Sparse General Matrix Multiplication (SpMM) is a fundamental kernel in iterative scientific computing and graph neural network inference. On single-GPU platforms, iterative SpMM suffers from two major performance bottlenecks: excessive memory traffic caused by repeated loading of Krylov basis vectors, and low computational efficiency due to irregular sparsity patterns. To address these challenges, this article proposes BLR-Krylov , an iterative SpMM optimization framework that integrates Communication-Avoiding Krylov (CA-Krylov) methods with a Block Low-Rank Sparse (BLR-Sparse) matrix format. BLR-Krylov first preprocesses sparse matrices into the BLR-Sparse format, where low-rank blocks are compressed through basis vector decomposition to reduce storage and arithmetic overhead. It then employs GPU-optimized matrix power kernels to batch-compute Krylov subspace basis vectors, effectively minimizing global memory accesses across iterations. Experimental results on multiple GPU architectures demonstrate that BLR-Krylov achieves a 4.0–6.0× speedup over existing communication-avoiding approaches in iterative workloads, increases global memory bandwidth utilization to 82%–87%, and improves tensor core utilization to 85%–92%, while maintaining numerical accuracy within 1 × 10 -6 . To facilitate reproducibility, partial source code is publicly available at https://github.com/19547035579zz-tech/BLR-Krylov.

In existing studies on neural networks (NNs) stabilization, stochastic disturbances are typically regarded as negative factors. In contrast, this paper systematically explores the positive role of stochastic disturbances in the stabilization of NNs and proposes a novel finite-time noise feedback control method. By rationally utilizing stochastic disturbances, the originally unstable fuzzy memristive NNs with reaction-diffusion components achieve finite-time stochastic stabilization. Meanwhile, some less conservative finite-time stabilization criteria are proposed, eliminating the requirement in classical criteria that Lyapunov function’s differential operator must be strictly negative. The novel criteria not only extend the application scope of existing stochastic stabilization from exponential stabilization to finite-time case, but also elaborately explore the relationship between noise intensity and the convergence speed of the system. Finally, the effectiveness of derived results is verified through simulation.

While control barrier functions (CBFs) are capable of providing safety guarantees, their effectiveness can degrade in the presence of model uncertainty and unexpected faults, particularly under actuator gain faults. To deal with these challenges, this paper proposes a probabilistically safe and adaptive control framework that integrates Gaussian processes (GPs) and online fault estimation into CBF-/high-order CBF-based methods. To handle the influence of model uncertainty, we leverage GP regression for the construction of CBFs, high-order CBFs, and an online estimator. In addition, the GP-based online estimator to estimate unknown actuator gain faults. Finally, two numerical examples are provided to validate two CBF-based methods and to demonstrate the effectiveness and superiority of these methods in ensuring safety compared to existing approaches.

This article investigates the mean square exponential stability for dynamic memristor-neutral stochastic cellular neural networks with time-varying delays (DM-NSDCNNs). Unlike general neural networks (NNs) analyzed in the voltage-current domain, DM-NSDCNNs are studied in the flux-charge domain, offering a significant advantage: all current, voltage, and power consumption vanish when the system reaches a steady state. In particular, dynamic memristor store the results of computation. To better utilize these properties, two distinct stochastic stability analysis techniques are considered, depending on the memristor's constitutive relations. For piecewise linear constitutive relation, the stability criteria are obtained by a novel approach based on the comparison principle and reductio ad absurdum. Moreover, the stability criteria for cubic nonlinear constitutive relation are established via stochastic analysis employing Lyapunov functional techniques. Finally, several numerical examples with different constitutive relations of DM-NSDCNNs are provided to verify the effectiveness and potential of the proposed results.

This article investigates finite/fixed-time synchronization (FTS/FXTS) for delayed inertial memristive neural networks (IMNNs) with time-varying actuator faults, a more practical scenario compared to the widely studied constant-fault case. Novel fault-tolerant controllers, including state-feedback and event-triggered schemes, are proposed to achieve synchronization under mixed delays. By establishing algebraic criteria via a nonreduced-order approach, explicit settling time estimates are derived while excluding Zeno behavior. The theoretical results are verified through simulations, and the proposed method is further applied to secure communication using synchronized IMNNs for image encryption.

This paper considers the interval estimation for delayed linear reaction-diffusion systems. To obtain the estimates of the states for delayed reaction-diffusion systems, a novel interval estimation scheme is proposed based on a spatial finite difference method and decoupling technology. First, the delayed reaction-diffusion system is discretized by the finite difference method, resulting in approximated delay differential equations. The bounds of the discretization errors are presented via a rigorous analysis. Then, we involve decoupling techniques into interval observer design for approximated delay differential equations, and its estimates are obtained. Moreover, combining the observations with the discretization errors, we provide the interval estimation of the delayed reaction-diffusion systems. Furthermore, a controller is designed using the observations to achieve the$H_{\infty}$performance. Finally, the proposed methods are validated by two numerical simulations.Note to Practitioners—This work is motivated by industrial problems instance of the thermal diffusion in CPU chips. Due to the significant cost of real-time measurement of chip’s temperature and the influence of environment, it is more feasible to obtain the thresholds of operating temperature based on known information and available measurements. To obtain the state thresholds, this paper focuses on designing interval observer and analysis of discretization error to guarantee the accuracy while reducing the impact of uncertainties. The methods in this paper is simple and fast to execute in practical engineering, and the discretization error does not need to be obtained through a priori numerical experiment. More importantly, the estimates include the worst-case during system operation, which is relatively practical in real applications. The proposed results aim to provide a helpful reference for controller synthesis and fault detection of spatio-temporal system with time delays, thereby promoting corresponding application research.

