Projective Synchronization of Discrete-Time Variable-Order Fractional Neural Networks With Time-Varying Delays.

This article is committed to studying projective synchronization and complete synchronization (CS) issues for one kind of discrete-time variable-order fractional neural networks (DVFNNs) with time-varying delays. First, two new variable-order fractional (VF) inequalities are built by relying on nabla Laplace transform and some properties of Mittag-Leffler function, which are extensions of constant-order fractional (CF) inequalities. Moreover, the VF Halanay inequality in discrete-time sense is strictly proved. Subsequently, some sufficient projective synchronization and CS criteria are derived by virtue of VF inequalities and hybrid controllers. Finally, we exploit numerical simulation examples to verify the validity of the derived results, and a practical application of the obtained results in image encryption is also discussed.

HyperComm: Hypergraph-based communication in multi-agent reinforcement learning.

In the realm of fully cooperative multi-agent reinforcement learning (MARL), effective communication can induce implicit cooperation among agents and improve overall performance. In current communication strategies, agents are allowed to exchange local observations or latent embeddings, which can augment individual local policy inputs and mitigate uncertainty in local decision-making processes. Unfortunately, in previous communication schemes, agents may potentially receive irrelevant information, which increases training difficulty and leads to poor performance in complex settings. Furthermore, most existing works lack the consideration of the impact of small coalitions formed by agents in the multi-agent system. To address these challenges, we propose HyperComm, a novel framework that uses the hypergraph to model the multi-agent system, improving the accuracy and specificity of communication among agents. Our approach brings the concept of hypergraph for the first time in multi-agent communication for MARL. Within this framework, each agent can communicate more effectively with other agents within the same hyperedge, leading to better cooperation in environments with multiple agents. Compared to those state-of-the-art communication-based approaches, HyperComm demonstrates remarkable performance in scenarios involving a large number of agents.

Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays.

The dynamics of integer-order Cohen-Grossberg neural networks with time delays has lately drawn tremendous attention. It reveals that fractional calculus plays a crucial role on influencing the dynamical behaviors of neural networks (NNs). This paper deals with the problem of the stability and bifurcation of fractional-order Cohen-Grossberg neural networks (FOCGNNs) with two different leakage delay and communication delay. The bifurcation results with regard to leakage delay are firstly gained. Then, communication delay is viewed as a bifurcation parameter to detect the critical values of bifurcations for the addressed FOCGNN, and the communication delay induced-bifurcation conditions are procured. We further discover that fractional orders can enlarge (reduce) stability regions of the addressed FOCGNN. Furthermore, we discover that, for the same system parameters, the convergence time to the equilibrium point of FONN is shorter (longer) than that of integer-order NNs. In this paper, the present methodology to handle the characteristic equation with triple transcendental terms in delayed FOCGNNs is concise, neoteric and flexible in contrast with the prior mechanisms owing to skillfully keeping away from the intricate classified discussions. Eventually, the developed analytic results are nicely showcased by the simulation examples.

Stability and Dynamics Analysis of Time-Delay Fractional-Order Large-Scale Dual-Loop Neural Network Model With Cross-Coupling Structure.

In recent years, the analysis of the dynamics of annular neural networks has received extensive attention and achieved some achievements. However, most of the current research merely focuses on the single-ring, low-dimension, two rings sharing one neuron cases, without considering the rich coupling modes between rings. In this article, a large-scale time-delay fractional-order dual-loop neural network model with cross-coupling structure is established, in which two rings complete information interaction through two shared neurons. Moreover, the Caputo fractional derivative is introduced in this article to describe the neural network more accurately. First, the transmission time delay between each neuron is selected as the key parameter leading to the bifurcation, and the characteristic equation of the network is creatively derived using the Coates flow graph method. Subsequently, through the holistic element method and magnitude angle formula, we simplify the analytical process. Then, we obtain the stability and Hopf bifurcation criterion of the network. Finally, the conclusions of the theoretical analysis are verified by a series of numerical simulations. The results show that the stability region of the network is closely related to the fractional order, the number of neurons, the distribution of neurons, and the self-feedback coefficients. Moreover, the time delays have a significant effect on the amplitude and period of the Hopf bifurcation.

