This paper is concerned with the stability analysis for continuous-time positive singular systems with time-varying delays. First, an auxiliary system is introduced to establish the positivity condition for singular time-delay systems. Based on the positivity condition, the stability criterion is obtained for the positive singular systems with constant delays. By analyzing the monotonic property of the system trajectory, we extend the stability condition to the cases with time-varying delays. A numerical simulation is employed to illustrate the effectiveness of our results.

This study addresses resilient human-in-the-loop (HiTL) formation-tracking of multi-UAV systems against $f$ -local Byzantine attacks. In the HiTL settings, a human operator plays a key role in detecting any physical hazard, monitoring the whole UAV swarm, and sending secure execution signals to a non-autonomous leader UAV. Moreover, there exists a fraction of Byzantine UAVs in the multi-UAV systems, which propagate incorrect information to their neighbors (called Byzantine edge attacks (BEAs)) and adopt false input signals (called Byzantine node attacks (BNAs)) when swarming. In order to suppress the above aggressive Byzantine attacks, this paper proposes a Byzantine-resilient hierarchical control scheme, including a virtual Digital Twin Layer (DTL) apart from a Cyber-Physical Layer (CPL). First, a distributed resilient estimation scheme is proposed on the DTL, which can realize resilient estimation on the state of the non-autonomous leader UAV against BEAs on the premise that the DTL topology is strongly $(2f+1)$ -robust. Second, a series of decentralized and chattering-free controllers is formulated on the CPL, which is resilient to both BNAs and inter-layered faults. The asymptotical control performance of the above controllers is strictly proven based on Cromwell-Bellman Lemma. To demonstrate the practicality of the theoretical results, a resilient HiTL multi-UAV systems experiment has been further conducted. The experimental results verify the effectiveness and practicality of the designed two-layered controllers against $f$ -local Byzantine attacks. Note to Practitioners —Owing to the wide application of multi-UAV systems, the resilience of the whole swarm against malicious attacks has grasped the great attention of both academia and industry. This work considers a rather aggressive kind of attacks, named Byzantine attacks, where a fraction of unidentified UAVs act as traitors. Inspired by the digital twin technology, a two-layered control architecture for multi-UAV systems is formatted, including a Digital Twin Layer (DTL) and a Cyber-Physical Layer (CPL). Here are the highlights: 1) Control Architecture: The DTL handles Byzantine edge attacks (BEAs), while the CPL addresses Byzantine node attacks (BNAs), ensuring reliable human-swarm cooperation in adversarial environments. 2) Resilient Estimation against BEAs: A novel resilient estimation scheme on the DTL is designed, using edge-based feedback, which can estimate the states of the leader UAV manipulated by human operators. 3) Adaptive Controller against BNAs and Inter-layered Faults: On the CPL, a decentralized adaptive controller with adjustable and exponential convergence is proposed, enhancing its precision and flexibility. 4) Practical Application: A UAV swarm formation-tracking experiment validates the control architecture’s effectiveness in human-in-the-loop scenarios, demonstrating its practicality in the realm of swarm robotics and human-swarm interaction.

This paper investigates the problems of reachable set estimation and synthesis for periodic positive systems with two different exogenous disturbances. The lifting method and the pseudoperiodic Lyapunov function method are adopted for the estimation problem. The reachable set bounding conditions are proposed by employing Lyapunov-based inequalities and the S-procedure technique. Two optimization methods are used to minimize the bounding hyper-pyramids of the reachable set. In addition, the state-feedback controller design conditions that make the reachable set of closed-loop systems lie within a given hyper-pyramid are derived. Finally, numerical examples are presented to illustrate the validity of the obtained conditions.

This article investigates the distributed Nash equilibrium (NE) seeking problem of uncertain multiagent systems in unreliable communication networks. In this problem, the action of each agent is subject to a class of nonlinear systems with uncertain dynamics, and the communication network among agents will be affected by the nonperiodic denial of service (DoS) attacks. Note that, in this insecure network environment, the existence of DoS attacks will directly destroy the connectivity of the network, which leads to performance degradation or even failure of the most existing distributed NE seeking algorithms. To address this problem, we propose a two-stage distributed NE seeking strategy, including the attack-resilient distributed NE estimator and the neuroadaptive tracking controller. The estimator based on the projection subgradient method and the consensus protocol can converge exponentially to virtual NE against DoS attacks. Then, the neuroadaptive tracking controller is designed for uncertain multiagent systems with the output of the estimator as the reference signal such that the actual action of all agents can reach NE. Based on the Lyapunov stability theory and improved average dwell time automaton, the stability of the estimator and the controller is proven, and all signals in the closed-loop system are uniformly bounded. Numerical examples are presented to verify the effectiveness of the proposed strategy.

This paper addresses a class of optimization problems with time-varying cost functions by proposing a fully distributed prescribed-time algorithm. The algorithm decomposes the overall optimization problem into three successive subproblems, which are solved sequentially. During the three stages of the algorithm, the estimation of the total cost function's average gradient information, consensus among the states, and tracking of the optimal state trajectories are achieved in turn. Given the segmentation strategy's demand for rapid convergence, the algorithm ensures convergence within a prescribed time. Using the Lyapunov method, it is shown that all three subproblems can be solved within any user-prescribed time, independent of the system's initial states or topology. To further exploit the independence of prescribed-time convergence from system states, the algorithm eliminates the reliance on system topology information in parameter settings by introducing adaptive parameters in place of traditional fixed ones, thus enabling fully distributed control. Finally, numerical simulations and an UAVs target tracking experiment are conducted to validate the effectiveness and practicality of the proposed algorithm.