In the control problems of multi-agent systems, collision avoidance is a fundamental safety requirement. One effective approach to ensure safety involves combining control barrier functions (CBFs) with quadratic programming (QP), where nominal control inputs are incorporated into QPs to achieve desired control objectives. Additionally, it is crucial to study the control performance of multi-agent systems to balance these objectives with control efforts. This work demonstrates that the performance index is closely related to the hyperparameters in the CBF-based QP controller, and the Bayesian optimization algorithm is used to optimize and improve performance. Firstly, a safe control approach is developed and a unified performance enhancement framework is established to optimize the performance index. Hyperparameters are then explored and categorized, introducing the concept of feasible hyperparameters to describe the attainability of control objectives. Subsequently, the constrained Bayesian optimization algorithm is employed to identify a set of feasible and optimal hyperparameters in a data-driven manner, even when the functional expressions of performance and constraints are unknown. Finally, experiments are conducted to demonstrate the feasibility of the proposed methods in multi-agent systems. Note to Practitioners—Both safety and optimality are of great importance in the control systems. The design and development of controllers for multi-agent systems are currently undergoing significant evolution. Academic researchers and industrial practitioners are actively refining controller designs to perform better in a variety of collaborative tasks. With practical applications in mind, there is a growing demand for control techniques capable of ensuring a safe operating environment while maintaining efficiency in energy consumption. Therefore, this paper aims to furnish practitioners and researchers with a safe control framework, facilitating the refinement of optimal control solutions for efficient collaboration among multiple agents.

In this paper, the fixed-time (FxT) and practical FxT consensus of discontinuous multi-agent systems (MASs) via adaptive intermittent control strategy are studied. New intermittent FxT stability lemmas incorporating the indefinite function and the unified exponent condition are established, which can include the existing periodically intermittent stability lemmas and aperiodic intermittent lemmas with negative definite derivatives. Considering that the MASs cannot realize the exact consensus under the inevitable external interferences, intermittent-type practical FxT stability lemmas are further obtained. The intermittent controllers and adaptive intermittent controllers are designed, which demonstrates the improvements over the existing control strategies since the chattering phenomenon and singularity do not appear. Notably, the control gains are time-varying, which are also different from the previous time-invariant ones. Based on the established stability lemmas, the FxT consensus and practical FxT consensus are achieved. Clearly, the practical FxT consensus of discontinuous MASs under the discontinuous-time controllers is achieved for the first time. The simulation confirms the applicability of the proposed methods and shows strong support for our theoretical findings.

This paper is concerned with the intermittent iterative learning control for robot manipulators with packet dropouts. A composite controller is presented by a proportional-derivative feedback and an iterative learning feedforward to deal with the dropouts. A modified reference trajectory is adopted to treat input intermittence. With the help of composite energy function, rigorous theoretical derivations are provided to ensure the convergence of the estimation error of the iterative estimator and the boundedness of the tracking error. The validity of the proposed method is demonstrated by simulation studies on a single-link manipulator and a two-degrees-of-freedom planar manipulator, respectively. Note to Practitioners—Robot manipulators have drawn significant attentions due to their wide industrial applications. Due to their repetitive feature, iterative learning control is an effective strategy to achieve high tracking accuracy for them. However, this strategy faces new challenges incurred from network environment, such as packet dropouts and how to save energy. To patch this gap, an interpolation method is exploited for an iterative estimator to handle packet dropouts and a modified reference trajectory is employed to tackle with input intermittence. Simulation studies with practical background is supplied to show the validity of the proposed method. Therefore, this paper lays a theoretical basis for the tracking control of robot manipulators in practical applications.

This paper addresses the problem of distributed formation-containment tracking control for uncertain multi-agent systems (MASs) with completely unknown system nonlinearities, denial-of-service (DOS) attacks, and switching communication topologies. To enhance the system robustness, neural networks (NNs) are utilized to identify the unknown nonlinear terms. Additionally, a novel distributed observer is designed to reconstruct the external unmeasured attack dynamics. To handle the switching topologies of MASs, a mechanism using piecewise continuous functions is proposed to counteract the unexpected controller actions during switching time instants. Furthermore, the clever design of barrier Lyapunov functions aids in achieving the required predefined performance. A fractional power nonlinear filter is introduced to tackle the problem of computational complexity. By applying the local neighborhood states information and the lyapunov stability theory, the presented control method evaluates the stability of the MASs and shows that the designed controller not only enables the system output to track a formation trajectory in the presence of external attacks but also converges the consensus errors into a predefined set. Finally, simulation results are provided to validate the effectiveness of the proposed control strategy.

This paper investigates the synchronization control of coupled memristive neural networks (CMNNs) and its application in secure communication. First of all, a CMNNs system model that accommodates input saturation and dead-zone is introduced duo to the actuator nonlinearity is a common problem in practical network control. On which basis, a secure communication scheme containing multiple information receivers is proposed, which strengthened the security of communication through the coupling characteristics between states. Next, by using the adaptive control method and the Lyapunov stability theory, an adaptive finite-time synchronization strategy is proposed for the considered CMNNs. Following, an adaptive fixed-time synchronization strategy is proposed to further improve the flexibility of control schemes and reduce the impact of system initial values. Each designed controller not only ensures the synchronization of the CMNNs, but also guarantees the stability of the designed secure communication system. In the end, feasibilities of synchronization strategies and communication scheme are proved through simulation experiments.

This paper mainly analyzes the finite-time stabilization of semi-Markov reaction-diffusion memristive neural networks (R-DMNNs) with unbounded time-varying delays. Firstly, the reaction-diffusion term and semi-Markov jumping are introduced into memristive neural networks, which relaxes the limitation of Markov switching on sojourn time and makes the model more applicable. Secondly, by constructing a suitable comparison function, the states of R-DMNNs converges to 0 directly, which can clearly estimate the upper limit of the settling time and simplify the complexity of the theoretical derivation. Furthermore, this paper removes the requirement of bounded and differentiable time delay, which provides a new perspective for understanding the finite-time stabilization of the neural networks with reaction-diffusion terms. Finally, one example illustrates the usefulness of the analysis results in this research.

