In nature, populations of organisms (e.g., wolves) exhibit a remarkable ability to coordinate their group actions, such as hunting prey or evading predators, despite the coexistence of cooperative and competitive interactions among individuals. Motivated by this intriguing phenomenon, this article investigates the cooperative consensus tracking control problem of multiagent systems (MASs) over cooperation–competition networks with asynchronous communications. That is, all followers can simultaneously achieve trajectory tracking of the leader agent, even if there exist competitive interactions between the followers and the leader. To portray the cooperation and competition level among agents, a new distance-based weight function is designed, which is more flexible than the fixed weight values in existing research works. Theoretically, the sufficient conditions for achieving consensus tracking control are obtained based on the convergence analysis method of infinite products of super-stochastic matrices. Finally, some numerical simulations are given to verify the effectiveness of the proposed consensus tracking control scheme.

This paper investigates the containment control performance analysis problem for double-integrator fractional-order multi-agent systems (MASs) with nonuniform time delays (NTDs). The primary focus is on evaluating the containment control performance by calculating the explicit delay margin. Firstly, the transfer function of the closed-loop error system is established by defining the containment control error. Then, the stability of the nonuniform delayed fractional-order closed-loop system is analyzed by using the frequency domain method, considering both undirected and directed communication topologies. Furthermore, the critical time delay (TD) is determined by generating the characteristic equation as a polynomial involving the sub-Laplacian matrix among the follower agents. Additionally, the containment convergence conditions for fractional-order MASs are derived. These conditions can be formulated based on delay margins and a set of inequalities involving the fractional order, eigenvalues of the Laplacian matrix, and control parameters. In summary, if all time delays (TDs) do not surpass the explicit delay margin, the containment control of the MAS is said to be realized; Otherwise, if all TDs surpass this margin, the MAS suffers from state divergence. Finally, two simulation examples are provided to verify the correctness of the theoretical results.

This paper examines the effect of multiple nonuniform time delays on the performance of containment tracking control for networked agent systems. At first, the distributed controllers are designed under undirected and directed interactive networks, respectively. Then, the corresponding characteristic equation of the closed-loop system is transformed into a quadratic polynomial with respect to the pure imaginary eigenvalue of the system to calculate the critical time delay. Finally, the explicit maximum allowable upper bound of time delay (called “delay margin”) for achieving containment tracking is obtained. To sum up, we tackle the containment tracking problem and obtain sufficient convergence conditions for networked agents with nonuniform communication delays, where the system can achieve containment tracking when all time delays are less than the obtained delay margin, i.e., all follower agents asymptotically converge to the convex hull formed by the leaders, and the system will not remain stable when all delays are greater than the obtained delay margin. The superiority of the obtained results is well verified by numerical examples.

In the era of Industry 5.0, the cooperation among components in Cyber-Physical Systems (CPS) plays a crucial role in achieving digital transformation and intelligent development. Distributed observers can simplify the design complexity of cooperative control schemes in intelligent networked industrial systems. However, the open nature of the information exchange network in these systems makes them vulnerable to cyber attacks. With this in mind, this paper designs a discrete-time secure adaptive distributed observer for networked agent systems under Denial of Service (DoS) attacks. The observer enables agents to monitor reference state information effectively, even when the system matrix is globally unknown and unstable. To enhance security, we propose adaptive secure update rules that respond to compromised communication links, ensuring the ability of the observer to generate reference trajectories during DoS attacks. Furthermore, sufficient algebraic conditions are obtained for the convergence of the proposed observer, employing the analysis approach based on infinite products of sub-stochastic matrices. Finally, some numerical simulation results are provided to verify the effectiveness of the proposed secure adaptive distributed observer.