feasibility of the sufficient conditions.

A multi-layer memristive recurrent neural network for solving static and dynamic image associative memory

Recent years have seen increased attention being given to recurrent neural networks in associative memory applications. The activation function is the core of the recurrent neural network for associative memory, but its hardware implementation is quite complicated. A novel multi-layer memristive recurrent neural network (MMRNN) is proposed, in which nano-scaled element memristor is employed as activation function. Its stability is proved by numerical analysis, which provides the theoretical premise for its application. There are three advantages: (i) Since the memristor is a passive device, the activation function circuit will be low power consumption; (ii) It can not only simplify the hardware circuit, but also facilitate the implementation of VLSI; (iii) MMRNN can realize the associative memory of both static and dynamic images. A series of theoretical analysis and numerical simulations demonstrated the effectiveness of the proposed MMRNN. The study helps to explore the dynamic image associative memory, and provides a new effective way to realize the associative memory of video.

Exponential Synchronization of Stochastic Memristive Recurrent Neural Networks Under Alternate State Feedback Control

This paper solves the exponential synchronization problem of two memristive recurrent neural networks with both stochastic disturbance and time-varying delays via periodically alternate state feedback control. First, a periodically alternate state feedback control rule is designed. Then, on the basis of the Lyapunov stability theory, some novel sufficient conditions guaranteeing exponential synchronization of drive-response stochastic memristive recurrent neural networks via periodically alternate state feedback control are derived. In contrast to some previous works about synchronization of memristive recurrent neural networks, the obtained results in this paper are not difficult to be validated, and complement, extend and generalize the earlier papers. Lastly, an illustrative example is provided to indicate the effectiveness and applicability of the obtained theoretical results.

Exponential Stabilization of Stochastic Memristive Recurrent Neural Networks Under Periodically Intermittent State Feedback Control

AbstractIn this paper, the exponential stabilization problem is investigated for a class of memristive time‐varying delayed neural networks with stochastic disturbance via periodically intermittent state feedback control. First, a periodically intermittent state feedback control rule is designed for the exponential stabilization of stochastic memristive time‐varying delayed neural networks. Then, by adopting appropriate Lyapunov‐Krasovskii functionals in light of the Lyapunov stability theory, some novel stabilization criteria are obtained to guarantee exponential stabilization of stochastic memristive time‐varying delayed neural networks via periodically intermittent state feedback control. Compared with existing results on stabilization of stochastic memristive time‐varying delayed neural networks, the obtained stabilization criteria in this paper are not difficult to verify. Finally, an illustrative example is given to illustrate the validity of the obtained results.

Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions

Abstract This paper is concerned with the finite-time synchronization for a class of drive-response fractional-order memristive recurrent neural networks with discontinuous activation functions. By using the theories of fractional-order differential inclusions and set-valued map, the finite-time synchronization problem for a class of drive-response fractional-order memristive recurrent neural networks with discontinuous activation functions is formulated under the framework of Filippov solution. Then, two novel state feedback controllers are designed according to state feedback control technique. In particular, based on the fractional Lyapunov stability theory, the finite-time stability theory and Young inequality, some novel algebraic synchronization criteria are obtained to ensure the finite-time synchronization of a class of drive-response fractional-order memristive recurrent neural networks with discontinuous activation functions. Moreover, we give the estimation of the upper bound of the settling time for synchronization. Finally, a simulation example is given to show the effectiveness of our theoretical results.

Finite‐time synchronization and adaptive synchronization of memristive recurrent neural networks with delays

SummaryThis paper solves the finite‐time synchronization and adaptive synchronization problems of drive‐response memristive recurrent neural networks with delays under two control methods. First, the state‐feedback control rule containing delays and the adaptive control rule are designed for realizing synchronization of drive‐response memristive recurrent neural networks in finite time. Then, on the basis of the Lyapunov stability theory, many algebraic sufficient conditions are obtained to guarantee finite‐time synchronization and adaptive synchronization of drive‐response memristive recurrent neural networks via two control methods, which are easily verified. In addition, the estimation of the upper bounds of the settling time of finite‐time synchronization is obtained. Lastly, to illustrate the effectiveness of the obtained theoretical results, two examples are given.

