Synchronization control of a class of memristor-based recurrent neural networks

Sliding mode control for uncertain fractional-order reaction-diffusion memristor neural networks with time delays

This paper investigates a sliding mode control method for a class of uncertain delayed fractional-order reaction-diffusion memristor neural networks. Different from most existing literature on sliding mode control for fractional-order reaction-diffusion systems, this study constructs a linear sliding mode switching function and designs the corresponding sliding mode control law. The sufficient theory for the globally asymptotic stability of the sliding mode dynamics are provided, and it is proven that the sliding mode surface is finite-time reachable under the proposed control law, with an estimate of the maximum reaching time. Finally, a numerical test is presented to validate the effectiveness of the theoretical analysis.

Passivity and passification of fractional-order memristive neural networks with time delays

A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.

Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance

Synchronization of memristive neural networks (MNNs) by using network control scheme has been widely and deeply studied. However, these researches are usually restricted to traditional continuous-time control methods for synchronization of the first-order MNNs. In this paper, we study the robust exponential synchronization of inertial memristive neural networks (IMNNs) with time-varying delays and parameter disturbance via event-triggered control (ETC) scheme. First, the delayed IMNNs with parameter disturbance are changed into first-order MNNs with parameter disturbance by constructing proper variable substitutions. Next, a kind of state feedback controller is designed to the response IMNN with parameter disturbance. Based on feedback controller, some ETC methods are provided to largely decrease the update times of controller. Then, some sufficient conditions are provided to realize robust exponential synchronization of delayed IMNNs with parameter disturbance via ETC scheme. Moreover, the Zeno behavior will not happen in all ETC conditions shown in this paper. Finally, numerical simulations are given to verify the advantages of the obtained results such as anti-interference performance and good reliability.

Quasisynchronization of Memristive Neural Networks With Communication Delays via Event-Triggered Impulsive Control

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.

Memristor Neural Networks for Linear and Quadratic Programming Problems

This article introduces a new class of memristor neural networks (NNs) for solving, in real-time, quadratic programming (QP) and linear programming (LP) problems. The networks, which are called memristor programming NNs (MPNNs), use a set of filamentary-type memristors with sharp memristance transitions for constraint satisfaction and an additional set of memristors with smooth memristance transitions for memorizing the result of a computation. The nonlinear dynamics and global optimization capabilities of MPNNs for QP and LP problems are thoroughly investigated via a recently introduced technique called the flux-charge analysis method. One main feature of MPNNs is that the processing is performed in the flux-charge domain rather than in the conventional voltage-current domain. This enables exploiting the unconventional features of memristors to obtain advantages over the traditional NNs for QP and LP problems operating in the voltage-current domain. One advantage is that operating in the flux-charge domain allows for reduced power consumption, since in an MPNN, voltages, currents, and, hence, power vanish when the quick analog transient is over. Moreover, an MPNN works in accordance with the fundamental principle of in-memory computing, that is, the nonlinearity of the memristor is used in the dynamic computation, but the same memristor is also used to memorize in a nonvolatile way the result of a computation.

Global Exponential Stability of Memristive Neural Networks With Mixed Time-Varying Delays

This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.

A Unified Framework Design for Finite-Time and Fixed-Time Synchronization of Discontinuous Neural Networks

In this article, the problems of finite-time/fixed-time synchronization have been investigated for discontinuous neural networks in the unified framework. To achieve the finite-time/fixed-time synchronization, a novel unified integral sliding-mode manifold is introduced, and corresponding unified control strategies are provided; some criteria are established for selecting suitable parameters for solving the related issue, namely, the dynamics of neural network can reach the designed sliding-mode manifold in finite/fixed time, and stay on it thereafter. Moreover, the estimations of setting time are given out. The established unified framework can bring in various protocols by choosing the different parameters of controllers and sliding-mode manifold, which extend previous related results. Finally, some numerical examples are introduced to show the effectiveness and superiority of resulting conclusions.

