Mittag-Leffler stability and application of delayed fractional-order competitive neural networks.

In the article, the Mittag-Leffler stability and application of delayed fractional-order competitive neural networks (FOCNNs) are developed. By virtue of the operator pair, the conditions of the coexistence of equilibrium points (EPs) are discussed and analyzed for delayed FOCNNs, in which the derived conditions of coexistence improve the existing results. In particular, these conditions are simplified in FOCNNs with stepped activations. Furthermore, the Mittag-Leffler stability of delayed FOCNNs is established by using the principle of comparison, which enriches the methodologies of fractional-order neural networks. The results on the obtained stability can be used to design the horizontal line detection of images, which improves the practicability of image detection results. Two simulations are displayed to validate the superiority of the obtained results.

Residual Temporal Convolutional Network With Dual Attention Mechanism for Multilead-Time Interpretable Runoff Forecasting.

As a pivotal subfield within the domain of time series forecasting, runoff forecasting plays a crucial role in water resource management and scheduling. Recent advancements in the application of artificial neural networks (ANNs) and attention mechanisms have markedly enhanced the accuracy of runoff forecasting models. This article introduces an innovative hybrid model, ResTCN-DAM, which synergizes the strengths of deep residual network (ResNet), temporal convolutional networks (TCNs), and dual attention mechanisms (DAMs). The proposed ResTCN-DAM is designed to leverage the unique attributes of these three modules: TCN has outstanding capability to process time series data in parallel. By combining with modified ResNet, multiple TCN layers can be densely stacked to capture more hidden information in the temporal dimension. DAM module adeptly captures the interdependencies within both temporal and feature dimensions, adeptly accentuating relevant time steps/features while diminishing less significant ones with minimal computational cost. Furthermore, the snapshot ensemble method is able to obtain the effect of training multiple models through one single training process, which ensures the accuracy and robustness of the forecasts. The deep integration and collaborative cooperation of these modules comprehensively enhance the model's forecasting capability from various perspectives. Ablation studies conducted validate the efficacy of each module, and through multiple sets of comparative experiments, it is shown that the proposed ResTCN-DAM has exceptional and consistent performance across varying lead times. We also employ visualization techniques to display heatmaps of the model's weights, thereby enhancing the interpretability of the model. When compared with the prevailing neural network-based runoff forecasting models, ResTCN-DAM exhibits state-of-the-art accuracy, temporal robustness, and interpretability, positioning it at the forefront of contemporary research.

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.

Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation.

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order-d ( d ≥ 3 ) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.

A memristive all-inclusive hypernetwork for parallel analog deployment of full search space architectures.

In recent years, there has been a significant advancement in memristor-based neural networks, positioning them as a pivotal processing-in-memory deployment architecture for a wide array of deep learning applications. Within this realm of progress, the emerging parallel analog memristive platforms are prominent for their ability to generate multiple feature maps in a single processing cycle. However, a notable limitation is that they are specifically tailored for neural networks with fixed structures. As an orthogonal direction, recent research reveals that neural architecture should be specialized for tasks and deployment platforms. Building upon this, the neural architecture search (NAS) methods effectively explore promising architectures in a large design space. However, these NAS-based architectures are generally heterogeneous and diversified, making it challenging for deployment on current single-prototype, customized, parallel analog memristive hardware circuits. Therefore, investigating memristive analog deployment that overrides the full search space is a promising and challenging problem. Inspired by this, and beginning with the DARTS search space, we study the memristive hardware design of primitive operations and propose the memristive all-inclusive hypernetwork that covers 2×1025 network architectures. Our computational simulation results on 3 representative architectures (DARTS-V1, DARTS-V2, PDARTS) show that our memristive all-inclusive hypernetwork achieves promising results on the CIFAR10 dataset (89.2% of PDARTS with 8-bit quantization precision), and is compatible with all architectures in the DARTS full-space. The hardware performance simulation indicates that the memristive all-inclusive hypernetwork costs slightly more resource consumption (nearly the same in power, 22%∼25% increase in Latency, 1.5× in Area) relative to the individual deployment, which is reasonable and may reach a tolerable trade-off deployment scheme for industrial scenarios.