A new method for exponential synchronization of memristive recurrent neural networks

This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs). A novel approach, switching matrix approach, is considered to study synchronization of MRNNs for the first time. All the matrices in the constructed Lyapunov–Krasovskii functional (LKF) are switching according to different switching rules. Based on the switching matrix approach, a new synchronization criterion is established in the form of linear matrix inequalities (LMIs). Compared with some existing methods, the switching matrix approach is more flexible and can improve the synchronization performance with low control cost. Finally, numerical simulations are provided to show the effectiveness and advantages of the proposed results.

Design disturbance attenuating controller for memristive recurrent neural networks with mixed time-varying delays

This paper investigates the design of disturbance attenuating controller for memristive recurrent neural networks (MRNNs) with mixed time-varying delays. By applying the combination of differential inclusions, set-valued maps and Lyapunov–Razumikhin, a feedback control law is obtained in the simple form of linear matrix inequality (LMI) to ensure disturbance attenuation of memristor-based neural networks. Finally, a numerical example is given to show the effectiveness of the proposed criteria.

Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays

This paper deals with the stabilization problem of memristive recurrent neural networks with inertial items, discrete delays, bounded and unbounded distributed delays. First, for inertial memristive recurrent neural networks (IMRNNs) with second-order derivatives of states, an appropriate variable substitution method is invoked to transfer IMRNNs into a first-order differential form. Then, based on nonsmooth analysis theory, several algebraic criteria are established for the global stabilizability of IMRNNs under proposed feedback control, where the cases with both bounded and unbounded distributed delays are successfully addressed. Finally, the theoretical results are illustrated via the numerical simulations.

Pinning Synchronization of Coupled Memristive Recurrent Neural Networks with Mixed Time-Varying Delays and Perturbations

In this paper, the pinning synchronization of coupled memristive recurrent neural networks (MNNs) with mixed time-varying delays and perturbations is investigated. Precisely, the considered coupled MNNs include the non-delay, discrete time-varying delays, distributed time delays, impulsive perturbations and stochastic perturbations. Comparing with the existing results, the new and simple feedback controller and adaptive feedback controller are designed to achieve exponential synchronization with pinning schemes. Based on the suitable Lyapunov functional and the definition of pinning control, with the aid of inequality techniques and differential inclusions theory, some effective and novel sufficient conditions are obtained to guarantee the synchronization of our proposed model. Finally, numerical examples are given to illustrate the effectiveness and reasonable of our theoretical results.

Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays

This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs) with heterogeneous time-varying delays (HTVDs). First, a novel discontinuous feedback control is designed, in which a tunable scalar is introduced. The tunable scalar makes the controller more flexible in reducing the upper bound of the control gain. Based on this control scheme, the double integral term can be successfully used to construct the LKF. Second, New method for tackling memristive synaptic weights and new estimation technique are presented. Third, based on the LKF and estimation technique, synchronization criterion is derived. In comparison with existing results, the established criterion is less conservatism thanks to the double integral term of the LKF. Finally, numerical simulations are presented to validate the effectiveness and advantages of the proposed results.

Region stability analysis and tracking control of memristive recurrent neural network

Memristor is firstly postulated by Leon Chua and realized by Hewlett–Packard (HP) laboratory. Research results show that memristor can be used to simulate the synapses of neurons. This paper presents a class of recurrent neural network with HP memristors. Firstly, it shows that memristive recurrent neural network has more compound dynamics than the traditional recurrent neural network by simulations. Then it derives that n dimensional memristive recurrent neural network is composed of 22n2 sub neural networks which do not have a common equilibrium point. By designing the tracking controller, it can make memristive neural network being convergent to the desired sub neural network. At last, two numerical examples are given to verify the validity of our result.