Anti-Synchronization of Delayed State-Based Switched Inertial Neural Networks

In this article, global anti-synchronization control for a class of state-based switched inertial neural networks (SBSINNs) with time-varying delays is considered. Based on the hybrid control strategies and Lyapunov stability theory, several criteria are obtained to ensure global anti-synchronization of the underlying SBSINNs. Furthermore, we consider the global asymptotic anti-synchronization directly from the SBSINNs themselves with a nonreduced-order method. Finally, a numerical simulation is given to illustrate the effectiveness of the results.

Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control

This paper considers the drive-response synchronization of memristive neural networks (MNNs) with unknown parameters, where the unbounded discrete and bounded distributed time-varying delays are involved. Aiming at the unknown parameters of MNNs, the updating law of weight in response system and the gain of adaptive controller are proposed to realize the synchronization of delayed MNNs. In view of the limited communication and bandwidth, the event-triggered mechanism is introduced to adaptive control, which not only decreases the times of controller update and the amount of data sending out but also enables synchronization when parameters of MNNs are unknown. In addition, a relative threshold strategy, which is relative to fixed threshold strategy, is proposed to increase the inter-execution intervals and to improve the control effect. When the parameters of MNNs are known, the algebraic criteria of synchronization are established via event-triggered state feedback control by exploiting inequality techniques and calculus theorems. Finally, one simulation is presented to validate the effectiveness of the proposed results.

Fuzzy Observer Constraint Based on Adaptive Control for Uncertain Nonlinear MIMO Systems With Time-Varying State Constraints

This article presents an adaptive output feedback approach of nonlinear multi-input-multi-output (MIMO) systems with time-varying state constraints and unmeasured states. An adaptive approximator is designed to approximate the unknown nonlinear functions existing in the state-constrained systems with immeasurable states. To deal with the tracking problem of such systems, a state observer with time-varying barrier Lyapunov functions (BLFs) is introduced in the controller design procedure. The backstepping design with time-varying BLFs is utilized to guarantee that all system states remain within the time-varying-constrained interval. The constant constraint is only the special case of the time-varying constraint which is more general in the real systems. The proposed control approach guarantees that all signals in the closed-loop systems are bounded and the tracking errors converge to a bounded compact set, and time-varying full-state constraints are never violated. A simulation example is given to confirm the feasibility of the presented control approach in this article.

Exponential Stabilization of Inertial Memristive Neural Networks With Multiple Time Delays

This article investigates the global exponential stabilization (GES) of inertial memristive neural networks with discrete and distributed time-varying delays (DIMNNs). By introducing the inertial term into memristive neural networks (MNNs), DIMNNs are formulated as the second-order differential equations with discontinuous right-hand sides. Via a variable transformation, the initial DIMNNs are rewritten as the first-order differential equations. By exploiting the theories of differential inclusion, inequality techniques, and the comparison strategy, the p th moment GES ( p ≥ 1 ) of the addressed DIMNNs is presented in terms of algebraic inequalities within the sense of Filippov, which enriches and extends some published results. In addition, the global exponential stability of MNNs is also performed in the form of an M-matrix, which contains some existing ones as special cases. Finally, two simulations are carried out to validate the correctness of the theories, and an application is developed in pseudorandom number generation.

Reliable control for positive switched systems with random nonlinearities

This paper proposes a reliable control of positive switched systems with random nonlinearities which may induce the security problem of the systems. The random nonlinearities are governed by stochastic variables obeying the Bernoulli distribution. A switched linear copositive Lyapunov function is employed for the systems. Using a matrix decomposition approach, the gain matrix of controller is formulated by the sum of nonnegative and non-positive components. A reliable controller is designed for positive switched systems with actuator faults by virtue of linear programming. Under the designed reliable controller, the systems can resist some possible security risks triggered by random nonlinearities and actuator faults. The obtained approach is developed for systems subject to exogenous disturbances. Finally, two examples are provided to verify the validity of the obtained results.