Fault-tolerant control (FTC) is an effective control method designed to maintain a faulty system within an acceptable risk level while ensuring its safety. However, handling both uncertainties and faults in a system remains challenging. In this article, we propose two probabilistic model-based adaptive FTC methods for faulty nonlinear systems with unknown dynamics. We study Gaussian process (GP) regression in two cases: 1) an offline learning-based control method and 2) an event-triggered online data-driven modeling method, to learn unknown system dynamics. Considering the computational complexity of GP regression in practical applications, we discuss the case of computational delays in real-time predictions. Moreover, we develop four theoretical criteria to ensure the probabilistic stability of closed-loop systems. Finally, numerical simulations validate the effectiveness of proposed control methods and demonstrate their competitiveness compared to existing approaches.

This article introduces hybrid-dependent event-triggered schemes for global asymptotical synchronization (GAS) of Takagi–Sugeno fuzzy memristive neural networks (FMNNs) with nondifferentiable time-varying delays. First, some schemes incorporating an exponential decay rate function with tunable parameters are established. Under these schemes, sufficient conditions for GAS of FMNNs are derived by formulating a delayed differential inequality. This approach eliminates the necessity for constructing complex Lyapunov functionals and effectively accommodates nondifferentiable delay terms. Notably, this is accomplished by a nonchattering event-triggered controller. In addition, Zeno behavior is precluded by proving the existence of a positive lower bound on the interexecution time. Finally, numerical simulation is provided to validate the effectiveness of these theoretical results.

This brief studies the hyper-exponential stabilization of neural networks (NNs) by event-triggered impulsive control, where the impulse instants are determined by the event-triggered conditions. In the presence of actuation delay, an event-triggered impulsive control scheme is devised. For reducing the sampling task of continuous detection, a periodic-detection scheme is also introduced. Within these frameworks, the occurrence of Zeno behavior is rigorously precluded, and some criteria are formulated to achieve the stabilization of the system with a hyper-exponential convergence rate. Moreover, a numerical simulation is provided to elucidate the validity of the theoretical findings.

Neural network adaptive iterative learning control (ILC) is developed in this article to treat strict-feedback nonlinear systems with unknown state delays and input saturation. These delays are treated by constructing the Lyapunov-Krasovskii (L-K) functions for each subsystem. A command filter is employed to avoid the derivative explosion caused by continuous differentiation of the virtual controller. Corresponding auxiliary systems are designed and integrated into the backstepping procedure to compensate input saturation and the unimplemented part of the filter. Hyperbolic tangent functions and radial basis function neural networks (RBF NNs) are employed to treat singularity and related unknown terms, respectively. The convergence of the resultant strict-feedback systems is ensured in the framework of composite energy function (CEF). Finally, a simulation example is adopted to substantiate the validity of the proposed algorithm.

In this article, the synchronization problem of memristive neural networks (MNNs) subjected to multiple failures is investigated. First, a general form of fault model is introduced into the MNNs, which can represent and summarize various process faults, actuator faults, and their coupling. Subsequently, with the help of designing intermediate variables, two types of fault function observers based on state feedback and output feedback are constructed, and their effectiveness is verified through a generalization of Halanay-type inequalities. Then, based on the designed observers and the event-triggered strategy, two classes of fault-tolerant synchronization schemes are designed for the considered MNNs. By adjusting the controller parameter conditions, finite-time and fixed-time synchronization or quasi-synchronization of the considered MNNs system can be achieved, respectively. Finally, the effectiveness of the provided fault observers and synchronization strategies is verified through simulation and comparison experiments.

This article investigates the finite-time stabilization problem of inertial memristive neural networks (IMNNs) with bounded and unbounded time-varying delays, respectively. To simplify the theoretical derivation, the nonreduced order method is utilized for constructing appropriate comparison functions and designing a discontinuous state feedback controller. Then, based on the controller, the state of IMNNs can directly converge to 0 in finite time. Several criteria for finite-time stabilization of IMNNs are obtained and the setting time is estimated. Compared with previous studies, the requirement of differentiability of time delay is eliminated. Finally, numerical examples illustrate the usefulness of the analysis results in this article.

In this article, the multistability problem of almost periodic solutions of fuzzy competitive neural networks (FCNNs) with time-varying delays is investigated. Considering more general activation functions, which are nonmonotonic and nonlinear, and incorporating the almost periodic property of the parameters in FCNNs, sufficient conditions for the multistability of almost periodic solutions are given. $\prod _{r=1}^{n}(L_{r}+1)$ stable almost periodic solutions are obtained, where $L_{r}$ depends on the geometric features of the activation functions, which enriches and extends the research on multistability in fuzzy systems. Furthermore, the extended domain of attraction based on the original state space is presented. Finally, numerical simulations are provided to verify the conclusions of this article.

This article examines the finite-time (F-T) synchronization issue for a class of recurrent neural networks (NNs) that have, respectively, bounded and unbounded time-varying delays. First, two novel F-T stability lemmas are presented in the form of generalized Halanay inequalities. Second, based on the obtained lemmas, some simple and easy-to-use F-T synchronization criteria are rendered for the considered NNs under two different Lyapunov functions. The results obtained in this article greatly reduce system constraints and are therefore more applicable. The validity of the theoretical results derived in this article is finally checked using three numerical instances.

This article aims to study event-triggered data-driven control of nonlinear systems via Q-learning. An input-output mapping is described by a pseudo-partial derivatives form. A Q-learning-based optimization criterion is provided to establish a data-driven control law. A dynamic penalty factor composed of tracking errors is supplied to accelerate errors convergence. Consequently, a novel triggering rule related to this factor and performance cost is proposed to save communication resources. Sufficient conditions are developed for guaranteeing the ultimately uniform boundedness of the resultant tracking errors system. Two simulation studies are executed to verify the effectiveness of the presented scheme.

