This article studies the multisynchronization of delayed coupled neural networks (DCNNs) with general activation functions (AFs) via impulsive control. At first, a kind of AFs is proposed, and the $\boldsymbol {n}$ -neuron subnetwork with this kind of AFs can produce $\boldsymbol {(p+1)^{n}}$ locally stable equilibrium points (EPs) or periodic orbits (POs) by judging $\boldsymbol {2n(p+1)}$ algebraic inequalities and a nonsingular $\boldsymbol {M}$ -matrix. Compared with some specific AFs, such as the Sigmoid AFs or the saturated AFs, the AFs proposed in this article are more general. In addition, a kind of impulsive controller is designed. Compared with a continuous-time control strategy, the impulsive control strategy proposed in this article can reduce the communication cost and save bandwidth. Moreover, sufficient conditions are given to ensure both dynamical multisynchronization (DMS) and static multisynchronization (SMS) of DCNNs by building the comparison system and using the Lagrange method of variation of parameters. Lastly, an example is illustrated to testify to the validity of the obtained results.

This paper investigates the exponential mean square stability with conditioning (EMSS-C) and state feedback controller design for a class of discrete-time stochastic systems characterized by infinite Markov jump parameters, constant time-delay, and multiplicative noises. Unlike traditional finite-state Markov jump systems, the countably infinite state space introduces significant complexity in stability analysis. By employing the Lyapunov functional approach and the infinite-dimensional Schur complement, we derive novel sufficient conditions for EMSS-C. Based on these conditions, by solving a set of linear matrix inequalities (LMIs), we synthesize a state feedback controller. Finally, the theoretical results are then validated via a numerical example, demonstrating their effectiveness and feasibility.

This paper investigates the finite-time and fixed-time synchronization problems of stochastic multi-links complex networks with multiple time-varying delays (SMCNM-TVD). To overcome the limitations of conventional control schemes in handling coupled stochastic disturbances and time-delay effects, two novel distributed controllers are proposed: a finite-time controller integrating sign-power feedback and a delay-integral compensation term, which enhances robustness against time-varying delays; and an enhanced fixed-time controller incorporating an additional high-order nonlinear term, which guarantees a settling-time upper bound that is completely independent of initial states. By constructing appropriate Lyapunov-Krasovskii functionals and employing graph-theoretic techniques, sufficient synchronization criteria together with explicit estimates of the convergence time are established. The proposed control strategies are further applied to islanded microgrids, and numerical simulations verify their effectiveness as well as the superiority of the fixed-time controller in convergence speed and determinism.

This paper constructs a coupled population-economy reaction-diffusion model with asymmetric density-dependent diffusion, aiming to theoretically reveal how the mechanism of “congestion inhibiting diffusion and agglomeration enhancing diffusion” drives the self-organization of urban and regional spatial patterns. The critical conditions for Turing instability and the characteristic wavelength are rigorously derived, clarifying the regulatory role of density-dependent parameters on the instability threshold. Furthermore, the amplitude equations are derived using weakly nonlinear analysis, revealing the selection and stability mechanisms of spatial patterns near the bifurcation point. The interaction between Hopf bifurcation and Turing instability is also explored, and by establishing coupled amplitude equations, the resulting rich spatiotemporal dynamics are characterized. Numerical simulations are in excellent agreement with theoretical predictions and further reveal that, compared to linear diffusion, the density-dependent diffusion significantly accelerates the formation of spatial heterogeneous structures by introducing dynamic feedback mechanisms.

This paper addresses the issue of approximate mean square exponential stability (AMSES) for infinite-dimensional stochastic systems (IDSS) with output delay via the event-triggered predictive control (ETPC) strategy . The design of ETPC integrates an improved repetitive explicit Euler numerical scheme with event-triggered control, aiming to eliminate the impact of output delay and reduce triggering frequency. By leveraging the event-triggered predictive control strategy, sufficient conditions for AMSES of IDSS with output delay are derived. The analytical approach employs the Yosida strong solution approximation theorem, Lyapunov stability theory, infinite-dimensional It & ocirc;'s formula and Gronwall's inequality to address both infinite-dimensionality and output delay challenges. Moreover, it is proven that Zeno behavior can be excluded. Additionally, numerical simulations are conducted for a class of stochastic reaction-diffusion neural networks to validate the effectiveness of the main results. The comparative simulation results demonstrate that ETPC can effectively compensate for output delay and stabilize the system.

