This work deals with the analysis and protocol design problems of the prescribed-time interval bipartite consensus of multi-agent systems on signed and directed graphs. A new distributed protocol with hybrid constant and time-varying feedbacks of local signed error is proposed, whose consensus time period is independent of the specific topology among agents and initial states of all agents. By introducing a series of well-structured Lyapunov functions, the technical difficulties arising from the asymmetrical Laplacian matrices of directed graphs are circumvented. The effectiveness of this prescribed-time protocol for multi-agent systems on signed digraphs with a spanning tree is proven both on structurally balanced digraphs and structurally unbalanced ones with a positive root subgraph. An illustrative simulation example and a prescribed-time bipartite formation experiment on a swarm of nano-quadcopters are implemented to show the validity and practicability of these proposed protocols.

This work studies the analysis and algorithm design problems of the distributed prescribed-time convex optimization of continuous-time multi-agent systems on undirected graphs. A new distributed algorithm with hybrid constant and time-specific update rates as well as predefined-time convergence guarantees is proposed, whose optimization period is independent of the initial states of all agents and the specific topology among agents. This algorithm consists of the following three cascading stages: 1) prescribed-time estimation of the average group gradients and Hessians over a time interval $T_1$ ; 2) prescribed-time consensus of all agents over a time interval $T_2$ ; 3) prescribed-time optimization to the global optimal point over a time interval $T_3$ , where $T_i>0$ , $i=1\sim 3$ , are three time intervals subject to $T=T_1+T_2+T_3$ with $T$ denoting a predefined time interval. Accordingly, it is possible to pre-assign the settling time arbitrarily according to task requirements. The validity of this new algorithm and the practicability of given theoretical results are illustrated via a simulation example and a prescribed-time optimal rendezvous formation experiment of an indoor unmanned aerial vehicle swarm.

This work solves the countermeasure design problems of distributed resilient output time-varying formation-tracking (TVFT) of heterogeneous multiagent systems (MASs) against general Byzantine attacks (GBAs). Inspired by the concept of Digital Twin, a hierarchical protocol equipped with a twin layer (TL) is proposed, which decouples the above problem into the defense against Byzantine edge attacks (BEAs) on the TL and the defense against Byzantine node attacks (BNAs) on the cyber–physical layer (CPL). First, a secure TL with respect to (w.r.t.) the high-order leader dynamics is designed, which achieves resilient estimation against BEAs. A trusted-node strategy against BEAs is proposed, which promotes network resilience by protecting almost the smallest fraction of crucial nodes on the TL. It is proven that strongly $(2f+1)$ -robustness w.r.t. the above trusted nodes is sufficient for the resilient estimation performance of the TL. Second, a decentralized adaptive and chattering-free controller against potentially unbounded BNAs is designed on the CPL. This controller has the merit of uniformly ultimately bounded (UUB) convergence and an assignable exponential decay rate when converging into the above UUB bound. To the best of our knowledge, this article is the first to achieve resilient output TVFT against GBAs, rather than under GBAs. Finally, the practicability and validity of this new hierarchical protocol are illustrated via a simulation example.

The analysis and design problems of formation-containment control for high-order linear time-invariant (LTI) multiagent systems (MASs) on directed graphs with observer-based output-feedback protocols are given in this work. To expand the feasibility of state formation configuration, two well-structured compensation signals are introduced for the leaders and followers in the protocols, respectively. Benefitting from the compensation signal of followers, the decoupling between formation control of leaders and containment control of followers is achieved. Thus, a necessary and sufficient condition is first established such that the formation-containment control for high-order LTI MASs can be achieved. Moreover, a heuristic iterative algorithm is developed to compute the controller gains, observer gains, as well as the compensation signals. Finally, two numerical examples are implemented to illustrate the time-varying formation-containment control of high-order MASs, which shows the validity and practicability of the theoretical results and algorithm.

This work solves the analysis and protocol design problems of the prescribed-time formation-containment (FC) control of double-integrator multi-agent systems (MASs) on directed graphs in the presence of unknown and time-varying actuator faults. First, a novel kind of distributed prescribed-time observers (DPTOs) is designed for the leaders and the followers, respectively, which could achieve distributed zero-error estimation on directed graphs within a predefined time interval. Based on this DPTO, a decentralized protocol equipped with a time-scaling function is proposed, which possesses both prescribed-time performance and fault-tolerant merits against both additive and multiplicative faults. This protocol ensures that the MAS achieves fault-tolerant FC in a cooperatively ultimately uniformly bounded sense after a prescribed time interval, while the formation error and containment error further converge to zero at an exponentially predefined speed. Also, the upper bounds of the tracking error, formation error, and containment error have been given explicitly. The effectiveness of the proposed DPTO-based protocol is proven via an illustrative simulation example.

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.