Global Stabilization of Fuzzy Memristor-Based Reaction-Diffusion Neural Networks

This article investigates the global stabilization problem of Takagi-Sugeno fuzzy memristor-based neural networks with reaction-diffusion terms and distributed time-varying delays. By using the Green formula and proposing fuzzy feedback controllers, several algebraic criteria dependent on the diffusion coefficients are established to guarantee the global exponential stability of the addressed networks. Moreover, a simpler stability criterion is obtained by designing an adaptive fuzzy controller. The results derived in this article are generalized and include some existing ones as special cases. Finally, the validity of the theoretical results is verified by two examples.

Nonlinear Networks With Mem-Elements: Complex Dynamics via Flux-Charge Analysis Method

Nonlinear dynamic memory elements, as memristors, memcapacitors, and meminductors (also known as mem-elements), are of paramount importance in conceiving the neural networks, mem-computing machines, and reservoir computing systems with advanced computational primitives. This paper aims to develop a systematic methodology for analyzing complex dynamics in nonlinear networks with such emerging nanoscale mem-elements. The technique extends the flux-charge analysis method (FCAM) for nonlinear circuits with memristors to a broader class of nonlinear networks N containing also memcapacitors and meminductors. After deriving the constitutive relation and equivalent circuit in the flux-charge domain of each two-terminal element in N , this paper focuses on relevant subclasses of N for which a state equation description can be obtained. On this basis, salient features of the dynamics are highlighted and studied analytically: 1) the presence of invariant manifolds in the autonomous networks; 2) the coexistence of infinitely many different reduced-order dynamics on manifolds; and 3) the presence of bifurcations due to changing the initial conditions for a fixed set of parameters (also known as bifurcations without parameters). Analytic formulas are also given to design nonautonomous networks subject to pulses that drive trajectories through different manifolds and nonlinear reduced-order dynamics. The results, in this paper, provide a method for a comprehensive understanding of complex dynamical features and computational capabilities in nonlinear networks with mem-elements, which is fundamental for a holistic approach in neuromorphic systems with such emerging nanoscale devices.

H∞ and l2-l∞ state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol

In this paper, a protocol-based finite-horizon H_∞ and l₂-l_∞ estimation approach is put forward to solve the state estimation problem for discrete-time memristive neural networks (MNNs) subject to time-varying delays and energy-bounded disturbances. The Round-Robin protocol is utilized to mitigate unnecessary network congestion occurring in the sensor-to-estimator communication channel. For the delayed MNNs, our aim is to devise an estimator that not only ensures a prescribed disturbance attenuation level over a finite time-horizon, but also keeps the peak value of the estimation error within a given range. By resorting to the Lyapunov-Krasovskii functional method, the delay-dependent criteria are formulated that guarantee the existence of the desired estimator. Subsequently, the estimator gains are obtained via figuring out a bank of convex optimization problems. The validity of our estimator is finally shown via a numerical example.

Lagrange Stability and Finite-Time Stabilization of Fuzzy Memristive Neural Networks With Hybrid Time-Varying Delays

This paper focuses on Lagrange exponential stability and finite-time stabilization of Takagi-Sugeno (T-S) fuzzy memristive neural networks with discrete and distributed time-varying delays (DFMNNs). By resorting to theories of differential inclusions and the comparison strategy, an algebraic condition is developed to confirm Lagrange exponential stability of the underlying DFMNNs in Filippov's sense, and the exponentially attractive set is estimated. When external input is not considered, global exponential stability of DFMNNs is derived directly, which includes some existing ones as special cases. Furthermore, finite-time stabilization of the addressed DFMNNs is analyzed by exploiting inequality techniques and the comparison approach via designing a nonlinear state feedback controller. The boundedness assumption of activation functions is removed herein. Finally, two simulations are presented to demonstrate the validness of the outcomes, and an application is performed in pseudorandom number generation.

New Criteria on Global Stabilization of Delayed Memristive Neural Networks With Inertial Item

In this paper, we are concerned with global stabilization for a kind of delayed memristive neural network with an inertial term. By building a new Lyapunov functional and designing a feedback controller, we obtain some new results on global stabilization of the addressed delayed memristive inertial neural networks (MINNs). An adaptive control strategy is also designed to realize the global stabilization. Compared with the reduced-order method used in the existing literature, we consider the stabilization directly from the MINNs themselves without a reduced-order method. In addition, the new results proposed here are shown as algebraic criteria, which are easy to test. At last, some simulations are given to show the validity of the derived criteria.