Combined transcriptomics and metabolomics to analyse the response of Cuminum cyminum L. under Pb stress.

Lead (Pb) can disrupt plant gene expression, modify metabolite contents, and influence the growth of plants. Cuminum cyminum L. is highly adaptable to adversity, but molecular mechanism by which it responds to Pb stress is unknown. For this study, transcriptomic and metabolomic sequencing was performed on root tissues of C. cyminum under Pb stress. Our results showed that high Pb stress increased the activity of peroxidase (POD), the contents of malondialdehyde (MDA) and proline by 80.03 %, 174.46 % and 71.24 %, respectively. Meanwhile, Pb stress decreased the activities of superoxide dismutase (SOD) and catalase (CAT) as well as contents of soluble sugars and GSH, which thus affected the growth of C. cyminum. In addition, Pb stress influenced the accumulation and transport of Pb in C. cyminum. Metabolomic results showed that Pb stress affected eight metabolic pathways involving 108 differentially expressed metabolites, primarily amino acids, organic acids, and carbohydrates. The differentially expressed genes identified through transcriptome analysis were mainly involved the oxidation reductase activity, transmembrane transport, phytohormone signaling, and MAPK signaling pathway. The results of this study will help to understand the molecular mechanisms of C. cyminum response to Pb stress, and provide a basis for screening seeds with strong resistance to heavy metals.

Robust Collision-Avoidance Formation Navigation of Velocity and Input-Constrained Multirobot Systems.

In this work, we consider the safe deployment problem of multiple robots in an obstacle-rich complex environment. When a team of velocity and input-constrained robots is required to move from one area to another, a robust collision-avoidance formation navigation method is needed to achieve safe transferring. The constrained dynamics and the external disturbances make the safe formation navigation a challenging problem. A novel robust control barrier function-based method is proposed which enables collision avoidance under globally bounded control input. First, a nominal velocity and input-constrained formation navigation controller is designed which uses only the relative position information based on a predefined-time convergent observer. Then, new robust safety barrier conditions are derived for collision avoidance. Finally, a local quadratic optimization problem-based safe formation navigation controller is proposed for each robot. Simulation examples and comparison with existing results are provided to demonstrate the effectiveness of the proposed controller.

Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design.

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.

A collective neurodynamic penalty approach to nonconvex distributed constrained optimization.

A nonconvex distributed optimization problem involving nonconvex objective functions and inequality constraints within an undirected multi-agent network is considered. Each agent communicates with its neighbors while only obtaining its individual local information (i.e. its constraint and objective function information). To overcome the challenge caused by the nonconvexity of the objective function, a collective neurodynamic penalty approach in the framework of particle swarm optimization is proposed. The state solution convergence of every neurodynamic penalty approach is directed towards the critical point ensemble of the nonconvex distributed optimization problem. Furthermore, employing their individual neurodynamic models, each neural network conducts accurate local searches within constraints. Through the utilization of both locally best-known solution information and globally best-known solution information, along with the incremental enhancement of solution quality through iterations, the globally optimal solution for a nonconvex distributed optimization problem can be found. Simulations and an application are presented to demonstrate the effectiveness and feasibility.

A Distributed k-Winners-Take-All Model With Binary Consensus Protocols.

This article concentrates on solving the k -winners-take-all (k WTA) problem with large-scale inputs in a distributed setting. We propose a multiagent system with a relatively simple structure, in which each agent is equipped with a 1-D system and interacts with others via binary consensus protocols. That is, only the signs of the relative state information between neighbors are required. By virtue of differential inclusion theory, we prove that the system converges from arbitrary initial states. In addition, we derive the convergence rate as O(1/t) . Furthermore, in comparison to the existing models, we introduce a novel comparison filter to eliminate the resolution ratio requirement on the input signal, that is, the difference between the k th and (k+1) th largest inputs must be larger than a positive threshold. As a result, the proposed distributed k WTA model is capable of solving the k WTA problem, even when more than two elements of the input signal share the same value. Finally, we validate the effectiveness of the theoretical results through two simulation examples.

