This paper investigates the existence of Nash equilibria in multi-player nonzero-sum differential games governed by hybrid impulsive systems, where one player applies impulse controls while the remainingNplayers adopt piecewise-continuous controls. The proposed framework captures complex dynamics in which gradual adjustments coexist with abrupt interventions, with applications in traffic management, power dispatch, and emergency response. First, the necessary conditions for the existence of hybrid-strategy Nash equilibrium are rigorously derived using a variational method. Second, under traditional convexity assumptions, a sufficiency theorem for equilibrium existence is provided. By further introducing pseudoconvexity and invexity, a weak convexity framework with broader applicability is proposed, significantly relaxing the regularity requirements on the cost functions. Finally, numerical simulations, including a power system load dispatch case, demonstrate the validity of the theoretical results.

This letter proposes a multimodal depression risk assessment (mDRA) framework to overcome the limitations of single-modal approaches and data fusion in depression detection from audio and text. The mDRA leverages advanced neural network models, including a BiLSTM model with ELMO embeddings for text analysis and a ResNet50 model to extract 2D heatmap features from audio inputs. A collaborative attention mechanism integrates cross-modal information to enhance diagnostic precision. Experiments on the EATD-Corpus (Chinese language) and DAIC-WoZ (English language) datasets demonstrate the framework's effectiveness, achieving F1-scores of 0.94 (18% improvement) and 0.88 (3% improvement), outperforming stateof-the-art methods. These improvements enhance the reliability of early depression risk screening across different languages, which is critical for timely intervention. When deployed on a cloud platform with a mobile interface, mDRA can facilitate user-friendly depression screening through interactive virtual conversations, showcasing potential for early-stage assessment.

This paper investigates N versus N attack-defense game problem of heterogeneous nonlinear multi-agent systems under the condition of actuator faults on the defensive side. Specifically, N attackers need to approach the target area as closely as possible in order to attack it, while N defenders need to approach the attackers as closely as possible and intercept them. We decompose this problem into two N-player nonzero-sum game problems. Based on differential game method, the optimal attacking game strategies for the attackers are first presented. Then, considering that the defenders contains actuator faults, this paper designs a fault observer for each defending agent based on adaptive estimation theory to estimate unknown actuator fault and proposes a novel optimal defense game strategy applicable for actuator fault. To address the problem that it is difficult to directly solve the optimal control strategies in nonlinear systems, we propose an online learning algorithm based on adaptive dynamic programming to obtain approximate solutions for the optimal cost functions and the optimal control strategies. The effectiveness of the proposed method is verified through theoretical analysis and simulation examples.

Brain–computer interface (BCI) is a cutting-edge technology that holds promise in the healthcare industry, where multimodal information integration is required to capture features of physiological signals from different equipments. Challenge remains as how to integrate and detect diversified time series, such as electroencephalogram (EEG) and audio, for anomaly detection. This article proposes a spatio–temporal dynamic graph spike neural network, termedDynGraphSpike, which is constituted by two brain-inspired perception modules, each driven by a dynamic graph neural network (DGNN), and one spike-based multisensory integration network. DGNN incorporates the Wilson-Cowan model to configure spatio– temporal dynamics of the nodes, and utilizes the phase locking values of EEG channels to reshape the edges. To merge EEG and audio, spiking neurons are used to construct the multisensory integration network. Experiments demonstrate that DynGraphSpike achieves a classification accuracy over 99%, outperforming the state-of-the-art methods. Ablation studies confirm that the Wilson–Cowan and spiking dynamics enhance feature alignment via temporal synchronization, as indicated by dynamic warping time scores. Together with spatio–temporal dynamics, DynGraphSpike has the potential to facilitate BCI technologies for disease diagnosis.

Due to the importance of the hybrid systems, the controllability for linear discrete-time impulsive hybrid systems with input delay (DIHSID) is investigated by resorting to the geometric and algebraic analytical methods in this article. First, the null reachability and controllability geometric conditions are studied. Specifically, the null reachable set and controllable set for every impulsive and switching sequence are obtained by the properties of the invariant subspace. Besides, a new subspace sequence is constructed to analyze the null reachability and controllability of DIHSID. Second, the complete controllability of DIHSID is investigated by algebraic methods. In the form of Gramian matrices, several sufficient complete controllability conditions for DIHSID are established without assuming the nonsingularity of all impulsive matrices. Furthermore, a less conservative complete controllability criterion that is necessary and sufficient is developed by introducing a row matrix of some Gramian matrices. Finally, two illustrating examples show the effectiveness of the developed controllability theory.

