Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control

Aperiodically intermittent quantized control-based exponential synchronization of quaternion-valued inertial neural networks

Inertial neural networks are proposed via introducing an inertia term into the Hopfield models, which make their dynamic behavior more complex compared to the traditional first-order models. Besides, the aperiodically intermittent quantized control over conventional feedback control has its potential advantages on reducing communication blocking and saving control cost. Based on these facts, we are mainly devoted to exploring of exponential synchronization of quaternion-valued inertial neural networks under aperiodically intermittent quantized control. Firstly, a compact quaternion-valued aperiodically intermittent quantized control protocol is developed, which can mitigate significantly the complexity of theoretical derivation. Subsequently, several concise criteria involving matrix inequalities are formulated through constructing a type of Lyapunov functional and employing a direct analysis approach. The correctness of the obtained results eventually is verified by a typical example.

Stability for IT2 T-S fuzzy systems under alternate event-triggered control

In this paper, an alternate event-triggered control is proposed to achieve stability of interval type-2 Takagi-Sugeno fuzzy systems. Comparing with the existing literature, this new control strategy displays an almost complete aperiodic feature which eliminates the conservativeness caused by time-triggered property of the traditional aperiodically intermittent control. Moreover, with two events being triggered alternately in this control strategy through examining two predetermined conditions, the efficiency of control can be further improved and the resources consumption can be greatly reduced. By employing the Lyapunov function and graph theory, several stability criteria are rigorously demonstrated. In addition, Zeno behavior is excluded in our system through obtaining a positive lower bound of the time interval between two triggering points. Subsequently, the validity of the presented strategy is evidenced by single-link robot arms systems. Finally, a numerical example is given to lend insight into the feasibility of our theoretical results.

Fixed-time projective synchronization of delayed memristive neural networks via aperiodically semi-intermittent switching control

This paper studies the fixed-time projective synchronization problem for a class of delayed memristive neural networks via aperiodically semi-intermittent switching control. Instead of using the common traditional controller containing two power exponent terms, a novel aperiodically semi-intermittent switching controller is designed, containing only one power exponent term which serves as a function of the state of the error system. With the aid of the extended differential inclusion framework, the analysis method, and the inequality technique, some new sufficient conditions are derived to guarantee fixed-time projective synchronization for the considered systems. Compared with periodically semi-intermittent control methods, the control time width of each section in aperiodically semi-intermittent control can be adjusted. Especially, the settling time is directly reckoned, which is closely related to the number of neurons and the maximum ratio of the second subinterval span in each non-periodic span to all non-periodic time spans rather than the initial value. Additionally, the projection synchronization has a strong practicality, as the projection coefficient can be adjusted for different needs instead of being fixed. Meanwhile, the study improves some previous related works. Ultimately, a numerical example is given to substantiate the correctness of the obtained results.

Feedback Pinning Control of Successive Lag Synchronization on a Dynamical Network

In nature and human society, successive lag synchronization (SLS) is an important synchronization phenomenon. Compared with other synchronization patterns, the control theory of SLS is very lacking. To this end, we first introduce a complex dynamical network model with distributed delayed couplings, and design both the linear feedback pinning control and adaptive feedback pinning control to push SLS to the desired trajectories. Second, we obtain a series of sufficient conditions to achieve SLS to a desired trajectory with global stability. What is more, the control flow of SLS is given to show how to pick the pinned nodes accurately and set the feedback gains as well. Finally, since time-varying delay is common, we extend the constant time delay in SLS to be time varying. We find that the proposed pinning control schemes are still feasible if the coupling terms are appropriately adjusted. The theoretical results are verified on a neural network and the coupled Chua's circuits.

Resilient H∞ State Estimation for Discrete-Time Stochastic Delayed Memristive Neural Networks: A Dynamic Event-Triggered Mechanism

In this article, a resilient H_∞ approach is put forward to deal with the state estimation problem for a type of discrete-time delayed memristive neural networks (MNNs) subject to stochastic disturbances (SDs) and dynamic event-triggered mechanism (ETM). The dynamic ETM is utilized to mitigate unnecessary resource consumption occurring in the sensor-to-estimator communication channel. To guarantee resilience against possible realization errors, the estimator gain is permitted to undergo some norm-bounded parameter drifts. For the delayed MNNs, our aim is to devise an event-based resilient H_∞ estimator that not only resists gain variations and SDs but also ensures the exponential mean-square stability of the resulting estimation error system with a guaranteed disturbance attenuation level. By resorting to the stochastic analysis technique, sufficient conditions are acquired for the expected estimator and, subsequently, estimator gains are obtained via figuring out a convex optimization problem. The validity of the H_∞ estimator is finally shown via a numerical example.