This work develops a predefined-time event-triggered adaptive tracking control method for a class of uncertain nonlinear systems (NSs) under output constraints. First, a unified barrier function is employed to prevent the output from violating the specified asymmetric constraint boundaries, thereby relaxing the conventional constraint boundary requirements. Moreover, the designed controller avoids the singularity problem and incorporates neural networks to estimate unknown smooth nonlinear functions. In the bargain, a Zeno-free event-triggered strategy is designed, enabling dynamic adjustment of the triggering conditions. Theoretical analysis demonstrates that the considered control strategy ensures that the system output tracks the reference signal within the scheduled time while staying within the constraint boundaries, and that all signals in the closed-loop system remain bounded. Ultimately, the feasibility of the developed control scheme is demonstrated via simulations.

This article focuses on the problem of adaptive practical fixed-time tracking control for a class of strict-feedback uncertain nonlinear systems subject to sensor faults. To achieve the control objective of this article, a series of radial basis function neural networks and a nonlinear fault-tolerant observer are introduced to approximate unknown nonlinearities and reconstruct unmeasurable states, respectively. Moreover, an adaptive fault compensation coefficient is employed to mitigate the effects of sensor faults, while the dynamic surface control technique is applied to alleviate the “differential explosion phenomenon” arising from the backstepping method. In addition, the proposed controller design method avoids the singularity problem inherent in fixed-time control strategies. Finally, the designed event-triggered controller can guarantee that all the signals are uniformly ultimately bounded in the presence of sensor faults, the tracking error converges to a small neighborhood of zero, the convergence time is independent of the initial system states and no Zeno behavior occurs.

This article focuses on cyber-physical systems subject to unknown disturbances and denial-of-service attacks. To ensure input-to-state stability, an event-triggered predictive control update scheme based on attack detection and a predictor is proposed. Firstly, a attack detection strategy is adopted, which makes full use of historical signals to detect whether the system is under attack at the current moment. Then, an attack detection-based control update scheme is proposed to compensate for state loss, and an event-triggered mechanism integrating detection and prediction is established to reduce resource consumption while ensuring system stability. The results show that the closed-loop cyber-physical systems can achieve input-to-state stability under the proposed control update scheme and event-triggered mechanism. An important advantage of the proposed control update scheme is that the cyber-physical systems select different state inputs according to the attack status at the event-triggered moment, thereby enabling the system to tolerate more adverse denial-of-service attacks. Finally, a simulation case is provided to verify the effectiveness of the proposed method.

The article investigates the differentially private consensus (DPC) problem for multi-agent systems (MASs) by designing an event-triggered logarithmic encoding-decoding (ETLED) scheme. Firstly, a DPC algorithm is proposed, where independent Laplacian noise is injected into the true states. This algorithm can protect the initial states of the agents and achieve the consensus of the MAS. Secondly, by integrating an event-triggered mechanism with a logarithmic encoding-decoding scheme, an ETLED scheme is developed. This scheme suppresses the impact of quantization errors without introducing additional design parameters and significantly reduces the communication frequency. Subsequently, by employing the Borel-Cantelli lemma and the martingale convergence theorem, almost sure consensus of the MAS is established. Furthermore, by leveraging Chebyshev’s inequality, it is demonstrated that the consensus value converges to a neighborhood of the average of the initial states. Additionally, differential privacy levels are rigorously analyzed for each agent and the overall MAS. Finally, the theoretical results are validated through a numerical example.

Abstract The asymptotic stability of Takagi–Sugeno (T–S) fuzzy systems is investigated by using multi-rate sampled-data control (MRSDC) and a refined fuzzy Lyapunov function (FLF). Firstly, a multi-rate sampling mechanism is introduced, to accommodate system variables with differing dynamic rates. It enables sensors to acquire data at rates aligned with variable characteristics and performance requirements. Secondly, to mitigate conservativeness in stability analysis, a refined FLF is constructed to fully exploit state information at multi-rate sampling instants. Based on this functional, a corresponding stability analysis method is developed and a control gain design algorithm is designed. Finally, simulation examples of a spring system and a truck-trailer system validate the effectiveness of the proposed method.