Explicit stability condition for delta fractional order systems with α∈(0,+∞).

This paper delves into the stability of time-advance delta fractional order systems, with a specific emphasis on the order range (0,+∞) rather than the conventional range (0,1). The delta Laplace transform is used to investigate the stability of the suggested system, and a mapping relation ρ=ss+1 is introduced. The explicit stability condition is provided, articulated in relation to a specific distribution of eigenvalues of the system matrix. To validate this condition, the paper establishes equivalence between the delta difference and the nabla difference. Furthermore, both quantitative and qualitative analyses are conducted on the range of the unstable region. Finally, the correctness of the developed results is validated by three examples.

Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion.

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov-Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.

Complete Stability of Delayed Recurrent Neural Networks With New Wave-Type Activation Functions.

Activation functions have a significant effect on the dynamics of neural networks (NNs). This study proposes new nonmonotonic wave-type activation functions and examines the complete stability of delayed recurrent NNs (DRNNs) with these activation functions. Using the geometrical properties of the wave-type activation function and subsequent iteration scheme, sufficient conditions are provided to ensure that a DRNN with n neurons has exactly (2m + 3)n equilibria, where (m + 2)n equilibria are locally exponentially stable, the remainder (2m + 3)n - (m + 2)n equilibria are unstable, and a positive integer m is related to wave-type activation functions. Furthermore, the DRNN with the proposed activation function is completely stable. Compared with the previous literature, the total number of equilibria and the stable equilibria significantly increase, thereby enhancing the memory storage capacity of DRNN. Finally, several examples are presented to demonstrate our proposed results.

Fast synchronization control and application for encryption-decryption of coupled neural networks with intermittent random disturbance.

In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied.

Fixed-time synchronization for two-dimensional coupled reaction-diffusion complex networks: Boundary conditions analysis.

This paper examines fixed-time synchronization (FxTS) for two-dimensional coupled reaction-diffusion complex networks (CRDCNs) with impulses and delay. Utilizing the Lyapunov method, a FxTS criterion is established for impulsive delayed CRDCNs. Herein, impulses encompass both synchronizing and desynchronizing variants. Subsequently, by employing a Lyapunov-Krasovskii functional, two FxTS boundary controllers are formulated for CRDCNs with Neumann and mixed boundary condition, respectively. It is observed that vanishing Dirichlet boundary contributes to the synchronization of the CRDCNs. Furthermore, this study calculates the optimal constant for the Poincaré inequality in the square domain, which is instrumental in analyzing FxTS conditions for boundary controllers. Conclusive numerical examples underscore the efficacy of the proposed theoretical findings.

Sliding Mode Control for Markov Jump Singularly Perturbed Systems Under Piecewise Homogeneous Stochastic Communication Protocol.

This work involves the sliding mode control (SMC) issue for a class of Markov jump singularly perturbed systems (MJSPSs) under consideration of unmatched external disturbances and communication constraints. For the first time, the piecewise homogeneous Markov chain (MC) which depends on the system mode and the controller mode is applied to control the scheduling of stochastic communication protocol (SCP), so that the MCs in the system models, the controller and the SCP constitute a three-layer nonstationary Markov model (NMM). This model perfectly describes the different objects of the three MCs and reflects the mutual regulation among them. The critical issue is to devise an adaptive controller and a sliding surface (SS) simultaneously under SCP scheduling. By applying a standard singular sliding mode surface, an appropriate nonstationary SMC law is established to promise the accessibility of the SS and the stability of the closed-loop system (CLS), and meet the expected performance indicator. Further, using the mode-dependent Lyapunov function and piecewise homogeneous Markov model method, sufficient criteria are obtained. The specific expression of the control gain is obtained by matrix decoupling technology. Finally, a numerical simulation is furnished to testify the correctness of the conclusion.