Almost Surely Exponential Synchronization of Complex Dynamical Networks Under Aperiodically Intermittent Discrete Observations Noise

This article deals with the almost surely exponential synchronization issue for complex dynamical networks (CDNs) under noise control. Different from most of the existing literature, aperiodically intermittent discrete observations noise control is proposed. It is worth noting that the state in noise work time is discretely observed rather than continuously. Meanwhile, some sufficient conditions are presented based on stochastic analytical techniques and the Lyapunov method. Besides, the upper bounds of noise rest rate and the time lag between two consecutive observations are estimated. Moreover, it is clear that CDNs are easier to achieve the almost surely exponential synchronization when noise control gain becomes larger. To demonstrate the effectiveness and feasibility of analytical results, two applications about single-link robot arm systems as well as second-order oscillator systems are given. At the same time, some numerical simulations are exhibited.

Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks

This paper focuses on investigating the finite-time projective synchronization of Caputo type fractional-order complex-valued neural networks with time delay (FOCVNNTD). Based on the properties of fractional calculus and various inequality techniques, by constructing suitable the Lyapunov function and designing two new types controllers, i.e., feedback controller and adaptive controller, two sufficient criteria are derived to ensure the projective finite-time synchronization between drive and response systems, and the synchronization time can effectively be estimated. Finally, two numerical examples are presented to verify the effectiveness and feasibility of the proposed results.

Master-Slave Synchronization of Delayed Neural Networks With Time-Varying Control

This brief investigates the master-slave synchronization problem of delayed neural networks with general time-varying control. Assuming a linear feedback controller with time-varying control gain, the synchronization problem is recast into the stability problem of a delayed system with a time-varying coefficient. The main theorem is established in terms of the time average of the control gain by using the Lyapunov-Razumikhin theorem. Moreover, the proposed framework encompasses some general intermittent control schemes, such as the switched control gain with external disturbance and intermittent control with pulse-modulated gain function, while some useful corollaries are consequently deduced. Interestingly, our theorem also provides a solution for regaining stability under control failure. The validity of the theorem and corollaries is further demonstrated with numerical examples.

State bounding for fuzzy memristive neural networks with bounded input disturbances

This paper investigates the state bounding problem of fuzzy memristive neural networks (FMNNs) with bounded input disturbances. By using the characters of Metzler, Hurwitz and nonnegative matrices, this paper obtains the exact delay-independent and delay-dependent boundary ranges of the solution, which have less conservatism than the results in existing literatures. The validity of the results is verified by two numerical examples.

Intermittent boundary stabilization of stochastic reaction-diffusion Cohen-Grossberg neural networks

Cohen-Grossberg neural networks (CGNNs) play an important role in many applications and the stabilization of this system has been well studied. This study considers the exponential stabilization for stochastic reaction-diffusion Cohen-Grossberg neural networks (SRDCGNNs) by means of an aperiodically intermittent boundary control. Both SRDCGNNs without and with time-delays are discussed. By employing the spatial integral functional method and Poincare's inequality, criteria are derived to ensure the controlled systems achieve mean square exponential stabilization. Based on these criteria, the effects of diffusion item, control gains, the minimum control proportion and time-delays on exponential stability are analyzed. Examples are given to illustrate the effectiveness of the obtained theoretical results.

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.

Exponential synchronization of stochastic delayed memristive neural networks via a novel hybrid control

This paper investigates the exponential synchronization issue of stochastic delayed memristive neural networks (SDMNNs) via a novel hybrid control (HC), where impulsive instants are determined by the state-dependent trigger condition. The switching and quantification strategies are applied to the event-based impulsive controller to cope with the challenges induced concurrently by interval parameters, impulses, stochastic disturbance and time-varying delays. Furthermore, the control costs can be reduced and communication channels and bandwidths can be saved by using this designed controller. Then, novel Lyapunov functions and new analytical methods are constructed, which can be used to realize the exponential synchronization of SDMNNs via HC. Finally, a numerical simulation is provided to demonstrate our theoretical results.