In dynamic systems with communication limitations and delay, the input-to-state stability (ISS) is crucial for ensuring system performance. In this article, the finite-time ISS (FTISS) of time-delay neural networks (NNs) with disturbances is investigated. First, by further considering the idea of finite-time contractive stability (FTCS), the prescribed performance is proposed for the considered NNs system, thereby achieving better learning ability and robustness. Next, in order to achieve the above research objectives, some stability conditions for the considered NNs with disturbances are given by constructing sequentially two classes of Lyapunov functions and a finite-time contractive function. Subsequently, a stabilization strategy is proposed to further reduce the parameter requirements of the NNs system and improve its application value. Finally, the numerical simulation and comparative experiments have verified the effectiveness of the stability strategy provided in this article.

This study, conducted in a Shenzhen district, assesses the necessity and cost-effectiveness of Ground Penetrating Radar (GPR) road inspections. The evaluation involves automatic identification of road defects, such as voids, cavities, and loose soil, followed by an analysis of their spatial distribution patterns, clustering effects, density, and correlation with the metro system. The study proposes an optimized strategy for large-scale road inspections based on the spatial distribution characteristics of identified defects, emphasizing the importance of more frequent inspections on vulnerable roads. The findings contribute to the efficient allocation of public funds, minimizing wasteful expenditures, and enhancing road operational safety.

This article is devoted to data-driven event-triggered adaptive dynamic programming (ADP) control for nonlinear systems under input saturation. A global optimal data-driven control law is established by the ADP method with a modified index. Compared with the existing constant penalty factor, a dynamic version is constructed to accelerate error convergence. A new triggering mechanism covering existing results as special cases is set up to reduce redundant triggering events caused by emergent factors. The uniformly ultimate boundedness of error system is established by the Lyapunov method. The validity of the presented scheme is verified by two examples.

By using the fault-tolerant control method, the synchronization of memristive neural networks (MNNs) subjected to multiple actuator failures is investigated in this article. The considered actuator failures include the effectiveness failure and the lock-in-place failure, which are different from previous results. First of all, the mathematical expression of the control inputs in the considered system is given by introducing the models of the above two types of actuator failures. Following, two classes of synchronization strategies, which are state feedback control strategies and event-triggered control strategies, are proposed by using some inequality techniques and Lyapunov stability theories. The designed controllers can, respectively, guarantee the realization of synchronizations of the global exponential, the finite-time and the fixed-time for the MNNs by selecting different parameter conditions. Then the estimations of settling times of provided synchronization schemes are computed and the Zeno phenomenon of proposed event-triggered strategies is explicitly excluded. Finally, two experiments are conducted to confirm the availability of given synchronization strategies.

As quaternion-valued memristor neural networks (MNNs) have important applications in many engineering fields and the information in the real world is often uncertain and inaccurate, therefore, in order to better apply to practice, it is necessary to study the dynamic behaviors of quaternion-valued MNNs with fuzzy logic. In this article, the event-based synchronization problem for quaternion-valued Takagi–Sugeno (T-S) fuzzy MNNs (QVT-SFMNNs) with time-varying delays is studied. Different from the existing synchronization results of MNNs, T-S fuzzy logic and quaternion are simultaneously considered in the MNNs, which makes the model more applicable. Based on some algebraic properties of quaternions, a novel event-based fuzzy controller and some static and dynamic event trigger conditions are designed. By constructing simple Lyapunov functions instead of complex Lyapunov functionals and using Halanay inequality, several sufficient criteria are given to ensure the global exponential synchronization between the considered QVT-SFMNNs. Meanwhile, the Zeno behaviors of the response QVT-SFMNN under different event trigger conditions are excluded. It is important to note that the results obtained in article are less conservative and applicable to low-dimensional complex-valued and real-valued MNNs. Finally, a numerical example is given to verify the validity of the obtained theoretical results.

This article is concerned with the mismatched quantized$H_{\infty }$output-feedback control of fuzzy Markov jump systems via a dynamic guaranteed cost triggering scheme. An event generator and a quantizer are set up at the sensor-to-controller side and the controller-to-actuator side, respectively. The quantization scheme is presented in terms of a multichannel configuration with different decoder/encoder parameters. A guaranteed cost dynamic event-triggered mechanism is built on instantaneous and averaged triggering errors, output cost, and preset bounds. A composite controller consisting of a static output-feedback and a nonlinear compensation is constructed to meet the desired system performance. Based on the Lyapunov stability theory, sufficient conditions are obtained such that the closed-loop system is stochastically stable with the prescribed$H_{\infty }$performance. A structural vertex separation technique and Finsler's Lemma are employed to decouple the control gain, the quantizer parameters, and the Lyapunov variable. Finally, the validity of proposed scheme is verified by a circuit example.

A dynamic event-based optimal learning scheme is provided in the paper for nonlinear systems subject to constrained inputs and stochastic disturbances. An actor-critic structure is constructed to learn the stochastic optimal solution, which includes critic fuzzy logic system (FLS) and actor FLS. The experience replay technique and gradient-descent adaption method are used to periodically tune the critic FLS, which can approximate the optimal cost function. Based on the static event-triggered control mechanism (ETCM), a dynamic ETCM is designed, which can incorporate past triggering information and generate a longer inter-event time. The actor FLS is updated at aperiodic jumping points, which can approximate the optimal control policy. The combination of dynamic ETCM and learning structure ensures the stochastic stability of closed-loop system. The efficiency of the controller is illustrated on a numerical example and a manipulator system.

This article concentrates on the prescribed-time cooperative output regulation problem (CORP) of linear heterogeneous multiagent systems (HMASs) under directed topology. First, a novel distributed observer with prescribed-time convergence is designed to estimate the state of the exosystem. Then, two distributed prescribed-time control protocols, one based on the agent's state, the other based on the agent's output, are proposed using the observed exosystem's state. It is shown that the CORP of linear HMASs with any different orders is solved in a prescribed (any user-chosen as needed) time. Unlike the existing finite-time control strategies, the settling time is guaranteed by the designed first-order smooth control protocols, independent of the system's initial values and the control parameters. Lastly, a numerical simulation is presented to verify our theoretical results.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

This article concentrates on the global exponential synchronization problem of multiple neural networks with time delay by the event-based output quantized coupling control method. In order to reduce the signal transmission cost and avoid the difficulty of obtaining the systems' full states, this article adopts the event-triggered control and output quantized control. A new dynamic event-triggered mechanism is designed, in which the control parameters are time-varying functions. Under weakened coupling matrix conditions, by using a Halanay-type inequality, some simple and easily verified sufficient conditions to ensure the exponential synchronization of multiple neural networks are presented. Moreover, the Zeno behaviors of the system are excluded. Some numerical examples are given to verify the effectiveness of the theoretical analysis in this article.