How to regulate pattern formations for malware propagation in cyber-physical systems.

Malware propagation can be fatal to cyber-physical systems. How to detect and prevent the spatiotemporal evolution of malware is the major challenge we are facing now. This paper is concerned with the control of Turing patterns arising in a malware propagation model depicted by partial differential equations for the first time. From the control theoretic perspective, the goal is not only to predict the formation and evolution of patterns but also to design the spatiotemporal state feedback scheme to modulate the switch of patterns between different modes. The Turing instability conditions are obtained for the controlled malware propagation model with cross-diffusion. Then, the multi-scale analysis is carried out to explore the amplitude equations near the threshold of Turing bifurcation. The selection and stability of pattern formations are determined based on the established amplitude equations. It is proved that the reaction-diffusion propagation model has three types of patterns: hexagonal pattern, striped pattern, and mixed pattern, and selecting the appropriate control parameters can make the pattern transform among the three patterns. The results of the analysis are numerically verified and provide valuable insights into dynamics and control of patterns embedded in reaction-diffusion systems.

Finite-time guarantee-cost H∞ consensus control of second-order multi-agent systems based on sampled-data event-triggered mechanisms.

This study presents a solution to the challenges of tracking consensus and guarantee-cost H∞ control in a specific set of second-order multi-agent systems with external disturbances. A proposed event-triggered control method based on periodic sampling data is presented for second-order multi-agent systems that include external disturbances. In contrast to the real-time monitoring of system state information used in the previous event-triggered mechanism, this approach collects system state information through periodic sampling. This ensures that the interval between two consecutive triggering moments is at least one sampling cycle, thereby preventing the controller from triggering infinitely within a finite time frame. A finite-time controller based on the sampled-data event-triggered mechanism is designed, and sufficient conditions to ensure the finite-time stability of the closed-loop system at a specified attenuation level are established using theoretical methods such as matrix analysis. For the given sampled-data event-triggered control protocol with a finite-time controller, a quadratic guarantee-cost function is introduced, and by designing control inputs and determining the parameters such as the finite-time upper bound T∗ and the H∞ performance index γ , the exact value of the upper bound of the system's guarantee-cost function under the action of the designed controller is derived. Finally, the feasibility of the proposed control scheme is verified through numerical simulation.

Composite adaptive fuzzy bipartite consensus of fractional-order multiagent systems with a switched event-triggered mechanism.

This paper focuses on online recorded-data-based composite adaptive fuzzy bipartite consensus control for uncertain fractional-order multiagent systems with interconnected terms and external disturbances by employing a switched-threshold-based event-triggered mechanism (ETM) under the backstepping structure. Fuzzy logic system is used as a universal function approximation to deal with function uncertainties that are not prone to model in the system. A new composite learning adaptive parameter design scheme that synthesizes both prediction error and tracking error is developed to enhance the tracking performance, where the prediction error is raised from the utilization of online recorded data and instantaneous data. A unique switched-threshold-based ETM is introduced, in which the information transmission between the sensor and the controller is imposed on one of the individuals. One merit of this work consists in that it can automatically and rapidly switch and adjust between the fixed threshold and relative threshold ETM according to the amplitude of input signals to balance the network resources and impede the occurrence of pulse phenomenon. In addition, it is theoretically proven that the proposed scheme can ensure that all internal signals of the closed-loop system are bounded and achieve local bipartite consistent errors through the fractional Lyapunov stability criterion. Finally, a numerical example is provided to confirm the feasibility of the proposed approach.

Final epidemic size and critical times for susceptible-infectious-recovered models with a generalized contact rate.