Fixed-time synchronization of delayed Cohen-Grossberg neural networks based on a novel sliding mode

This paper has discussed fixed-time synchronization of discontinuous Cohen-Grossberg neural networks with time-varying delays and matched disturbances based on sliding mode control technology. First, a novel sliding-mode surface is established. And, the dynamics on the sliding-mode surface can be achieved in the fixed time by employing the Gudermannian function. Then, considering the effect of delay, two different control schemes are introduced to ensure the fixed time reachability of the sliding mode. In addition, some useful criteria are given out for fixed-time synchronization of neural networks, and the setting time is formulated in a straightforward way. Finally, some examples and simulations are presented to verify the validity of the proposed results.

Finite-time synchronization of memristor neural networks via interval matrix method

In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.

Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method

In this paper, we propose a novel analysis method to investigate the finite-time synchronization (FTS) control problem of the drive-response inertial memristive neural networks (IMNNs) with mixed time-varying delays (MTVDs). Firstly, an improved control scheme is proposed under the delay-independent conditions, which can work even when the past state cannot be measured or the specific time delay function is unknown. Secondly, based on the assumption of bounded activation functions, we establish a new Lemma, which can effectively deal with the difficulties caused by memristive connection weights and MTVDs. Thirdly, by constructing a suitable Lyapunov functions and using a new inequality method, novel sufficient conditions to ensure the FTS for the discussed IMNNs are obtained. Compared with the existing results, our results obtained in a more general framework are more practical. Finally, some numerical simulations are given to substantiate the effectiveness of the theoretical results.

Passivity Analysis for Quaternion-Valued Memristor-Based Neural Networks With Time-Varying Delay

This paper is concerned with the problem of global exponential passivity for quaternion-valued memristor-based neural networks (QVMNNs) with time-varying delay. The QVMNNs can be seen as a switched system due to the memristor parameters are switching according to the states of the network. This is the first time that the global exponential passivity of QVMNNs with time-varying delay is investigated. By means of a nondecomposition method and structuring novel Lyapunov functional in form of quaternion self-conjugate matrices, the delay-dependent passivity criteria are derived in the forms of quaternion-valued linear matrix inequalities (LMIs) as well as complex-valued LMIs. Furthermore, the asymptotical stability criteria can be obtained from the proposed passivity criteria. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

Stabilization of Second-Order Memristive Neural Networks With Mixed Time Delays via Nonreduced Order

In this brief, we investigate a class of second-order memristive neural networks (SMNNs) with mixed time-varying delays. Based on nonsmooth analysis, the Lyapunov stability theory, and adaptive control theory, several new results ensuring global stabilization of the SMNNs are obtained. In addition, compared with the reduced-order method used in the existing research studies, we consider the global stabilization directly from the SMNNs themselves without the reduced-order method. Finally, we give some numerical simulations to show the effectiveness of the results.

Perceptrons from memristors

Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. Our results show that both perform as expected for perceptrons, including satisfying Minsky-Papert's theorem. As a consequence of the Universal Approximation Theorem, they also show that memristors are universal function approximators. By using memristors for both the neurons and the synapses, our models pave the way for novel memristor-based neural network architectures and algorithms. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms.

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks.

Exponential Stabilization of Fuzzy Memristive Neural Networks With Hybrid Unbounded Time-Varying Delays

This paper is concerned with exponential stabilization for a class of Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with unbounded discrete and distributed time-varying delays. Under the framework of Filippov solutions, algebraic criteria are established to guarantee exponential stabilization of the addressed FMNNs with hybrid unbounded time delays via designing a fuzzy state feedback controller by exploiting inequality techniques, calculus theorems, and theories of fuzzy sets. The obtained results in this paper enhance and generalize some existing ones. Meanwhile, a general theoretical framework is proposed to investigate the dynamical behaviors of various neural networks with mixed infinite time delays. Finally, two simulation examples are performed to illustrate the validity of the derived outcomes.