Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains

Protocol-Based Synchronization of Stochastic Jumping Inertial Neural Networks Under Image Encryption Application

This work investigates the protocol-based synchronization of inertial neural networks (INNs) with stochastic semi-Markovian jumping parameters and image encryption application. The semi-Markovian jumping process is adopted to characterize INNs under sudden complex changes. To conserve the limited available network bandwidth, an adaptive event-driven protocol (AEDP) is developed in the corresponding semi-Markovian jumping INNs (S-MJINNs), which not only reduces the amount of data transmission but also avoids the Zeno phenomenon. The objective is to construct an adaptive event-driven controller so that the drive and response systems maintain synchronous relationships. Based on the appropriate Lyapunov functional, integral inequality, and free weighting matrix, novel criteria are derived to realize the synchronization. Moreover, the desired adaptive event-driven controller is designed under a semi-Markovian jumping process. The proposed method is demonstrated through a numerical example and an image encryption process.

Stability and synchronization of fractional-order reaction-diffusion inertial time-delayed neural networks with parameters perturbation

This study is centered around the dynamic behaviors observed in a class of fractional-order generalized reaction-diffusion inertial neural networks (FGRDINNs) with time delays. These networks are characterized by differential equations involving two distinct fractional derivatives of the state. The global uniform stability of FGRDINNs with time delays is explored utilizing Lyapunov comparison principles. Furthermore, global synchronization conditions for FGRDINNs with time delays are derived through the Lyapunov direct method, with consideration given to various feedback control strategies and parameter perturbations. The effectiveness of the theoretical findings is demonstrated through three numerical examples, and the impact of controller parameters on the error system is further investigated.

Protocol-based control for semi-Markov reaction-diffusion neural networks

This paper addresses the asynchronous control problem for semi-Markov reaction-diffusion neural networks (SMRDNNs) under probabilistic event-triggered protocol (PETP) scheduling. A semi-Markov process with a deterministic switching rule is introduced to characterize the stochastic behavior of these networks, effectively mitigating the impacts of arbitrary switching. Leveraging statistical data on communication-induced delays, a novel PETP is proposed that adjusts transmission frequencies through a probabilistic delay division method. The dynamic adjustment of event trigger conditions based on real-time neural network is realized, and the responsiveness of the system is enhanced, which is of great significance for improving the performance and reliability of the communication system. Additionally, a dynamic asynchronous model is introduced that more accurately captures the variations between system modes and controller modes in the network environment. Ultimately, the efficacy and superiority of the developed strategies are validated through a simulation example.

Dynamic Event-Triggered Control for GSES of Memristive Neural Networks Under Multiple Cyber-Attacks

In this article, the dynamic event-triggered control problem of memristive neural networks (MNNs) under multiple cyber-attacks is considered. A novel dynamic event-triggering scheme (DETS) and the corresponding event-triggered controller are proposed by taking into consideration both denial-of-service and deception attacks (DoS-DAs). Then, a key lemma is established to show that the dynamic event-triggered controller can be used to solve the globally stochastically exponential stability (GSES) issue of concerned MNN under multiple cyber-attacks. Meanwhile, a novel Lyapunov functional is proposed based on the actual sampling pattern. It is shown that under our proposed dynamic event-triggered controller and Lyapunov functional, the concerned MNN can achieve GSES in the presence of DoS-DAs. In addition, our results include relevant results on event-triggered control of MNN with static event-triggering scheme (SETS) or without cyber-attacks as special cases. The effectiveness of the proposed event-triggered controller under multiple cyber-attacks is illustrated by a simulation example.

Exponential Stabilization of Semi-Markov Reaction-Diffusion Memristive NNs via Event-Based Spatially Pointwise-Piecewise Switching Control

This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.