This article investigates a generalized type of multistability about almost periodic solutions for memristive Cohen–Grossberg neural networks (MCGNNs). As the inevitable disturbances in biological neurons, almost periodic solutions are more common in nature than equilibrium points (EPs). They are also generalizations of EPs in mathematics. According to the concepts of almost periodic solutions and$\Psi$-type stability, this article presents a generalized-type multistability definition of almost periodic solutions. The results show that$(K+1)^n$generalized stable almost periodic solutions can coexist in a MCGNN with$n$neurons, where$K$is a parameter of the activation functions. The enlarged attraction basins are also estimated based on the original state space partition method. Some comparisons and convincing simulations are given to verify the theoretical results at the end of this article.

This article is devoted to analyzing the multistability and robustness of competitive neural networks (NNs) with time-varying delays. Based on the geometrical structure of activation functions, some sufficient conditions are proposed to ascertain the coexistence of equilibrium points, of them are locally exponentially stable, where represents a dimension of system and is the parameter related to activation functions. The derived stability results not only involve exponential stability but also include power stability and logarithmical stability. In addition, the robustness of stable equilibrium points is discussed in the presence of perturbations. Compared with previous papers, the conclusions proposed in this article are easy to verify and enrich the existing stability theories of competitive NNs. Finally, numerical examples are provided to support theoretical results.

This article addresses the consensus tracking control of multiagent systems (MASs) via a quadratic programming (QP) optimization framework, where the control Lyapunov function (CLF) condition serves as a constraint. The optimal controllers, derived through the QP solver, not only ensure the tracking control objective but also minimize the cost functions of agents. To enhance energy efficiency, discontinuous control methods, such as intermittent control strategy and event-triggered mechanism, are employed in the control framework. The CLF-based QP controllers are only updated at specific time instants, in order to reduce the frequency of QP problem-solving. In addition to considering optimization, the proposed methods are extended to uncertain MASs to enhance robustness, where the uncertainty is modeled by Gaussian process regression. In the end, simulation results are provided to demonstrate the feasibility of the theoretical analysis.

This article mainly studies the multistability of complex-valued neural networks (CVNNs) with general periodic-type activation functions. In order to improve the storage capacity of associative memory, a general periodic-type activation function is introduced which obtains three different numbers of equilibrium points (EPs), including unique, finite, and countable infinite. The existence and stability of equilibria are investigated based on Brouwer’s fixed point theorem andM-matrix method. By means of a sign function on complex numbers, stability is confirmed using a new norm on the absolute values of the real and imaginary parts. The attraction basins of exponentially stable equilibria are estimated, which are bigger than the subspaces of the original division. Also, the design of associative memory is given. Finally, two numerical simulation examples verify the obtained results.

This brief discusses the reachable set estimation (RSE) problem for memristive neural networks (MNNs) involving time-varying delays and bounded disturbances. The reachable sets of the considered MNNs under zero and nonzero initial conditions are estimated by two novel algebraic criteria, respectively. Compared with the existing results, the conclusions are easy to verify, and the obtained reachable sets are more accurate. Finally, the validity of the theoretical results is illustrated by two examples.

This article discusses the coexistence and dynamical behaviors of multiple equilibrium points (Eps) for fractional-order complex-valued memristive neural networks (FCVMNNs) with delays. First, based on the state space partition method, some sufficient conditions are proposed to guarantee that there are multiple Eps in one FCVMNN. Then, the Mittag-Leffler stability of those multiple Eps is proved by using the Lyapunov function. Simultaneously, the enlarged attraction basins are obtained to improve and extend the existing theoretical results in the previous literature. In addition, some existing stability results in the literature are special cases of a new result herein. Finally, two illustrative examples with computer simulations are presented to verify the effectiveness of theoretical analysis.

This article focuses on the robust$\mathcal {H}_{\infty }$synchronization of two types of coupled reaction–diffusion neural networks with multiple state and spatial diffusion couplings by utilizing pinning adaptive control strategies. First, based on the Lyapunov functional combined with inequality techniques, several sufficient conditions are formulated to ensure$\mathcal {H}_{\infty }$synchronization for these two networks with parameter uncertainties. Moreover, node-based pinning adaptive control strategies are devised to address the robust$\mathcal {H}_{\infty }$synchronization problem. In addition, some criteria of$\mathcal {H}_{\infty }$synchronization for these two networks under parameter uncertainties are developed via edge-based pinning adaptive controllers. Finally, two numerical examples are presented to verify our results.

There are lots of many-objective optimization problems (MaOPs) in real-world applications, which often have many decision variables. Although a variety of methods have been proposed to solve MaOPs, with the increasing number of decision variables or objective functions, the performance of these algorithms deteriorates appreciably. In view of this, this article proposes a method to solve large-scale MaOPs (LSMaOPs) based on dimension reduction and a solving knowledge-guided evolutionary algorithm (KGEA). First, a dimension reduction method of objective functions is proposed. By clustering and aggregating the objective functions based on their correlation, the dimension of the original LSMaOP is effectively reduced. In addition, the correlations between the reduced objective functions are relatively low, so they can better represent different preferences. Then, we propose a solving KGEA to solve the transformed LSMaOP. In order to get a better set of initial solutions, a population initialization method by mirror partitioning the decision space is given, in which we dynamically modify the sampling probability according to the performance of solutions contained in each subdomain. At the same time, the algorithm will continuously supplement new excellent individuals using the solving knowledge obtained in the evolution of the population. To examine the performance of the proposed method, we carried out a number of comparative experiments. The experimental results demonstrated that the proposed algorithm can effectively tackle LSMaOPs.

