This work investigates the impulsive optimal control problem for second-order hybrid systems that combines discrete dynamics with continuous dynamics based on adaptive dynamic programming. An impulsive optimal control protocol is proposed, and a parallel computation method is introduced to reduce computational time. Furthermore, a specialized mechanism is developed to adjust the selection tendency of impulsive intervals. Finally, an illustrative example is provided to demonstrate the feasibility of the proposed method.

This paper investigates the coupled interplay among public opinion, mass media, and epidemic spreading through a co-evolutionary multilayer network framework. We develop a Susceptible-Alert-Infected-Susceptible (SAIS) model on the physical layer, coupled with a dynamic opinion layer that captures groups' perceived severity of the epidemic. A key feature of the model is a parameter-level coupling mechanism, whereby opinions-shaped by mass media and social interactions-directly modulate infection and recovery rates. The opinion dynamics evolve on a directed signed graph, incorporating both cooperative and antagonistic inter-group interactions as well as media influence. We rigorously establish the well-posedness of the system and derive opinion-dependent reproduction numbers to characterize epidemic thresholds. Analytical and numerical results reveal that the interaction between media-driven alertness and social influence generates rich dynamical behaviors, leading to multiple stable equilibria. By examining different regimes of the reproduction numbers, we identify diverse epidemic-opinion scenarios and discuss their potential strategic implications.

This paper investigates the formation problem of unmanned aerial vehicles under spatiotemporal coupling constraints. Firstly, unlike existing stability theories based on predefined-time, this paper designs a predefined-time formation controller based on time-based generator and sliding mode control technology, which mitigates the initial input saturation issue. Secondly, a collision prediction mechanism is designed based on the artificial potential field method, which avoids unnecessary obstacle avoidance behavior when unmanned aerial vehicles detect non threatening obstacles and reduces redundant resource consumption. Finally, simulation results are presented to indicate that the proposed scheme enables the unmanned aerial vehicles to achieve formation and reconstruct the formation within the predefined-time after obstacle avoidance.

In this paper, an event-triggered time-varying formation tracking control for a class of second-order nonlinear multi-agent systems (MAS) operating within a constrained region is investigated. To mitigate the negative effects of external unknown disturbance, a novel disturbance observer with performance guarantees is proposed, enabling precise disturbance estimation. Using the artificial potential field (APF) method, a repulsive potential function is introduced to prevent inter-agent collisions as well as collisions with environmental obstacles. To reduce continuous communication and frequent system updates, a sliding mode technique is incorporated into the formation tracking controller, utilizing an event-triggered mechanism. The controller is also applicable to the formation control of MAS in switching-constrained regions. The achievement of the specified time-varying geometric formation is rigorously demonstrated through the Lyapunov framework. Numerical simulations are presented to validate the effectiveness of the theoretical results.

In order to investigate how different levels of vigilance affect the spread of a virus and changes in public opinion, this article introduces a network-based susceptible-exposed-infectious-vigilant (SEIV)-Opinion model. The model incorporates vigilance influence functions that depend on infection and recovery rates, which are associated with opinion states. A basic reproduction number dependent on both the viral transmission state and public opinion dynamics is constructed to analyze the conditions for virus eradication or pandemic persistence. These findings indicate that during severe epidemics, people are very concerned about the epidemic, leading to an increased vigilance, thereby significantly slowing the spread of the virus. On the other hand, during milder epidemics, people do not respond adequately to the threat of the epidemic, and thus are less vigilant and have less impact on the spread of the virus. These insights correlate closely with real-world trends. This article uses numerical simulations to demonstrate and confirm these patterns under various conditions.