Ultra-Short-Term Offshore Wind Power Prediction Based on PCA-SSA-VMD and BiLSTM

In order to realize the economic dispatch and safety stability of offshore wind farms, and to address the problems of strong randomness and strong time correlation in offshore wind power forecasting, this paper proposes a combined model of principal component analysis (PCA), sparrow algorithm (SSA), variational modal decomposition (VMD), and bidirectional long- and short-term memory neural network (BiLSTM). Firstly, the multivariate time series data were screened using the principal component analysis algorithm (PCA) to reduce the data dimensionality. Secondly, the variable modal decomposition (VMD) optimized by the SSA algorithm was applied to adaptively decompose the wind power time series data into a collection of different frequency components to eliminate the noise signals in the original data; on this basis, the hyperparameters of the BiLSTM model were optimized by integrating SSA algorithm, and the final power prediction value was obtained. Ultimately, the verification was conducted through simulation experiments; the results show that the model proposed in this paper effectively improves the prediction accuracy and verifies the effectiveness of the prediction model.

Preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters

This study addresses the preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters. Employing a preassigned-time stable control strategy, two distinct controllers with varying power exponent parameters are designed to ensure that synchronization can be achieved within a predefined time frame. Unlike existing finite/fixed-time results, a priori specification of the settling time is addressed. Furthermore, Green's formula and boundary conditions are efficiently applied to overcome potential symmetry loss. Additionally, the activation function's constraint range is more lenient compared to existing constraints. Finally, the effectiveness of the presented methods are demonstrated through two examples.

The Optimization of Control Parameters: Finite-Time Bipartite Synchronization of Memristive Neural Networks With Multiple Time Delays via Saturation Function

This article studies the memristive neural networks with multiple time delays (MNNsMTDs). The topology of networks is signed, which contains both cooperative and competitive relationships. Two controllers without time delays are designed to achieve finite-time bipartite synchronization (FTBS) and practical FTBS (PFTBS) of MNNsMTDs. A novel controller with a saturation function rather than a sign function is proposed to avoid chattering. Along with the Lyapunov function method, some mathematical techniques, and scaling inequalities, some sufficient conditions for FTBS and PFTBS of MNNsMTDs are attained. Besides, this article also concerns fixed-time bipartite synchronization (FXBS) and practical FXBS (PFXBS) of MNNsMTDs. An optimization model is designed to obtain some optimal control parameters. An algorithm based on particle swarm optimization (PSO) is provided to solve this model. Some numerical examples are included to demonstrate the correctness and applicability of the approaches.

Adaptive Neural Network-Based Observer Design for Switched Systems With Quantized Measurements

This study is concerned with the adaptive neural network (NN) observer design problem for continuous-time switched systems via quantized output signals. A novel NN observer is presented in which the adaptive laws are constructed using quantized measurements. Then, persistent dwell time (PDT) switching is considered in the observer design to describe fast and slow switching in a unified framework. Accurate estimations of state and actuator efficiency factor can be obtained by the proposed observer technique despite actuator degradation. Finally, a simulation example is provided to illustrate the effectiveness of the developed NN observer design approach.

Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction-diffusion terms

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction-diffusion terms (FDRDMNNs) in sense of Riemann-Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results.

State Observer Design of Coupled Genetic Regulatory Networks With Reaction-Diffusion Terms via Time-Space Sampled-Data Communications

In this paper, state observation of coupled reaction-diffusion genetic regulatory networks (GRNs) with time-varying delays is investigated under Dirichlet boundary conditions. First, the above GRNs are constructed to model gene regulatory properties, where the feedback regulation function of the GRNs is assumed to exhibit the Hill form and a novel method to deal with it is introduced. Then a time-space sampled-data state observer is designed for the mentioned networks and new criteria are established by utilizing the Lyapunov stability theory and the inequality techniques of Halanay et al. Finally, the validity of the theoretical results is proved by numerical examples.

Finite-time synchronization of reaction-diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme

The finite-time synchronization issue of reaction-diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2ⁿ controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.

Space-Dividing-Based Cluster Synchronization of Reaction-Diffusion Genetic Regulatory Networks via Intermittent Control

In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.