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 paper addresses the consensus control problem of heterogeneous multi-UAV systems against Byzantine attacks. A drone compromised by Byzantine attacks transmits erroneous values to its neighbors while applying wrong input signals for itself, which is aggressive and challenging to defend. Inspired by the concept of digital twin technology, we introduce a new hierarchical protocol equipped with a virtual twin layer (TL), which decouples the challenges into two defense schemes: one against Byzantine edge attacks on the TL and the other against Byzantine node attacks on the cyber-physical layer (CPL). In the TL, we provide a topology reconfiguration strategy that enhances the resilience of the communication network by judiciously adding a minimal number of key edges. We rigorously demonstrate that the control strategy attains asymptotic consensus within a finite timeframe, given that the topology on the TL adheres to a strongly $(2f+1)$ -robustness criterion. Within the CPL, decentralized chattering-free controllers are proposed to ensure the resilient output consensus for the heterogeneous multi-UAV systems against Byzantine node attacks. Furthermore, the derived consensus controller exhibits an exponential convergence characteristic. The effectiveness and practicality of the obtained theoretical results are verified by a UAV swarm flight experiment. Note to Practitioners —Cooperative control of UAVs presents significant prospects for application and development, becoming a focal point of automatic control. By modeling UAV swarms as multi-agent systems, various complex distributed control methods have been conveniently proposed and implemented economically in practical systems. However, when certain agents are compromised and interfere with their neighbors, the whole network may become highly susceptible to failure. This paper specifically studies the resilient consensus control against the significant active internal threats, Byzantine attacks. The published results have primarily focused on cases where the leader UAV has no input signals. In practical applications, however, the leader often has a pre-established trajectory sent by the host and the followers are unaware of this input information. This significantly complicates the task of identifying Byzantine attackers. In this work, we introduce a new hierarchical protocol inspired by the concept of digital twin technology, which decouples the challenges into defense against Byzantine edge attacks on the TL and the defense against Byzantine node attacks on the cyber-physical layer. The experiment shows the feasibility and security of our control scheme, which provides valuable guidance for the practical applications of drones.

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.

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 paper proposes a predictive position control of long-stroke planar motors to achieve micrometer-scale positioning under long-stroke time-varying trajectory tracking for use in high-precision positioning applications. The motivation consists in the potential application of model predictive control in long-stroke planar motors for high-precision positioning systems. This control is the first of its kind for planar motors. A dynamic model of a long-stroke planar motor developed in the laboratory is built, and then a predictive model is established to predict future positions of the motor. An additional term is introduced to a cost function to improve the positioning accuracy, which provides an output feedback control action to the motor for reducing the model error of the predictive model. By minimizing the cost function, an analytically explicit solution of the optimal control sequence is obtained, which makes the computational burden of the controller low. The stability of the control system is discussed based on the closed-loop state-space model. Moreover, the selection of stable control parameters is theoretically given. Simulation and experimental results demonstrate the effectiveness of the proposed control method of long-stroke planar motors for use in high-precision positioning applications.