This paper proposes an adaptive fixed-time tracking control strategy for a class of MIMO stochastic nonlinear systems subject to output constraints and input nonlinearities. To cope with dead-zone/saturation effects, an input transformation is first introduced. A general time-dependent barrier function is then employed to ensure that the system output remains within the prescribed bounds. Building on these tools, a singularity-free adaptive fixed-time controller integrating a Nussbaum function with a switching function is developed. The proposed method guarantees that the tracking error converges in probability to a small neighborhood of the origin within a fixed time, while ensuring that all closed-loop signals remain bounded in probability. The effectiveness of the proposed method is validated through simulation case studies.

This article presents a data-driven control method to address the local asymptotic stabilization problem of discrete-time neural networks (DNNs) under input saturation. To reduce communication load, a memory-type EM (MEM) is first designed to mitigate the superfluous triggers. Then, a memory-dependent Lyapunov function (MLF) is constructed to accommodate the memory term introduced by the MEM. Based on the designed MEM, the MLF and two data-based system representations, a data-based stabilization criterion is developed, and an estimated region of attraction (ERA) is determined. Simultaneously, the feedback gain and the trigger matrix are co-designed to guarantee the local stability of the closed-loop system. A notable feature of the proposed approach is that the proposed stabilization criteria rely solely on accessible data, without necessitating full knowledge of the system matrices. It makes the approach well-suited for practical applications where precise modeling is difficult or infeasible. Furthermore, a hybrid optimization scheme combining the linear objective minimization method and the particle swarm optimization (PSO) algorithm is presented to maximize the size of the ERA. Finally, two numerical simulations are given to validate the effectiveness of the proposed optimization algorithm, illustrate the influence of data size, and demonstrate the advantages of the designed MEM in stabilizing DNNs.

This paper addresses fixed-time bipartite synchronization in memristive neural networks with cooperation and competition interactions. For the purpose of establishing an easily analyzable error system model, the interval matrix techniques are utilized to overcome the impact of memristive connection weights, while signed graph theory and coordinate transformation methods are employed to handle cooperation and competition interactions. An event-triggered switching controller without Zeno behavior is designed aiming to achieve the fixed-time bipartite synchronization while conserving network bandwidth. Then, the fixed-time bipartite synchronization criteria for coopetition memristive neural networks are obtained via Lyapunov stability theory and inequality techniques. Leveraging the sparrow search algorithm and fixed-time bipartite synchronization criteria, the solution algorithm for optimizing the control parameters is established to minimize the settling time’s upper bound. Simulations confirm the control strategy’s efficacy and performance advantages in solving fixed-time bipartite synchronization.

This paper develops and analyzes a fully discrete numerical scheme for the time-fractional Burgers equation with a Caputo–Hadamard derivative, which incorporates a logarithmic kernel particularly suitable for modeling ultraslow diffusion processes. The proposed scheme combines a nonuniform L1 approximation on exponentially graded meshes for temporal discretization with a local discontinuous Galerkin method for spatial discretization. By employing a discrete fractional Grönwall inequality, we prove unconditional stability and optimal L2 error estimates of order min{2 − α, rα} in time and k + 1 in space, where α ∈ (0, 1) is the fractional order, r is the mesh grading parameter, and k is the polynomial degree. Numerical experiments validate the theoretical convergence rates. Furthermore, we integrate the forward solver into a Broyden–Fletcher–Goldfarb–Shanno optimization framework to simultaneously estimate the fractional order α and the viscosity coefficient μ from noisy observations. A comparative study with the classical Caputo model demonstrates that the Caputo–Hadamard formulation yields significantly more accurate parameter calibration for processes exhibiting ultraslow diffusion, emphasizing the critical importance of selecting a fractional operator consistent with the underlying physical mechanism.