This article is devoted to designing a novel aperiodic sampled-data-based event-triggered control strategy for Takagi–Sugeno fuzzy systems. First, via taking the structural features of fuzzy subsystems and the available information of fuzzy membership functions into consideration, an improved fuzzy-dependent adaptive event-triggered mechanism, which designs different adaptive event-triggered mechanisms for corresponding fuzzy subsystems, is proposed to provide extra design flexibility and further optimize communication efficiency. Then, the two-side looped-functional method and dynamic partitioning approach are introduced in the construction of the novel Lyapunov–Krasovskii functional (LKF). These two methods contribute to deriving preferable stability criterion and stabilization approach via relaxing the positive definite constraint on LKF and fully utilizing the inner system state during the whole aperiodic sampling interval. Eventually, two simulation examples are introduced to verify the effectiveness of the proposed control strategy and its advantages in lightening communication frequency.

This article studies finite-time stabilization of delayed neural networks (DNNs) whose activation functions are discontinuous. Several sufficient conditions for guaranteeing finite-time stabilization of considered DNNs are obtained by constructing appropriate controllers with giving upper bounds of control time. Subsequently, based on the existing definition of energy consumption, the required energy to achieve stabilization is estimated. To quantify the cost of control, an evaluation index function is constructed to analyze the tradeoff between control time and consumed energy. Ultimately, acquired results are verified by simulating two numerical examples.

Recently, dynamic memristor (DM)-cellular neural networks (CNNs) have received widespread attention due to their advantage of low power consumption. The previous works showed that DM-CNNs have at most 318 equilibrium points (EPs) with$n=16$cells. Since time delay is unavoidable during the process of information transmission, the goal of this article is to research the multistability of DM-CNNs with time delay, and, meanwhile, to increase the storage capacity of DM-delay (D)CNNs. Depending on the different constitutive relations of memristors, two cases of the multistability for DM-DCNNs are discussed. After determining the constitutive relations, the number of EPs of DM-DCNNs is increased to$3^{n}$with$n$cells by means of the appropriate state-space decomposition and the Brouwer’s fixed point theorem. Furthermore, the enlarged attraction domains of EPs can be obtained, and$2^{n}$of these EPs are locally exponentially stable in two cases. Compared with standard CNNs, the dynamic behavior of DM-DCNNs shows an outstanding merit. That is, the value of voltage and current approach to zero when the system becomes stable, and the memristor provides a nonvolatile memory to store the computation results. Finally, two numerical simulations are presented to illustrate the effectiveness of the theoretical results, and the applications of associative memories are shown at the end of this article.

This brief focuses on reachable set estimation for memristive complex-valued neural networks (MCVNNs) with disturbances. Based on algebraic calculation and Gronwall-Bellman inequality, the states of MCVNNs with bounded input disturbances converge within a sphere. From this, the convergence speed is also obtained. In addition, an observer for MCVNNs is designed. Two illustrative simulations are also given to show the effectiveness of the obtained conclusions.

In this article, the estimation of time cost for stochastic consensus of second-order nonlinear multiagent systems (MASs) is investigated. Compared with previous studies, the effect of noise and nonlinear inherent dynamics of agents are considered. In order to achieve the finite/fixed-time stochastic consensus while minimizing energy consumption, the pinning protocols are designed, which only need to control a small fraction of agents. Sufficient conditions for the stochastic consensus are established by employing the stability theory of stochastic differential equations and the algebra graph theory. Finally, the proposed protocols are verified through numerical simulation on the consensus of unmanned aerial vehicles (UAVs) system.

In this article, the global asymptotic stability of a class of recurrent neural networks (RNNs) with generalized piecewise constant argument (GPCA) is investigated. By the Banach fixed point theorem (BFPT) and comparison principle, a set of improved criteria are presented to guarantee the existence and uniqueness (EU) of the solutions and global asymptotic stability of equilibrium point for the considered RNNs. Compared with the existing results, this article not only reduces the requirements for system parameters, but also provides more criteria in different forms, which greatly improve the feasible range of the obtained criteria. The effectiveness of the obtained results are tested by some numerical examples.

This article investigates fault detection (FD) for discrete-time T–S fuzzy systems via an iterative interval estimation method. By means of system output and the iterative estimation of unknown disturbances, two iterative subsystems are employed to establish iterative state reconstruction free of faults. Resorting to a structure separation technique and the$H_{\infty }$requirement imposed on estimated errors, a sufficient condition is formulated in terms of linear matrix inequality to guarantee the asymptotically stability of the error systems. With the help of the zonotope reachability technique, the state interval without faults consideration is rebuilt in terms of the error boundary. Subsequently, an FD scheme is proposed by checking residual signals whether exceed the residual interval generated from the established error interval. Simulation comparison is provided to verify the validity of the proposed iterative FD scheme.

Safety is always one of the most critical principles for a control system. This article investigates a safety-critical control scheme for unknown structured systems by using the control barrier function (CBF) method. Benefiting from the dynamic regressor extension and mixing (DREM), an extended elementwise parameter identification law is utilized to dismiss the uncertainty. It is shown that the proposed control scheme can always ensure safety in the identification process with injected excitation noise. Besides, the elementwise identification process using DREM can minimize the theoretical conservatism of the safe adaptation law compared to other existing adaptive CBF (aCBF) algorithms. The stability of the proposed safe control scheme is proven, where the safety is guaranteed by constructing appropriate forward invariant aCBF. Furthermore, the robustness of our algorithms under bounded disturbances is analyzed. Finally, the proposed framework is tested on two simulation-based examples, including the adaptive cruise control problem where the slope resistance of the following vehicle is robustly estimated in finite time against small disturbances, and the potential crash risk is avoided by our safe control scheme. These examples illustrate the effectiveness of our algorithm.