Event-triggered impulsive quasi-synchronization for BAM neural networks with reliable redundant channel.

This work addresses the quasi-synchronization of delay master-slave BAM neural networks. To improve the utilization of channel bandwidth, a dynamic event-triggered impulsive mechanism is employed, in which data is transmitted only when a preset event-triggered mechanism or a forced impulse interval is satisfied. In addition, to guarantee the reliability of information transmission, a reliable redundant channel for BAM neural networks is adopted, whose transmission scheduling strategy is designed on the basis of the packet dropouts rate of the main communication channels. Further, an algorithm is employed to reduce the quasi-synchronization range of the error systems and the controllers are obtained. At last, a simulation result is shown to illustrate the effectiveness of the presented strategy.

Memory Fusion Controller of Fractional-Order Systems With Sliding Memory Window Under Intermittent Sampled-Data Transmission.

This work proposes a memory fusion controller design methodology for sampled-data control of fractional-order (FO) systems with sliding memory window. Composed of finite-dimensional previous inputs, the devised controller is capable of handling hereditary effect and meanwhile enabling pseudo state to satisfy general integer-order (IO) discrete plant at sampling instants. Additionally, the asymptotical stability of controller and sampling error are further guaranteed. The developed fusion controller provides an "out-of-the-box" method for users who are not familiar with FO calculus and significantly facilitates the corresponding analysis. The above mentioned approach is thereafter employed in a more sophisticated case, that is, the coordination control of FO multiagent systems (MASs) subjects to intermittent sampled-data transmission. It is proved that the achievement of consensus only relates to the connectivity of communication graph. Numerical results are presented finally to substantiate the proposed control strategy.

Resilient Output Containment Control of Heterogeneous Multiagent Systems Against Composite Attacks: A Digital Twin Approach.

This article delves into the distributed resilient output containment control of heterogeneous multiagent systems against composite attacks, including Denial-of-Service (DoS) attacks, false-data injection (FDI) attacks, camouflage attacks, and actuation attacks. Inspired by digital twin technology, a twin layer (TL) with higher security and privacy is employed to decouple the above problem into two tasks: 1) defense protocols against DoS attacks on TL and 2) defense protocols against actuation attacks on the cyber-physical layer (CPL). Initially, considering modeling errors of leader dynamics, distributed observers are introduced to reconstruct the leader dynamics for each follower on TL under DoS attacks. Subsequently, distributed estimators are utilized to estimate follower states based on the reconstructed leader dynamics on the TL. Then, decentralized solvers are designed to calculate the output regulator equations on CPL by using the reconstructed leader dynamics. Simultaneously, decentralized adaptive attack-resilient control schemes are proposed to resist unbounded actuation attacks on the CPL. Furthermore, the aforementioned control protocols are applied to demonstrate that the followers can achieve uniformly ultimately bounded (UUB) convergence, with the upper bound of the UUB convergence being explicitly determined. Finally, we present a simulation example and an experiment to show the effectiveness of the proposed control scheme.

Data-Driven Event-Triggered Adaptive Dynamic Programming Control for Nonlinear Systems With Input Saturation.

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.

Distributed Neurodynamic Models for Solving a Class of System of Nonlinear Equations.

This article investigates a class of systems of nonlinear equations (SNEs). Three distributed neurodynamic models (DNMs), namely a two-layer model (DNM-I) and two single-layer models (DNM-II and DNM-III), are proposed to search for such a system's exact solution or a solution in the sense of least-squares. Combining a dynamic positive definite matrix with the primal-dual method, DNM-I is designed and it is proved to be globally convergent. To obtain a concise model, based on the dynamic positive definite matrix, time-varying gain, and activation function, DNM-II is developed and it enjoys global convergence. To inherit DNM-II's concise structure and improved convergence, DNM-III is proposed with the aid of time-varying gain and activation function, and this model possesses global fixed-time consensus and convergence. For the smooth case, DNM-III's globally exponential convergence is demonstrated under the Polyak-Lojasiewicz (PL) condition. Moreover, for the nonsmooth case, DNM-III's globally finite-time convergence is proved under the Kurdyka-Lojasiewicz (KL) condition. Finally, the proposed DNMs are applied to tackle quadratic programming (QP), and some numerical examples are provided to illustrate the effectiveness and advantages of the proposed models.

