Finite-time consensus and collision avoidance control algorithms for multiple AUVs

In this paper, finite-time position consensus and collision avoidance problems are investigated for multi-AUV (autonomous underwater vehicle) systems. First, based on the homogeneous control method, finite-time position consensus algorithms are proposed for both leaderless and leader–follower multi-AUV systems without considering collisions between the AUVs. Specifically, in the leader–follower case, a novel distributed finite-time observer is developed for the followers to estimate the leader’s velocity. Second, by constructing collision avoidance and connectivity maintenance functions, modified consensus algorithms containing corresponding gradient terms are presented for multi-AUV systems of both cases, which guarantee collision avoidance, connectivity maintenance, velocity matching, and consensus boundedness. Simulations demonstrate the effectiveness of the proposed control algorithms.     

Leader-following finite-time consensus in second-order multi-agent networks with nonlinear dynamics

Robust finite-time consensus problems in leader-following multi-agent directed networks with second-order nonlinear dynamics are considered in this paper. By using matrix theory, algebraic graph theory and finite-time control scheme, a class of continuous distributed control algorithms are designed in a quite unified way for each follower agent to reach consensus in a finite time. A numerical example is also employed to illustrate the effectiveness and correctness of our theoretical results.     

Homogeneous finite-time consensus tracking of high-order-integrator agents by parametric approach

Finite-time consensus tracking of high-order-integrator multi-agent systems (MAS) is investigated under an undirected topology. When the leader's control input is known to all followers, the homogeneous finite-time control for a high-order integrator is extended to a distributed protocol for the corresponding MAS, and a set of control gains are found by the parametric approach for robust control, such that the multiple agents are simultaneously stabilised in finite time by keeping all characteristic polynomials Hurwitz. When it is only known to the leader's neighbouring followers, a distributed observer is presented for each follower to estimate it in finite time, and the combined observer-based protocol achieves finite-time consensus tracking in a fully distributed fashion. Simulation examples illustrate the effectiveness of the proposed scheme.     

Novel distributed robust adaptive consensus protocols for linear multi-agent systems with directed graphs and external disturbances

This paper addresses the distributed consensus protocol design problem for linear multi-agent systems with directed graphs and external unmatched disturbances. Novel distributed adaptive consensus protocols are proposed to achieve leader–follower consensus for any directed graph containing a directed spanning tree with the leader as the root node and leaderless consensus for strongly connected directed graphs. It is pointed out that the adaptive protocols involve undesirable parameter drift phenomenon when bounded external disturbances exist. By using the σ modification technique, distributed robust adaptive consensus protocols are designed to guarantee the ultimate boundedness of both the consensus error and the adaptive coupling weights in the presence of external disturbances. All the adaptive protocols in this paper are fully distributed, relying on only the agent dynamics and the relative states of neighbouring agents.     

Finite-time consensus for multi-agent systems via nonlinear control protocols

This paper investigates the fnite-time consensus problem of multi-agent systems with single and double integrator dynamics,respectively.Some novel nonlinear protocols are constructed for frst-order and second-order leader-follower multi-agent systems,respectively.Based on the fnite-time control technique,the graph theory and Lyapunov direct method,some theoretical results are proposed to ensure that the states of all the follower agents can converge to its leader agent s state in fnite time.Finally,some simulation results are presented to illustrate the efectiveness of our theoretical results.     

Robust consensus algorithm for second-order multi-agent systems with external disturbances

This article investigates the problem of robust consensus for second-order multi-agent systems with external disturbances. Based on a non-smooth backstepping control technique, a class of novel continuous non-smooth consensus algorithms are proposed for the multi-agent network with/without communication delays. The controller design is divided into two steps. First, for the kinematic subsystem, the velocity is regarded as a virtual input and designed such that the states consensus can be achieved asymptotically. Then for the dynamic subsystem, a finite-time control law is designed such that the virtual velocity can be tracked by the real velocity in a finite time. Under the proposed control law, it is shown that if the communication topology graph contains a directed spanning tree, the states consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region around the origin. By building a relationship between control parameters and the bound of steady tracking errors, it is demonstrated that the disturbance rejection performance of the resulting closed-loop system can be enhanced by adjusting the fractional power in the non-smooth controller. Finally, an example is given to verify the efficiency of the proposed method.     