This work studies the issue of global h-synchronization about high-order delayed inertial neural networks via a second-order response system (SORS) approach. Note that the h-synchronization is a flexible definition which can generalize different special synchronization types by choosing different regulation function$\hbar $. By constructing a regulation function-dependent Lyapunov–Krasovskii functional (RFD–LKF), a novel delay-dependent global h-synchronization criterion is obtained. Furthermore, an adaptive control algorithm is designed to estimate control gains online, which is useful to guarantee global h-synchronization performance as well as to decrease the control cost. And finally, the superiority of the method is verified via three numerical examples.

Dynamic memristor (DM)-cellular neural networks (CNNs), which replace a linear resistor with flux-controlled memristor in the architecture of each cell of traditional CNNs, have attracted researchers’ attention. Compared with common neural networks, the DM-CNNs have an outstanding merit: when a steady state is reached, all voltages, currents, and power consumption of DM-CNNs disappeared, in the meantime, the memristor can store the computation results by serving as nonvolatile memories. The previous study on stability of DM-CNNs rarely considered time delay, while delay is quite common and highly impacts the stability of the system. Thus, taking the time delay effect into consideration, we extend the original system to DM-D(delay)CNNs model. By using the Lyapunov method and the matrix theory, some new sufficient conditions for the global asymptotic stability and global exponential stability with a known convergence rate of DM-DCNNs are obtained. These criteria generalized some known conclusions and are easily verified. Moreover, we find DM-DCNNs have$3^{n}$equilibrium points (EPs) and$2^{n}$of them are locally asymptotically stable. These results are obtained via a given constitutive relation of memristor and the appropriate division of state space. Combine with these theoretical results, the applications of DM-DCNNs can be extended to other fields, such as associative memory, and its advantage can be used in a better way. Finally, numerical simulations are offered to illustrate the effectiveness of our theoretical results.

This article aims at analyzing and designing the multivalued high-capacity-associative memories based on recurrent neural networks with both asynchronous and distributed delays. In order to increase storage capacities, multivalued activation functions are introduced into associative memories. The stored patterns are retrieved by external input vectors instead of initial conditions, which can guarantee accurate associative memories by avoiding spurious equilibrium points. Some sufficient conditions are proposed to ensure the existence, uniqueness, and global exponential stability of the equilibrium point of neural networks with mixed delays. For neural networks with${n}$neurons,${m}$-dimensional input vectors, and${2k}$-valued activation functions, the autoassociative memories have${(2k)^{n}}$storage capacities and heteroassociative memories have min${\{(2k)^{n},(2k)^{m}\}}$storage capacities. That is, the storage capacities of designed associative memories in this article are obviously higher than the${2^{n}}$and min${\{2^{n},2^{m}\}}$storage capacities of the conventional ones. Three examples are given to support the theoretical results.

This article solves the problems of finite-time control and settling-time estimation for fractional-order quaternion-valued fuzzy neural networks (FQFNNs) with time delays. A novel fractional differential inequality is established to estimate the settling time of the addressed system, which is more general and less conservative than the existing results. In addition, owing to the noncommutativity of multiplication of quaternions, the decomposition method is usually adopted to discuss the finite-time stabilization (FTS) of quaternion-valued neural networks, which inevitably doubles the dimensionality of the system and brings a great computational burden. To avoid the aforementioned issues, some new properties of the quaternion-valued signum function are presented for exploring the FTS of FQFNNs by the direct quaternion method without any decomposition. Then, 1-norm and 2-norm control strategies are designed to stabilize the addressed system in finite time, and several sufficient criteria are derived to ensure the FTS of FQFNNs. Finally, the validity of the obtained theoretical results and the superiority of the proposed estimation method are illustrated by numerical simulations.

As a class of randomized learner model, stochastic configuration networks (SCNs) have been successfully applied in a few data analytics tasks. Given the industrial big data modeling tasks, however, the original SCNs potentially lead to excessive training time. To this end, this article extends SCNs to a hybrid parallel version, termed hybrid parallel SCNs (HPSCNs). In the hybrid parallel learning algorithm, two SCNs are synchronously constructed. The difference between the two of them is that one employs a point-incremental algorithm, and another one adopts a block-incremental algorithm. Moreover, a data parallel method is established based on a dynamic block strategy to accelerate the establishment of candidate node pool for each SCN. Additionally, this article proposes an adaptive hyperparameter adjustment method, which allows the hyperparameters in the supervisory mechanism to be automatically adjusted along with the learning process. Comparative experiments are first conducted through four large-scale benchmark datasets, followed by the fully discussion on the algorithm parameters. Finally, a practical industrial application case is made, where a grinding particle size soft sensor is developed based on HPSCN, showing the effectiveness of the proposed algorithm.

This article studies the observer-based adaptive synchronization of multiagent systems (MASs) with unknown parameters under attacks. First, to estimate the state of agents, the observer for MAS is introduced. When disturbance, nonlinear function, and system model uncertainty are not considered, the nominal controller is proposed to achieve synchronization and state estimation. Then, in order to eliminate the effect of unknown parameters in the disturbance, nonlinear function, and system model uncertainty, the adaptive controller with switching term is introduced. However, the attack will lead to the destruction of the network topology so as the destruction of the nominal controller. By constructing an appropriate Lyapunov function, we analyze the effect caused by attacks, and the security control law is given to make sure the synchronization of the MASs under attacks. Finally, a numerical simulation is given to verify the validness of the obtained theorem.