In this article, we consider the design of dynamic transmission scheduling policies for the industrial network systems sharing scarce communication resources. Only a few subsystems can obtain channel access for information updates to close their control loops at each time step, which highlights the necessity of designing optimal transmission scheduling schemes to achieve a minimum average linear quadratic cost of the industrial network systems. We first propose a greedy state-error-dependent scheduling (SES) policy based on the one-step expected profit and discuss its stability employing the Lyapunov function method. After formulating the scheduling optimization as a Markov decision process problem and relaxing with a soft constraint, we develop a heuristic near-optimal solution that guarantees the optimality of certainty equivalent controllers, namely, Whittle’s index-inspired error-dependent scheduling (WIES). A stochastic stability condition of WIES is further given based on f-ergodicity. Due to low computational complexity and ease of implementation, the proposed schemes are suitable for large-scale heterogeneous industrial network systems. Finally, simulation results show that the proposed policies outperform the existing round-robin, holding-time-prioritized, and error-aware scheduling schemes.

This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications.

This article studies the dynamic transmission-scheduling problem of rate-limited networked control systems with multiple loops. It is critical to develop an optimal-scheduling policy because, due to limited spectrum resources and energy budgets, only partial subsystems may have access to shared channels at each time step to update the plant states affected by stochastic disturbances. An adaptive event-triggered stochastic scheduling policy is proposed based on the one-step-ahead comparison error of state estimation between the sensor and controller. By formulating the scheduling problem as a constrained multiagent partially observable Markov decision process, a multiagent reinforcement learning algorithm is proposed to search for the optimal parameters of the scheduling policy. And an edge-assisted learning architecture is introduced to facilitate its implementation. An explicit performance index of the optimal scheduling is further obtained, revealing the effects of system disturbances, observation noises, and the communication rate constraint. Moreover, two numerical examples are given to validate the proposed scheduling policy, showing that it outperforms several competitive scheduling schemes. Due to the low computational complexity, the proposed scheduling may have an advantage in large-scale heterogeneous control systems, e.g., the flow and pressure control in fluid transport pipelines.

In this article, we investigate the routing problem of packet networks through multiagent reinforcement learning (RL), which is a very challenging topic in distributed and autonomous networked systems. In specific, the routing problem is modeled as a networked multiagent partially observable Markov decision process (MDP). Since the MDP of a network node is not only affected by its neighboring nodes' policies but also the network traffic demand, it becomes a multitask learning problem. Inspired by recent success of RL and metalearning, we propose two novel model-free multiagent RL algorithms, named multiagent proximal policy optimization (MAPPO) and multiagent metaproximal policy optimization (meta-MAPPO), to optimize the network performances under fixed and time-varying traffic demand, respectively. A practicable distributed implementation framework is designed based on the separability of exploration and exploitation in training MAPPO. Compared with the existing routing optimization policies, our simulation results demonstrate the excellent performances of the proposed algorithms.

This paper aims at solving the bipartite containment problem for linear singular multi-agent systems (MASs) with multiple dynamic leaders over general signed digraphs, where each leader can be autonomous or dynamically evolving via interactions with its neighboring leaders. To this end, we first establish some properties for the Laplacian matrices of signed digraphs. Then, three distributed observer-based bipartite containment protocols are proposed using different local output information. Multi-step algorithms for constructing the corresponding proposed protocols are also given. It is shown that under the proposed control protocols, bipartite containment can be achieved for any admissible initial states provided that the underlying signed digraph is weakly connected. Compared to the existing related works, the major contribution of present work is that the developed results are applicable for arbitrary weakly connected signed digraphs, no matter whether they are sign-symmetric or sign-asymmetric and whether they are structurally balanced or unbalanced. Two numerical examples are finally given to demonstrate the validity of our results.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance.

This paper addresses the sampled-data state estimation problem for complex networks using partial nodes' measurements. A hybrid observer network with partial control is developed to estimate the state information. The key point of the hybrid observer network is that the state observer network is continuous-time by introducing an output predictor. Besides, the hybrid observer only requires a fraction of nodes' sampled measurements with partial control technique. It reduces the state estimation cost and improves the estimation effectiveness. Some criteria are developed to guarantee that the proposed observer network is an exponential observer. Finally, simulation example validates the proposed approach.

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.

In this paper, distributed iterative algorithms for consensus problems are considered for multiagent networks. Each agent randomly contacts with other agents at each instant and receives corrupted information due to the noisy channel from its neighborhood. Neighbors of each agent are cooperative or competitive, i.e., the elements in the adjacent weight matrix may be positive or negative. In such a framework, asymptotic consensus and mean square consensus problems are investigated, based on random graph theory and stochastic stability theory. The control gains have been designed such that cooperation-competition random multiagent networks can reach almost sure consensus and mean square consensus. Simulation examples are finally given to illustrate the effectiveness of the obtained results.