This paper proposes a novel large-scale group decision-making (LSGDM) framework based on complex network theory. First, by enhancing the clustering efficiency of the Louvain algorithm through complex network theory, this framework enables community classification of a large-scale expert group, thereby reduce the complexity of the expert network and improve decision-making efficiency. Second, a novel communicability-driven expert influence identification model within expert social networks is designed, and a new consensus feedback mechanism is proposed. This approach comprehensively considers both the individual influence of experts and the impact of their interactions to guide consensus-reaching, which can accurately reflect the actual flow of information within the network. Third, by extending the Best-Worst Method and Shannon Entropy Method to the context of fuzzy information, a balance between subjectivity and objectivity is obtained, which can make more accurate and interpretable decision results. The proposed method is validated through a case study on green material selection. Moreover, its superiority is further demonstrated through comparative experiments. The results show that our method demonstrates a 9.89% reduction in opinion revision costs with accelerated consensus-reaching efficiency.

The time-varying formation problem of singular multi-agent systems under sampled data with multiple leaders is investigated in this paper. Firstly, a data-sampled time-varying formation control protocol is proposed in the current study where the communication among followers merely occurred at sampling instants, which can save the controller communication energy significantly. Secondly, necessary and sufficient conditions for the feasibility of the formation function are provided. In addition, an approach is presented to design the formation tracking control under sampled data with multiple leaders. Finally, numerical simulations validate the efficacy of the theoretical results.

A consensus protocol has been developed for a category of multi-agent systems(MASs) that are susceptible to DoS attacks and unknown input disturbance, considering two aspects: the online state cannot be obtained under unknown input disturbance by agent and common communication cannot be accomplished among agents under DoS attacks. Firstly, an improved proportion-integral observer is designed based on the Luenberger observer, which estimate to the agent’s state through the output information of the agent; Secondly, in order to resist the impact of DoS attacks and unknown input disturbance on MASs, a communication protocol with disturbance estimation is designed; By using theories such as stability theory, linear matrix inequality(LMI) and algebraic graph theory, sufficient conditions for the system to achieve security consensus is obtained; Finally, numerical experiments were conducted to verify the effectiveness of the relevant theories.

This article investigates the group consensus via pinning control for continuous‐time first‐order and second‐order multi‐agent systems (MASs) with reference states. For the group consensus of first‐order MASs, the dependence between the agent's state and the control input is considered. For second‐order MASs, group consensus control without the velocity information of agents is considered. Instead, the virtual velocity estimation controller is designed. Meanwhile, for the designed control protocols, not only under fixed topology, but also under switching topology are considered. It is demonstrated that group consensus could be obtained under the proposed control protocols by using graph theory and stability theory. Finally, a series of numerical examples are provided to verify the control performance of the propounded control protocols.

In this paper, a fixed-time time-varying formation tracking controller is proposed for second-order multi-agent systems (MASs) with region constraints based on adaptive observation. A practical finite-time disturbance observer (DO) with an adaptive update law is proposed to eliminate the negative effects of disturbance. Using the sliding mode control technique, a novel fixed-time time-varying region constraints formation tracking controller is designed and the upper bound of convergence time is given. The simulation results show that the disturbance is estimated accurately and quickly by the designed DO, the desired time-varying regular hexagonal formation is realized within the upper bound of convergence time, and all agents remain within the constraint region, which verifies the effectiveness and feasibility of the theoretical results.

In this paper, fast finite-time time-varying formation tracking control for second-order multi-agent systems with external disturbance and region constraints is investigated. The ubiquitous control input response delay is considered. A predictor-based state transformation is employed to obtain the ideal equivalent systems without control input response delay. Considering the difficulty of measuring external disturbance, a fast finite-time observer with the sliding mode technique is proposed to estimate the disturbance, which positively compensates the system. By adopting the sliding mode control strategy, a novel fast finite-time formation tracking controller is proposed. Sufficient conditions for the formation tracking control with region constraints are obtained. Numerical simulations are employed to validate the feasibility and effectiveness of the theoretical results.