基于梯度估计的多智能体系统有限时间分布式优化

现有多智能体系统分布式优化算法大多具有渐近收敛速度,且要求系统的网络拓扑图为无向图或有向平衡图,在实际应用中具有一定的保守性.本文研究了具有强连通拓扑的多智能体系统有限时间分布式优化问题.首先,基于非光滑分析和Lyapunov稳定性理论设计了一个有限时间分布式梯度估计器.然后,基于该梯度估计器提出了一种适用于强连通有向图的有限时间分布式优化算法,实现了多智能体系统中智能体的状态在有限时间内一致收敛到全局最优状态值.与现有的有限时间分布式优化算法相比,新提出的有限时间优化算法适用于具有强连通拓扑的多智能体系统,放宽了系统对网络拓扑结构的要求.此外,本文基于Nussbaum函数方法对上述优化算法进行了拓展解决了含有未知高频增益符号的多智能体系统分布式优化问题.最后,通过仿真实例对提出的分布式优化算法的有效性进行了验证.     

Adaptive Finite-time Consensus for Second-order Nonlinear Multi-agent Systems with Input Quantization

In this paper, the adaptive finite-time consensus (FTC) control problem of second-order nonlinear multi-agent systems (MASs) with input quantization and external disturbances is studied. With the help of finite time control technology, a novel distributed adaptive control protocol is constructed to achieve FTC performance for second-order nonlinear MASs by using the recursive method. The control input is quantized through a hysteresis quantizer, which reduces the communication rate of arbitrary two agents. The unknown functions are approximated by adopting the radial basis function neural networks. Under the consensus protocols and adaptive laws, it can be proved that velocity errors of arbitrary two agents reach a small region of zero in finite time as well as position errors. Finally, the effectiveness of the proposed method is illustrated via a simulation example.

     

Distributed consensus for multi-agent systems with delays and noises in transmission channels

This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols.     

Finite-time consensus for multi-agent systems with globally bounded convergence time under directed communication graphs

In this paper, we study the finite-time consensus problems with globally bounded convergence time also known as fixed-time consensus problems for multi-agent systems subject to directed communication graphs. Two new distributed control strategies are proposed such that leaderless and leader-follower consensus are achieved with convergence time independent on the initial conditions of the agents. Fixed-time formation generation and formation tracking problems are also solved as the generalizations. Simulation examples are provided to demonstrate the performance of the new controllers.     

带扰动的多非完整移动机器人分布式有限时间一致性控制

论文研究多个非完整移动机器人在控制输入存在干扰时,有限时间一致性控制问题.利用坐标变换,将多移动机器人系统的一致性问题转化为非完整约束链式系统的一致性问题,在控制输入带有未知有界干扰的条件下,设计了一种分布式控制算法,并利用Lyapunov理论证明了该算法能够使移动机器人的各个状态在有限时间内达到一致.最后通过数值仿真验证了算法的有效性.     

Global finite-time attitude consensus tracking control for a group of rigid spacecraft

The problem of finite-time attitude consensus for multiple rigid spacecraft with a leader–follower architecture is investigated in this paper. To achieve the finite-time attitude consensus, at the first step, a distributed finite-time convergent observer is proposed for each follower to estimate the leader's attitude in a finite time. Then based on the terminal sliding mode control method, a new finite-time attitude tracking controller is designed such that the leader's attitude can be tracked in a finite time. Finally, a finite-time observer-based distributed control strategy is proposed. It is shown that the attitude consensus can be achieved in a finite time under the proposed controller. Simulation results are given to show the effectiveness of the proposed method.     

Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics

The leader–follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations.     

Finite-time consensus control for second-order multi-agent systems without velocity measurements

This paper investigates the finite-time consensus problem for second-order multi-agent systems with unknown velocities and disturbances. By introducing the second-order sliding mode observer, two novel distributed finite-time protocols with only relative position measurements are proposed for the both cases with known and unknown boundaries of disturbances. On the basis of Lyapunov stability theorem and homogeneous theory, it is proved that the consensus can be achieved in finite time. Simulation examples are provided to show the effectiveness of the theoretical results.     

基于一类连续非线性函数的多智能体系统有限时间一致性

针对存在时滞的多智能体系统,提出了基于一类连续非线性函数的有限时间一致性算法.利用Lyapunov有限时间稳定性理论和矩阵理论,给出了这类算法使得系统能够在有限时间内达到一致的充分条件,进而给出了一个满足条件的有限时间一致性算法,并对该算法的收敛性进行分析,得到了系统的收敛时间.数值仿真验证了所提出算法的有效性.     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

输入与速度饱和的异构多智能体系统的一致性

针对由一阶与二阶智能体构成的异构多智能体系统具有输入和速度饱和特性,系统无法达到一致性的问题,构建了无领航者和有领航者的异构多智能体分布式控制器,并给出了系统达到一致性的充分条件。通过Lyapunov稳定性理论和Lasalle不变集原理推导出了系统稳定性的充分条件,并以此计算出了通信增益的取值范围。对具有输入和速度饱和特性的无领航者异构多智能体系统进行数值仿真,结果显示,当选取的通信增益不在合适的范围内时,无领航者的异构多智能体系统无法实现一致性;而通过提出的增益选取方法选取通信增益时,异构多智能体系统可以克服输入和速度的饱和特性,进而实现异构多智能体系统的半全局一致性。对具有输入和速度饱和特性的领航跟随异构多智能体系统进行数值仿真的结果则证明了通信增益的计算方法也适用于异构多智能体系统的半全局领航跟随一致性控制。     

基于滑模的二阶多智能体快速抗扰一致性

针对带有外部未知扰动的二阶多智能体系统的领导—跟随有限时间一致性问题，本文设计出一种带有时变增益的有限时间干扰观测器，用以实现对每个跟随智能体中未知扰动的快速估计，在此基础上，本文结合超螺旋积分滑模控制方法并利用邻居智能体的位置和速度信息设计一种快速抗扰一致性协议，该协议能够保证存在非线性动态的多智能体系统有限时间一致性控制并能抑制抖振现象.同时，利用李亚普诺夫函数进行了稳定性的证明.最后，通过Matlab数值仿真进一步验证了所提出协议的可行性.     

Exponential finite-time couple-group consensus for agents in cooperative-competitive networks via pinning method

This paper investigates the exponential finite-time couple-group consensus problem for multi-agent systems via pinning control method. Considering the hybrid cooperative and competitive interactions among the agents, a new nonlinear distributed control protocol is proposed. Under the pinning control scheme, the criteria for guaranteeing the system with weakly connected communication topology achieve exponential couple-group consensus in finite time are obtained, and the pinning control strategies are presented as well. Furthermore, the results show that the settling time for the system to reach consensus is independent of the initial states of the agents. Finally, the correctness of our results is verified by some simulations.     

完全分布式异构多智能体系统有限时间跟踪

针对异构二阶非线性多智能体系统有限时间跟踪问题,提出一种完全分布式一致性控制方法,消除对于误差上界与Laplacian矩阵特征值等全局信息的依赖.设计一种只包含局部信息的有限时间一致性协议,并提出自适应增益的分布式切换机制,使得各增益以分段常数的方式进行调节,简化了相邻两次切换时间区间内稳定性分析过程.通过反证法证明多智能体系统必将实现有限时间一致性,并且自适应增益保持有界.仿真结果验证了所提出的完全分布式一致性协议的有效性.