A time-varying formation tracking (TVFT) control method under denial-of-service (DoS) attacks is proposed for a class of multi-uncrewed aerial vehicle (UAV) system with unknown nonlinearity. The neural network approximation is utilized to mitigate the impact of nonlinear dynamics on the tracking performance. Meanwhile, the switching topologies are adopted to ensure the reliability of the communication topology. Considering the resource constraints of the system communication network, an improved integral event-triggered mechanism is devised to further decrease the triggering frequency in comparison to the traditional event-triggered one. By using the multi-Lyapunov function, the tracking error is proved to be bounded. Simulations convincingly demonstrate the effectiveness and merits of the developed TVFT and the integral event-triggered method. Note to Practitioners—Multi-UAV systems are widely utilized in both civil and military domains, with communication networks serving as crucial channels for information exchange among UAVs. However, these communication networks are often vulnerable to various types of attacks. Therefore, the control problems of multi-UAV systems under DoS attacks are of great importance. A switching event-triggered control protocol is developed for multi-UAV systems to facilitate effective formation tracking in the presence of DoS attacks. This protocol employs switching topologies to enhance the reliability and flexibility of the communication network. The improved event-triggered mechanism effectively balances the system performance and the communication consumption.

This paper presents a novel event-triggered approach for regulating energy prices of heterogeneous agent-based demand response including prosumer groups and energy companies. First, a price-based demand response management (PDRM) model is developed using networked evolutionary game theory. Then, a necessary and sufficient criterion is proposed to verify the stabilizability of the controlled PDRM system, significantly reducing iterative complexity compared to existing methods. By utilizing truth matrices, an algorithm is proposed to calculate the event-triggered feedback gain matrices and determine the triggering times. The proposed matrix-based event-triggered control guarantees that the strategies of all participants converge to the target game equilibrium set while reducing the update frequencies of the controller. Finally, the simulation results demonstrate the effectiveness of the proposed method.

This article explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on the internal model are proposed for the case with perfect and imperfect information, respectively. Different from the existing algorithms based on gradient dynamics, by introducing the integral of the gradient of cost functions on the basis of the passivity theory, the rules are proposed to force the strategies of all agents to evolve to the Nash equilibrium, regardless of the effect of disturbances. The convergence of the two strategy-updating rules is analyzed via the Lyapunov stability theory, passivity theory, and singular perturbation theory. Simulations are performed to illustrate the effectiveness of the proposed methods.

This article proposes a resilient distributed Nash equilibrium (NE) seeking algorithm for noncooperative games with multiple double-integrator agents who suffer from false data injection (FDI) attacks. A malicious attacker injects false data into agents’ actuators and sensors so that agents’ strategies deviate from the NE of the game with the compromised control inputs and interactive information. First, the robustness of the seeking algorithm against the FDI attacks is analyzed. Then, to mitigate the effect of the attacks on agents’ strategies, the false data injected in the actuators and sensors are regarded as extended states which can be observed by extended state observers (ESOs). Thus, a resilient NE seeking algorithm is proposed based on ESOs. The resilient algorithm can drive the system to converge to the NE without requiring any information about the nature of the attacks. An explicit criterion is given to ensure the effectiveness of the designed algorithms. An example is given to illustrate the results.

In this article, a class of continuous-time noncooperative games in networks of double-integrator agents is explored. The existing methods require that agents communicate with their neighbors in real time. In this article, we propose two discrete-time communication schemes based on the designed continuous-time strategy-updating rule for the efficient use of communication resources. First, the property of the designed continuous-time rule is analyzed to ensure that all agents’ strategies can reach the Nash equilibrium (NE). Then, we propose, respectively, periodic and event-triggered communication schemes for the discrete-time interactions among agents. The rule in the periodic case is implemented synchronously. The rule in the event-triggered case is executed asynchronously without Zeno behaviors. All agents in both cases can reach the NE asymptotically by interacting with neighbors at discrete times. Simulations are performed in networks of Cournot competition to illustrate the effectiveness of the proposed methods.

This paper addresses the consensus problem of linear multiagent systems via nonlinear couplings. First, we show that the multiagent system can achieve consensus via nonlinear couplings provided the coupling strength surpasses a threshold, which depends on the smallest nonzero eigenvalue of the interaction graph Laplacian. Second, an adaptive coupling protocol is proposed to adjust the coupling strength without any usage of global information. Some numerical simulations are given to illustrate the effectiveness of the proposed protocols.

In this article, we are concerned with the synchronization problem of Kuramoto oscillators under the sampled-data updating law. This article is motivated by the needs of synchronization of Kuramoto oscillators in the presence of periodic and asynchronous coupling updates. Based on the periodical sampled-data method, a sufficient condition ensuring synchronization under periodic updates is derived. In order to relax the requirement of having all data updated simultaneously, an event-triggered law is designed to implement asynchronous coupling updates. Our synchronization analysis does not rely on any linearization technique around equilibrium points. Instead, we employ the Lyapunov stability theory and nonsmooth analysis technique to deduce the synchronization conditions and estimate the region of attraction. The effectiveness of the proposed sampled-data coupling is illustrated by numerical simulations.

In this article, we consider the distributed synchronization problem of dynamic networked systems with adaptive nonlinear couplings. Based on how the information is collected, the interactions between subsystems are characterized by nonlinear relative state couplings and nonlinear absolute state couplings. In both cases, we show that the considered nonlinear interactions can be used to simulate the couplings with disturbed relative or absolute states. In order to implement the nonlinear couplings in a fully distributed fashion, adaptive control laws are proposed for the adjustment of coupling strengths between connected subsystems. It is shown that the connected network topology is sufficient to ensure the synchronization of dynamic networked systems with the proposed adaptive nonlinear coupling methods. Different from many existing works, the σ -modification technique is used to suppress the increase of the coupling strengths with an additional benefit of preventing the coupling strengths from increasing. Simulation examples are given to assess the performance of the proposed adaptive nonlinear couplings.

The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.