Synchronization of Memristive Complex-Valued Neural Networks With Time Delays via Pinning Control Method

This article concentrates on the synchronization problem of memristive complex-valued neural networks (CVNNs) with time delays via the pinning control method. Different from general control schemes, the pinning control is beneficial to reduce the control cost by pinning the fractional nodes instead of all ones. By separating the complex-valued system into two equivalent real-valued systems and employing the Lyapunov functional as well as some inequality techniques, the asymptotic synchronization criterion is given to guarantee the realization of synchronization of memristive CVNNs. Meanwhile, sufficient conditions for exponential synchronization of the considered systems is also proposed. Finally, the validity of our proposed results is verified by a numerical example.

Memristor-Based Neural Network Circuit of Full-Function Pavlov Associative Memory With Time Delay and Variable Learning Rate

Most memristor-based Pavlov associative memory neural networks strictly require that only simultaneous food and ring appear to generate associative memory. In this article, the time delay is considered, in order to form associative memory when the food stimulus lags behind the ring stimulus for a certain period of time. In addition, the rate of learning can be changed with the length of time between the ring stimulus and food stimulus. A memristive neural network circuit that can realize Pavlov associative memory with time delay is designed and verified by the simulation results. The designed circuit consists of a synapse module, a voltage control module, and a time-delay module. The functions, such as learning, forgetting, fast learning, slow forgetting, and time-delay learning, are implemented by the circuit. The Pavlov associative memory neural network with time-delay learning provides a reference for further development of the brain-like systems.

Intermittent Discrete Observation Control for Synchronization of Stochastic Neural Networks

In this paper, to investigate the exponential synchronization of stochastic neural networks, a new periodically intermittent discrete observation control (PIDOC) is first proposed. Different from the existing periodically intermittent control, our control in control time is feedback control based on discrete-time state observations (FCDSOs) instead of a continuous-time one. By employing the Lyapunov method, graph theory, and theory of differential inclusions, the exponential synchronization of stochastic neural networks with a discontinuous right-hand side is realized by PIDOC and some sufficient conditions are presented. Especially, when control width tends to control period, PIDOC will be reduced to a general FCDSO and we give some detailed discussions. Then, we provide some corollaries about synchronization in mean square, asymptotical synchronization in mean square, and exponential synchronization of stochastic neural networks under FCDSO. Finally, some numerical simulations are provided to demonstrate our analytical results.

Improved Sliding Mode Control for Finite-Time Synchronization of Nonidentical Delayed Recurrent Neural Networks

This brief further explores the problem of finite-time synchronization of delayed recurrent neural networks with the mismatched parameters and neuron activation functions. An improved sliding mode control approach is presented for addressing the finite-time synchronization problem. First, by employing the drive-response concept and the synchronization error of drive-response systems, a novel integral sliding mode surface is constructed such that the synchronization error can converge to zero in finite time along the constructed integral sliding mode surface. Second, a suitable sliding mode controller is designed by relying on Lyapunov stability theory such that all system state trajectories can be driven onto the predefined sliding mode surface in finite time. Moreover, it is found that the presented control approach can be conveniently verified and does not need to solve any linear matrix inequality (LMI) to guarantee the finite-time synchronization of delayed recurrent neural networks. Finally, three numerical examples are exploited to demonstrate the effectiveness of the presented control approach.

Finite-Time Stability of Delayed Memristor-Based Fractional-Order Neural Networks

This paper studies one type of delayed memristor-based fractional-order neural networks (MFNNs) on the finite-time stability problem. By using the method of iteration, contracting mapping principle, the theory of differential inclusion, and set-valued mapping, a new criterion for the existence and uniqueness of the equilibrium point which is stable in finite time of considered MFNNs is established when the order α satisfies . Then, when , on the basis of generalized Gronwall inequality and Laplace transform, a sufficient condition ensuring the considered MFNNs stable in finite time is given. Ultimately, simulation examples are proposed to demonstrate the validity of the results.

Quasi-Synchronization of Delayed Memristive Neural Networks via Region-Partitioning-Dependent Intermittent Control

This paper aims at investigating the master-slave quasi-synchronization of delayed memristive neural networks (MNNs) by proposing a region-partitioning-dependent intermittent control. The proposed method is described by three partitions of non-negative real region and an auxiliary positive definite function. Whether the control input is imposed on the slave system or not is decided by the dynamical relationships among the three subregions and the auxiliary function. From these ingredients, several succinct criteria with the associated co-design procedure are presented such that the synchronization error converges to a predetermined level. The proposed intermittent control scheme is also applied to the event-triggered control, and an intermittent event-triggered mechanism is devised to investigate the quasi-synchronization of MNNs correspondingly. Such mechanism eliminates the events in rest time, and then it reduces the amount of samplings. Finally, two illustrative examples are presented to verify the effectiveness of our theoretical results.

Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme

In this paper, the real-valued memristive neural networks (MNNs) are extended to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established. The problem of master-slave synchronization of this type of networks is investigated in this paper. Two types of controllers are designed: the traditional feedback controller and the event-triggered controller. Corresponding synchronization criteria are then derived based on Lyapunov method. Moreover, it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy proposed in this work. Finally, corresponding simulation examples are proposed to demonstrate the correctness of the proposed results derived in this work.

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.

Closed-loop control of nonlinear neural networks: The estimate of control time and energy cost

This paper concentrates on an estimate of the upper bounds for control time and energy cost of a class of nonlinear neural networks (NNs). By constructing the appropriate closed-loop controller u^S and utilizing the inequality technique, sufficient conditions are proposed to guarantee achieving control target in finite time of the considered systems. Then, the estimate of the upper bounds for the control energy cost of the designed controller u^S is proposed. Our results provide a new controller which can ensure the realization of finite time control and energy consumption control for a class of nonlinear NNs. Meanwhile, the obtained results contribute to qualitative analysis of some nonlinear systems. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

Global Anti-Synchronization of Complex-Valued Memristive Neural Networks With Time Delays

This paper formulates a class of complex-valued memristive neural networks as well as investigates the problem of anti-synchronization for complex-valued memristive neural networks. Under the concept of drive-response, several sufficient conditions for guaranteeing the anti-synchronization are given by employing suitable Lyapunov functional and some inequality techniques. The proposed results of this paper are less conservative than existing literatures due to the characteristics of memristive complex-valued neural networks. Moreover, the proposed results are easy to be validated with the parameters of system itself. Finally, two examples with numerical simulations are showed to demonstrate the efficiency of our theoretical results.

Fixed-time synchronization of coupled memristor-based neural networks with time-varying delays

This paper investigates the fixed-time synchronization of Memristor-based neural networks with time-delayed and coupled. In view of the retarded differential inclusions theory, drive-response concept, the authors give some sufficient conditions to ensure the fixed-time synchronization issue of Memristor-based neural networks. Two novel state-feedback controllers and adaptive controller are designed such that the system can realize fixed-time complete synchronization by means of inequality technique and non-smooth analysis theory. It is worth to point out that, without desiring values of the initial conditions or under the linear growth condition of the controller, the settling time of fixed-time synchronization is estimated. Finally, an example is given to further illustrate the benefits of the proposed switched control approach.

Novel aperiodically intermittent stability criteria for Markovian switching stochastic delayed coupled systems

This paper concerns p th moment exponential stability of stochastic coupled systems with multiple time-varying delays, and Markovian switching topologies via intermittent control. Compared with previous research results, the mathematical model of this kind of stochastic coupled systems with multiple time-varying delays and Markovian switching topologies is studied for the first time. The intermittent control designed in this paper is aperiodical, which is more general in practice. Moreover, the restriction between control width and time delays is removed. By constructing a new differential inequality on delayed dynamical systems with Markovian switching topologies and combining the graph-theoretic approach with M-matrix theory, two sufficient criteria are derived to guarantee p th moment exponential stability of systems. Moreover, the exponential convergence rate has a close relationship with the maximum ratio of the rest width to the aperiodical time span (the sum of the control width and the rest width). Finally, we employ the theoretical results to study the exponential stability of stochastic coupled oscillators with multiple time-varying delays and Markovian switching topologies. Meanwhile, a numerical example is presented to illustrate the effectiveness and feasibility of the proposed results.

Event-Triggered State Estimation for Delayed Stochastic Memristive Neural Networks With Missing Measurements: The Discrete Time Case

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time stochastic memristive neural networks (DSMNNs) with time-varying delays and missing measurements. The DSMNN is subject to both the additive deterministic disturbances and the multiplicative stochastic noises. The missing measurements are governed by a sequence of random variables obeying the Bernoulli distribution. For the purpose of energy saving, an event-triggered communication scheme is used for DSMNNs to determine whether the measurement output is transmitted to the estimator or not. The problem addressed is to design an event-triggered estimator such that the dynamics of the estimation error is exponentially mean-square stable and the prespecified disturbance rejection attenuation level is also guaranteed. By utilizing a Lyapunov-Krasovskii functional and stochastic analysis techniques, sufficient conditions are derived to guarantee the existence of the desired estimator, and then, the estimator gains are characterized in terms of the solution to certain matrix inequalities. Finally, a numerical example is used to demonstrate the usefulness of the proposed event-triggered state estimation scheme.