The issue of group consensus for heterogeneous fractional-order multi-agent systems under the cooperation-competition networks with time delays is investigated in this paper. Novel group consensus control protocols with input and communication delays are designed based on cooperative-competitive interaction. The considered multi-agent systems consists of fractional order dynamics with the single integrator and the double integrator, and the speed of agents is not known. The matrix theory, frequency domain approach and graph theory are used to figure out the sufficient conditions for group consensus under the switching and fixed topology, respectively. Finally, numerical simulation examples are given to verify the correctness of the theoretical results.

Formation control of multi-agent systems(MASs)has been applied in various fields,such as autonomous navigation and target encirclement,due to its ability to facilitate coordina-tion and achieve the desired formation or space configura-tion.Bearing-based formation control offers greater prac-ticality than position-based or distance-based approaches since bearing information is inexpensive and simple to ac-quire,such as utilizing optical cameras.

The group consensus problem of heterogeneous fractional-order multi-agent systems with data packet losses and communication delays is investigated in this paper, and data packet losses are described by the Bernoulli-distribution. Inspired by genetic and the infinite memory property of the Caputo fractional derivative, a novel group consensus control protocol based on sampled data is designed. Sufficient conditions for mean-square group consensus of heterogeneous fractional-order multi-agent systems are derived by using matrix theory, Gerschgorin disc theorem and graph theory. Finally, numerical simulation examples are given to verify the correctness of the theoretical results.

This paper studies the fixed-time coordinated tracking problem of second-order nonlinear multi-agent systems with unknown disturbances. Based on the fixed-time distributed observer, a non-singular terminal sliding mode protocol is proposed, which could avoid singularity and achieve exact convergence. By using graph theory and Lyapunov stability method, sufficient conditions and the upper bound of setting time for fixed-time coordinated tracking are obtained. Numerical examples are given to show the effectiveness of theoretical results.

This paper studies the mean-square consensus of second-order hybrid multi-agent systems over jointly connected topologies. Systems with time-varying delay and multiplicative noise are considered. The date sampling control technique is adopted. Through matrix transformation, a positive definite matrix transformed by the Laplacian matrix is obtained, where the Laplacian matrix is a connected subgraph divided by the jointly connected topologies. By using graph theory, matrix theory and Lyapunov stability theory, sufficient conditions and the upper bound of time delays for the mean-square consensus are obtained. Finally, several simulations are presented to demonstrate the validity of the control method.

This article investigates the group consensus problem for heterogeneous multiagent systems with time delays via pinning control. Under the designed control protocol, agents in the system could be grouped arbitrarily, and agents in the same subgroup could converge to a constraint position. Meanwhile, the kinetics of agents in the same subgroup could be same or different. Both the fixed and switching topologies are considered. Based on the frequency domain method and stability theory, sufficient conditions for the system achieve group consensus are derived. Finally, several numerical examples are presented to verify the performance of the control protocol.

This paper addresses the issue of dynamic mean-square consensus for second-order hybrid multi-agent systems. Time-varying delays and multiplicative noises are considered. New distributed control protocols are designed based on data-sampled information of neighbor agents. Equivalently using the error system based on Laplacian matrix, the method could make a dynamic consensus both under the fixed and switching topologies. By adopting stochastic system theory, Lyapunov stability method and linear matrix inequality theory, several sufficient conditions for the dynamic mean-square consensus are obtained. The upper bound of time delay and the discrete-time sampling period of hybrid multi-agent systems under a stochastic noises environment are inferred. Several simulations are presented to demonstrate the effectiveness of the proposed methods.

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated. For cooperative-competitive network, two different control protocols, fixed-time group consensus and fixed-time event-triggered group consensus, are designed. It is demonstrated that there is no Zeno behavior under the designed event-triggered control. Meanwhile, it is proved that for an arbitrary initial state of the system, group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory. Finally, a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.

This article studies the time-varying formation (TVF) problem of multiagent systems (MASs) with different time delays. By designing the control protocol, the followers could achieve the desired TVF. Considering different communication delays, based on graph theory and stability theory, sufficient conditions for the system to realize TVF are obtained. Finally, the numerical example is employed to validate the effectiveness of theoretical results.