This paper focuses on the multistability analysis of delayed fuzzy cellular neural network (DFCNN) with discontinuous sawtooth-type activation function (DSAF). By applying Brouwer’s fixed-point theorem and the geometric characteristics of the DSAF, the existence and stability of multiple equilibrium points (EPs) are established. It can be demonstrated that DFCNN with DSAF has at least 7^n EPs, 6^n of which are located at the points of continuity (POCs) of the DSAF, and the remaining EPs are located at the points of discontinuity (PODs) of the DSAF. Moreover, sufficient conditions for the 4^n EPs located at the POCs of the DSAF to exhibit local exponential stability have been provided. Secondly, increasing the number of peak points can extend DSAF to more general situations. It can be demonstrated that the n-DFCNN has at least (2h+3)^n EPs with the DSAF having h peak points, (h+2)^n of them are locally exponentially stable. Moreover, the method of increasing the number of peak points increases the number of total/stable EPs without altering the sufficient conditions or the computational complexity. Finally, the availability of the results in this paper is verified by two numerical examples.

In this paper, the problem of mean-square bipartite synchronization of coopetition neural networks under deception attacks is considered. Firstly, the zero-row-sum Laplacian matrix is derived via coordinate transfor mation methods. Based on the characteristics of deception attacks, an appropriate pinning sampled-data control strategy is designed, thereby deriving the error system model. Next, a nonpositive-definite discontinuous interval-dependent looped-function is constructed, and based on this, a new lemma regarding mean-square bipartite synchronization is proposed. Subsequently, by combining discrete Lyapunov theory and inequality techniques, a linear matrix inequality-based criterion for mean square bipartite synchronization is derived. Finally, a numer ical example is provided to validate the effectiveness and advantages of the constructed Lyapunov function in reducing the minimum allowable coupling strength, increasing the maximum allowable sampling interval, and enhancing the maximum allowable deception attack rate.

This paper presents distributed output-feedback optimization for uncertain high-order nonlinear multi-agent systems (MASs) subject to unknown input delay. First, appropriate auxiliary systems and Lyapunov-Krasovskii functional (LKF) are implemented to counteract the effects of unknown input delay. In addition, to address the challenges posed by nonlinear uncertainties and unmeasurable system states, a neural networks (NNs)-based state observer employing radial basis function (RBF) NNs has been developed. Subsequently, distributed optimal coordinators (DOCs) are employed to reformulate output consensus as tracking problem for MASs. In the context of actor-critic reinforcement learning (RL) architecture, distributed optimal controller is designed using RL algorithm combined with backstepping technique. Leveraging Lyapunov stability theory, it is rigorously demonstrated that the tracking error of the output relative to the optimal solution can be reduced to an arbitrarily small magnitude. Finally, simulation examples are conducted to validate the efficacy of the introduced algorithm.

This paper investigates the stabilization problem for discrete-time infinite Markov jump linear systems with multiplicative noise and indefinite weighting matrices over an infinite horizon. A generalized framework is established, demonstrating that mean-square stabilizability is equivalent to the solvability of a countably infinite set of generalized algebraic Riccati equations. Under conditions of exact observability and specific structural constraints, an optimal stabilizing controller with guaranteed convergence is designed, thereby providing theoretical foundations for practical applications where performance indices lack positive definiteness.

A novel aperiodically intermittent impulse control (AIIC) method is proposed to investigate the exponential synchronization in mean square (ESMS) of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps (ISIDSP). The AIIC control strategy inherits the flexibility of aperiodically intermittent control, including the variable control period, adjustable control interval length, and the discretization of impulsive control. In addition, this article introduces a novel mild Itô's formula. By leveraging semigroup theory, the contraction mapping principle, and graph theory, along with constructing the Lyapunov function, the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established. Furthermore, the mean-square exponential synchronization problem of the above systems is resolved, and the constraints within the mild solution domain are alleviated. These criteria clarify the impact of control parameters, control intervals and network topology on ESMS. The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes, and the validity of the results is verified using numerical simulations.

This article investigates the security control issue of delayed coupled fuzzy inertial neural networks (FINNs) under deception attacks. Aiming to alleviate the influence of deception attacks, a fuzzy sampling data security controller is designed. A theoretical structure is formulated to analyze the behavior of the closed-loop system under deceptive interference. On this basis, by constructing a suitable set of Lyapunov functionals (LKFs) and employing inequality techniques, criteria guaranteeing exponential synchronization are established using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is demonstrated via numerical simulations and encryption and decryption analysis. Results show that, affected by deception attacks, the coupling FINNs can achieve exponential synchronization through our developed security control approach.