SMONAC: Supervised Multiobjective Negative Actor-Critic for Sequential Recommendation.

Recent research shows that the sole accuracy metric may lead to the homogeneous and repetitive recommendations for users and affect the long-term user engagement. Multiobjective reinforcement learning (RL) is a promising method to achieve a good balance in multiple objectives, including accuracy, diversity, and novelty. However, it has two deficiencies: neglecting the updating of negative action Q values and limited regulation from the RL Q-networks to the (self-)supervised learning recommendation network. To address these disadvantages, we develop the supervised multiobjective negative actor-critic (SMONAC) algorithm, which includes a negative action update mechanism and multiobjective actor-critic mechanism. For the negative action update mechanism, several negative actions are randomly sampled during each time updating, and then, the offline RL approach is utilized to learn their Q values. For the multiobjective actor-critic mechanism, accuracy, diversity, and novelty Q values are integrated into the scalarized Q value, which is used to criticize the supervised learning recommendation network. The comparative experiments are conducted on two real-world datasets, and the results demonstrate that the developed SMONAC achieves tremendous performance promotion, especially for the metrics of diversity and novelty.

Convergence Analysis of Online Gradient Method for High-Order Neural Networks and Their Sparse Optimization.

In this article, we investigate the boundedness and convergence of the online gradient method with the smoothing group L1/2 regularization for the sigma-pi-sigma neural network (SPSNN). This enhances the sparseness of the network and improves its generalization ability. For the original group L1/2 regularization, the error function is nonconvex and nonsmooth, which can cause oscillation of the error function. To ameliorate this drawback, we propose a simple and effective smoothing technique, which can effectively eliminate the deficiency of the original group L1/2 regularization. The group L1/2 regularization effectively optimizes the network structure from two aspects redundant hidden nodes tending to zero and redundant weights of surviving hidden nodes in the network tending to zero. This article shows the strong and weak convergence results for the proposed method and proves the boundedness of weights. Experiment results clearly demonstrate the capability of the proposed method and the effectiveness of redundancy control. The simulation results are observed to support the theoretical results.

Fuzzy Boundary Sampled-Data Control for Nonlinear Parabolic DPSs.

For a nonlinear parabolic distributed parameter system (DPS), a fuzzy boundary sampled-data (SD) control method is introduced in this article, where distributed SD measurement and boundary SD measurement are respected. Initially, this nonlinear parabolic DPS is represented precisely by a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model. Subsequently, under distributed SD measurement and boundary SD measurement, a fuzzy boundary SD control design is obtained via linear matrix inequalities (LMIs) on the basis of the T-S fuzzy parabolic PDE model to guarantee exponential stability for closed-loop parabolic DPS by using inequality techniques and a LF. Furthermore, respecting the property of membership functions, we present some LMI-based fuzzy boundary SD control design conditions. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

Adaptive event-triggered extended dissipative synchronization of delayed reaction-diffusion neural networks under deception attacks.

Under spatially averaged measurements (SAMs) and deception attacks, this article mainly studies the problem of extended dissipativity output synchronization of delayed reaction-diffusion neural networks via an adaptive event-triggered sampled-data (AETSD) control strategy. Compared with the existing ETSD control methods with constant thresholds, our scheme can be adaptively adjusted according to the current sampling and latest transmitted signals and is realized based on limited sensors and actuators. Firstly, an AETSD control scheme is proposed to save the limited transmission channel. Secondly, some synchronization criteria under SAMs and deception attacks are established by utilizing Lyapunov-Krasovskii functional and inequality techniques. Then, by solving linear matrix inequalities (LMIs), we obtain the desired AETSD controller, which can satisfy the specified level of extended dissipativity behaviors. Lastly, one numerical example is given to demonstrate the validity of the proposed method.

Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances.

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.