This article concentrates on finite-time stabilization and energy consumption estimation for nonlinear systems with and without delay. By constructing an appropriate controller and utilizing inequality techniques, sufficient conditions are proposed to guarantee the finite-time stability of the delayed nonlinear system. Furthermore, the energy consumption produced in system controlling is estimated by inequality techniques. Then, we formulate similar results for the delay-free case. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

Sewer pipe is an essential infrastructure in the city as it undertakes the transportation and circulation of wastewater resources. But sewer pipe it is easy to have faults and cause serious secondary urban accidents, such as road holes and road collapse. Because of the complex underground circumstance, inspecting large-area sewer pipes using closed-circuit television or periscope television is difficult. In this study, we proposed a collaborative sewer pipe inspection approach by using novel low-cost pipe robotic capsules, which capture the images of the pipeline inner walls when floating with the water flow. A set of workers collaboratively drop and salvage capsules to cover a large-area pipe network. The routes of workers and pipe capsules are optimized by a meta-heuristic algorithm integrating local search and simulated annealing. The deep neural network is used to recognize faults from raw captured images. A field experiment in Shenzhen was conducted to evaluate the performance of the proposed approach. The results demonstrate that it outperforms the naive inspection method with a shorter travel distance and less waiting time. It is also effective for inspecting the large-area sewer pipe networks with an overall precision of 0.92. It will help us to eliminate the potential safety risk of the public and promote the level of urban governance.

This article shows a focus on the positivity and stability of Cohen-Grossberg-type time-delay memristor neural networks. We start by providing the existence and unique theorem of solutions for time-delay memristor neural networks to the case of unbounded delays. It is clear to find that the discriminate criterion of the existence and uniqueness of solutions about the argumented system with unbounded delays plays an important role in other related unbounded time-delay systems. Leveraging the Lyapunov method along with memristor nonlinearity, sufficient and necessary conditions for positivity and stability of Cohen-Grossberg-type memristor neural networks under unbounded delays are gained. Our proposed criteria don't need any strictly restrictive conditions. These theoretical results derived here will be helpful to understand the convergence performance of memristor electrical systems.

This article focuses on the observer-based quasi-synchronization problem of delayed dynamical networks with parameter mismatch under impulsive effect. First, since the state of each node is unknown in the real situation, the state estimation strategy is proposed to estimate the state of each node, so as to design an appropriate synchronization controller. Then, the corresponding controller is constructed to synchronize the slave nodes with their leader node. In this article, we take the impulsive effect into consideration, which means that an impulsive signal will be applied to the system every so often. Due to the existence of parameter mismatch and time-varying delay, by constructing an appropriate Lyapunouv function, we will eventually obtain a differential equation with constant and time-varying delay terms. Then, we analyze its trajectory by introducing the Cauchy matrix and prove its boundedness by contradiction. Finally, a numerical simulation is presented to illustrate the validness of obtained results.

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.

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.

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.

In this paper, a new mechanism, Multiple Users Cooperative Communication (MUCC) in LTE, is proposed. The detailed system designs are presented, which includes the definition of B-UE (Benefitted UE) and S-UE (Supporting UE), bearer management, protocol stack, MAC PDU (Protocol Data Unit) enhancement and signaling flow. Provisioning some S-UE could relay the B-UE's data to the B-UE via short range communication technology. The eNB may send the B-UE's data to the B-UE directly or to an S-UE cooperating with the B-UE. Since the scheduled UE is always the one with the best Channel Quality Indicator (CQI), the multi-users diversity gain can be acquired. The system simulation results are also presented, which prove the benefit of the MUCC.

ABSTRACT We consider the problem of optimal power allocation and optimal user selection in a layered multicast transmission over quasi‐static Rayleigh fading channels. A scheme based on superposition coding is proposed in which basic multicast streams and enhanced multicast streams are superimposed and transmitted by a base station, while users with worse channel conditions can only decode basic multicast streams, and users with better channel conditions can decode both basic and enhanced multicast streams. In this paper, subject to fixed user selection ratios, the optimal power allocation for each stream that maximizes average throughput is investigated, and the impact of power allocation on average outage probability is discussed. Finally, subject to fixed transmit power and power allocation, the optimal user selection ratio for enhanced multicast streams is also studied. Numerical results show that the optimized layered multicast scheme outperforms the conventional multicast scheme in terms of average throughput. Copyright © 2010 John Wiley & Sons, Ltd.

The conventional cooperative protocols have to face some problems in practical broadcast and multicast systems because feedback channel is unavailable. An adaptive cooperative relay protocol, which can be adopted in future broadcast systems, is proposed in this paper. The outage probability performance of this protocol is analyzed over Nakagami-m fading channel, and the asymptotic expression of outage probability for proposed protocol is derived. It is compared with the conventional Decode-and-Forward and Amplify-and-Forward protocols. A combination of numerical simulation and theoretical analysis, including the optimal numbers of relays and the impact on the system performance are further analyzed for different channel states. According to these results, the advantages and characteristics of this protocol are confirmed.

Inner cell interference (INCI) is avoided in common multicell orthogonal frequency division multiplex access (OFDMA) systems but inter cell interference (ICI) still exist. The system throughput is severely degraded by ICI, especially at cell edge. Several schemes have been proposed to handle this problem by coordinating the way to allocate spectrum resource to each cell. Since the allocation of spectrum has effects on ICI mitigation and the spectral efficiency, a wise strategy to consider those two factors is required. In this paper, the power division reuse partitioning scheme with successive interference cancellation (PDICS) for OFDMA uplink transmission is discussed. PDICS balances ICI mitigation and spectral efficiency by appropriate frequency allocation and power distribution. To improve frequency efficiency, the frequency reuse factor is chosen as 0.5, so INCI exists. To minimize INCI, successive interference cancellation is suggested. The simulation results show that PDICS has better performance of throughput and symbol error rate (SER) than the conventional schemes.

The capacity of relay channel is determined not only by the number of relays but also the relations among them. Cooperation among relays will greatly improve the network capacity by further reducing information uncertainty. Based on this theory, this paper introduces cooperative two-relay channel models with or without path loss, as well as the method for their capacity analysis. In these models, the work mode of the relays has two schemes, that is, the two relays select the same or different codebooks respectively. On calculating the capacity, we will analyze it without path loss firstly. Then based on this very result, we will further analyze the capacity with path loss. A numerical example without path loss is given in order to certify the result. It shows that the capacity is confined to the combination of the broadcast channel and multi-access channel and by finding the best way of power allocations we can achieve the maximum channel capacity.