During the spread of an infectious disease, the contact rate or the incidence rate may affect disease characteristics. For simplicity, most disease models assume standard incidence or mass action rates to calculate the basic reproduction number, final epidemic size, and peak time of an epidemic. For standard incidence, the contact rate remains constant resulting in the incidence rate is inversely proportional to the population size, while for the mass action rate, this contact rate is proportional to the total population size resulting in the incidence rate is independent of the population size. In this paper, we consider susceptible-infectious-recovered epidemic models with a generalized contact rate C(N) and a nonlinear incidence rate in view of the behavioral change from susceptible or infectious individuals when an infectious disease appears. The basic reproduction number and the final size equation are derived. The impact of different types of contact rates on them is studied. Moreover, two critical times (peak time and epidemic duration) of an epidemic are considered. Explicit formulas for the peak time and epidemic duration are obtained. These formulas are helpful not only for taking early effective epidemic precautions but also for understanding how the epidemic duration can be changed by acting on the model parameters, especially when the epidemic model is used to make public health policy.

Asynchronous Sliding-Mode Control for Discrete-Time Networked Hidden Stochastic Jump Systems With Cyber Attacks.

In this study, asynchronous sliding-mode control (SMC) for discrete-time networked hidden stochastic jump systems subjected to the semi-Markov kernel (SMK) and cyber attacks is investigated. Considering the statistical characteristic of the SMK, which is challenging to acquire in engineering, this study recognizes the SMK to be incomplete. Due to the mode mismatch between the original system and the control law in the operating process, a hidden semi-Markov model is proposed to describe the considered asynchronous situation. The main aim of this study is to construct an asynchronous SMC mechanism based on an incomplete SMK framework under the condition of random denial-of-service attacks so that the resulting closed-loop system can realize the mean-square stability. By virtue of the upper bound of the sojourn time in each mode, innovative techniques are developed for mean-square stability analysis under an incomplete SMK. Furthermore, an asynchronous SMC scheme is designed to achieve the reachability of the quasi-sliding mode. Finally, the effectiveness is verified using an electronic throttle model.

Cluster Synchronization of Finite-Field Networks.

This technical paper investigates the cluster synchronization of finite-field networks (FFNs) based on the algebraic state space representation. By resorting to the semi-tensor product of matrices, the cluster synchronization of an FFN can be completely converted into the set stability of state trajectory. Then, a necessary and sufficient condition for the cluster synchronization of FFNs is obtained based on the invariant subset and one-step transition matrix. In particular, the obtained results are applicable to check the leader-follower synchronization and group consensus of FFNs. Finally, a numerical example is given to illustrate the feasibility of the obtained results.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

Event-triggered impulsive cluster synchronization of coupled reaction-diffusion neural networks and its application to image encryption.

This paper investigates the cluster synchronization of coupled neural networks with reaction-diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images.

Neurodynamic approaches for multi-agent distributed optimization.

This paper considers a class of multi-agent distributed convex optimization with a common set of constraints and provides several continuous-time neurodynamic approaches. In problem transformation, l1 and l2 penalty methods are used respectively to cast the linear consensus constraint into the objective function, which avoids introducing auxiliary variables and only involves information exchange among primal variables in the process of solving the problem. For nonsmooth cost functions, two differential inclusions with projection operator are proposed. Without convexity of the differential inclusions, the asymptotic behavior and convergence properties are explored. For smooth cost functions, by harnessing the smoothness of l2 penalty function, finite- and fixed-time convergent algorithms are provided via a specifically designed average consensus estimator. Finally, several numerical examples in the multi-agent simulation environment are conducted to illustrate the effectiveness of the proposed neurodynamic approaches.

Event-triggered aperiodic intermittent control for linear time-varying systems.

This paper considers the aperiodic intermittent control (AIC) for linear time-varying systems (LTVSs), where the occurrence instants are determined by an event triggering mechanism based on Lyapunov functions. For LTVSs, most of the existing results are demanded that the feedback controls are exerted all the time. In fact, in many practical applications, the applied controls are unnecessary/impossible to be imposed all the time. Therefore, the event-triggered AIC is introduced in this paper for LTVSs, and the uniformly stability, globally asymptotic stability and finite-time stability are proposed for LTVSs with event-triggered AIC, respectively. In addition, by using the piecewise constant feedback control method, effective intermittent controllers are designed for LTVSs. Finally, we present two numerical examples to illustrate the efficacy of the derived results.