In this paper, some consensus problems are considered for time-delay multiagent networks with directed topologies. Since agents are driven by not only long-term but instant contact with their neighbors, dynamic behaviors of agents can be described by impulsive differential equations. A period of non time-delay and time-delay information and instantaneous information are adopted in the proposed algorithms. Moreover, robust problems with the corresponding ${H_{\infty }}$ performance are investigated for multiagent networks with external disturbances. Sufficient conditions are obtained such that consensus can be exponentially reached for multiagent networks with/without external disturbances. Numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

This paper studies a class of heterogeneous delayed impulsive neural networks with memristors and their collective evolution for multisynchronization. The multisynchronization represents a diversified collective behavior that is inspired by multitasking as well as observations of heterogeneity and hybridity arising from system models. In view of memristor, the memristor-based impulsive neural network is first represented by an impulsive differential inclusion. According to the memristive and impulsive mechanism, a fuzzy logic rule is introduced, and then, a new fuzzy hybrid impulsive and switching control method is presented correspondingly. It is shown that using the proposed fuzzy hybrid control scheme, multisynchronization of interconnected memristor-based impulsive neural networks can be guaranteed with a positive exponential convergence rate. The heterogeneity and hybridity in system models, thus, can be indicated by the obtained error thresholds that contribute to the multisynchronization. Numerical examples are presented and compared to demonstrate the effectiveness of the developed theoretical results.

Inspired by security applications in the industrial Internet of things, this paper focuses on the usage of impulsive neural network (NN) synchronization technique for intelligent image protection against illegal swiping and abuse. A class of nonlinear interconnected NNs with transmission delay and random impulse effect is first formulated and analyzed in this paper. In order to make network protocols more flexible, a randomized broadcast impulsive coupling scheme is integrated into the protocol design. Impulsive synchronization criteria are then derived for the chaotic NNs in the presence of nonlinear protocol and random broadcast impulse, with the impulse effect discussed. Illustrative examples are provided to verify the developed impulsive synchronization results and to show its potential application in image encryption and decryption.

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.

Neural networks (NNs) have emerged as a powerful illustrative diagram for the brain. Unveiling the mechanism of neural-dynamic evolution is one of the crucial steps toward understanding how the brain works and evolves. Inspired by the universal existence of impulses in many real systems, this paper formulates a type of hybrid NNs (HNNs) with impulses, time delays, and interval uncertainties, and studies its global dynamic evolution by a robust interval analysis. The HNNs incorporate both continuous-time implementation and impulsive jump in mutual activations, where time delays and interval uncertainties are represented simultaneously. By constructing a Banach contraction mapping, the existence and uniqueness of the equilibrium of the HNN model are proved and analyzed in detail. Based on nonsmooth Lyapunov functions and delayed impulsive differential equations, new criteria are derived for ensuring the global robust exponential stability of the HNNs. Convergence analysis together with illustrative examples show the effectiveness of the theoretical results.

This paper investigates distributed coordination of a team of wheeled mobile robots for multiple moving targets interception over a convex domain. In order to successfully intercept potential intruders entering the mission domain from different orientations, mobile robots are dynamically deployed to monitor the whole area and track moving targets once they are detected at a certain location. Due to the lack of knowledge about the numbers and online dynamic models of targets, a time-varying priority function indicating the most probable area where these targets may appear is introduced to increase the chance of intercepting them. Meanwhile, a target switching mechanism is employed to decide when targets should be considered by each mobile robot for interception task. Based on this priority function, a novel distributed coverage control law is designed to guarantee that wheeled mobile robots asymptotically converge to their generalized Centroidal Voronoi Tessellation and minimize the cost function with respect to those moving targets. Simulation results are given to present the advantage of the proposed approach over traditional coverage control strategy.

This paper proposes a control framework, called pulse-modulated intermittent control, which unifies impulsive control and sampled control. Specifically, the concept of pulse function is introduced to characterize the control/rest intervals and the amplitude of the control. By choosing some specified functions as the pulse function, the proposed control scheme can be reduced to sampled control or impulsive control. The proposed control framework is applied to consensus problems of multiagent systems. Using discretization approaches and stability theory, several necessary and sufficient conditions are established to ensure the consensus of the controlled system. The results show that consensus depends not only on the network topology, the sampling period and the control gains, but also the pulse function. Moreover, a lower bound of the asymptotic convergence factor is derived as well. For a given pulse function and an undirected graph, an optimal control gain is designed to achieve the fastest convergence. In addition, impulsive control and sampled control are revisited in the proposed control framework. Finally, some numerical examples are given to verify the effectiveness of theoretical results.