Finite-time consensus protocols for networks of dynamic agents by terminal iterative learning

This paper aims to address finite-time consensus problems for multi-agent systems under the iterative learning control framework. Distributed iterative learning protocols are presented, which adopt the terminal laws to update the control input and are offline feedforward design approaches. It is shown that iterative learning protocols can guarantee all agents in a directed graph to reach the finite-time consensus. Furthermore, the multi-agent systems can be enabled to achieve a finite-time consensus at any desired terminal state/output if iterative learning protocols can be improved by introducing the desired terminal state/output to a portion of agents. Simulation results show that iterative learning protocols can effectively accomplish finite-time consensus objectives for both first-order and higher order multi-agent systems.     

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.     

Distributed adaptive consensus control of Lipschitz nonlinear multi-agent systems using output feedback

This paper addresses output-feedback-based distributed adaptive consensus control of multi-agent systems having Lipschitz nonlinear dynamics. Distributed dynamic protocols are designed based on the relative outputs of neighbouring agents and the adaptive coupling weights, under which consensus is reached between the nonlinear systems for all undirected connected communication topologies. Extension to the case of Lipschitz nonlinear multi-agent systems subjected to external disturbances is further studied, and a robust adaptive fully distributed consensus protocol is suggested. By application of a decoupling technique, necessary and sufficient conditions for the existence of these consensus protocols are provided in terms of linear matrix inequalities. Finally, numerical simulation results are demonstrated to validate the effectiveness of the theoretical results.     

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.     

Robust iterative learning protocols for finite-time consensus of multi-agent systems with interval uncertain topologies

This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results.     

有限时间一致无迹Kalman滤波器

本文研究多个传感器测量非线性系统时的分布式无迹Kalman滤波器(Unscented Kalman filter, UKF)的设计问题.借助离散多智能体系统有限时间平均一致算法的思想, 针对无向通信和有向通信网络分别设计了两种不同的滤波算法.对于无向连通的通信拓扑, 利用节点存储的一致性算法的迭代值构造差向量, 由该差向量构成的Hankel矩阵的核来得到分布式无迹Kalman滤波器, 并通过利用误差协方差矩阵的逆来构造Lyapunov函数, 基于随机稳定性引理证明了该有限时间一致无迹Kalman滤波器的稳定性.对于有向强连通的通信拓扑, 结合比率一致和Hankal矩阵的核来设计分布式无迹Kalman滤波器, 该滤波器的稳定性与无向通信拓扑的滤波器相同.最后, 通过仿真例子来验证所提滤波器的跟踪效果.     

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.     

Iterative learning approaches to design finite-time consensus protocols for multi-agent systems

In this paper, the finite-time output consensus problem of multi-agent systems is considered by using the iterative learning control (ILC) approach. Two classes of distributed protocols are constructed from the two-dimensional system point of view (with time step and iteration number as independent variables), and are termed as iterative learning protocols. If learning gains are chosen appropriately, then all agents in a directed graph can be enabled to achieve finite-time consensus with the iterative learning protocols. Moreover, all agents in a directed graph can be guaranteed to reach finite-time consensus at any desired terminal output if the iterative learning protocols are improved by introducing the desired terminal output to some (not necessarily all) of the agents. Simulation results are finally presented to illustrate the performance and effectiveness of our iterative learning protocols.     

无速度输入多智能体系统的一致性

本文研究了有无引导者的多智能体系统在非线性协议下的一致性问题.当智能体速度信息无法获知时,分别针对有无引导者的多智能体系统设计了包含辅助系统和智能体相对位移信息的非线性分布式协议.借助图论、Lyapunov稳定性理论、Barbalat引理等方法,推导出有无引导者的多智能体系统在连通无向通讯网络中实现一致的充分条件,其次,设计了一种新的能使引导–追随者多智能体系统在有向通讯网络中实现期望一致的协议.最后,数值仿真验证了结果的正确性.     

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。     

线性和非线性动态异构多自主体系统的有限时间一致性（英文）

In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems.Some sufficient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights.At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

线性和非线性动态异构多自主体系统的有限时间一致性

研究了由线性和非线性动态自主体组成的异构多自主体系统的有限时间一致性问题.针对该异构系统提出了非线性的一致性协议,并分别给出了无领航者和有领航者情形下异构系统在有限时间内实现一致性的充分条件.所得结果还推广到具有有向通信拓扑且满足细致平衡条件的多自主体系统情形.最后,给出一些仿真结果来验证所得结论的正确性和有效性.     

Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics

In this paper, we discuss the finite-time consensus problem for leaderless and leader–follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader–follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.     

Consensus of heterogeneous multi-agent systems without velocity measurements

This article considers the consensus problem of heterogeneous multi-agent system composed of first-order and second-order agents, in which the second-order integrator agents cannot obtain the velocity (second state) measurements for feedback. Two different consensus protocols are proposed. First, we propose a consensus protocol and discuss the consensus problem of heterogeneous multi-agent system. By applying the graph theory and the Lyapunov direct method, some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader-following networks. Second, due to actuator saturation, we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi-agent system. Finally, some examples are presented to illustrate the effectiveness of the obtained criterions.     

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.     

Finite-time consensus of time-varying nonlinear multi-agent systems

This paper investigates the problem of leader–follower finite-time consensus for a class of time-varying nonlinear multi-agent systems. The dynamics of each agent is assumed to be represented by a strict feedback nonlinear system, where nonlinearities satisfy Lipschitz growth conditions with time-varying gains. The main design procedure is outlined as follows. First, it is shown that the leader–follower consensus problem is equivalent to a conventional control problem of multi-variable high-dimension systems. Second, by introducing a state transformation, the control problem is converted into the construction problem of two dynamic equations. Third, based on the Lyapunov stability theorem, the global finite-time stability of the closed-loop control system is proved, and the finite-time consensus of the concerned multi-agent systems is thus guaranteed. An example is given to verify the effectiveness of the proposed consensus protocol algorithm.     

Finite-time consensus for controlled dynamical systems in network

The key challenges in networked dynamical systems are the component heterogeneities, nonlinearities, and the high dimension of the formulated vector of state variables. In this paper, the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift. For each model structure that defines homogeneous and heterogeneous multi-system behaviour, we derive protocols leading to finite-time consensus. For each model evolving in networks forming a homogeneous or heterogeneous multi-system, protocols integrating sufficient conditions are derived leading to finite-time consensus. Likewise, for the networking topology, we make use of fixed directed and undirected graphs. To prove our approaches, finite-time stability theory and Lyapunov methods are considered. As illustrative examples, the homogeneous multi-unicycle kinematics and the homogeneous/heterogeneous multi-second order dynamics in networks are studied.     

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.     

Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances

In this paper, finite-time consensus tracking is investigated via time-varying feedback for uncertain nonlinear multi-agent systems (NMASs). The presence of inherent uncertainties and disturbances in the NMASs highlights the main novelty : (1) The inherent uncertainties imply that more serious unknowns and time-variations are allowed in the nonlineartities and the control coefficients of the NMASs. (2) The inherent disturbances mean that the upper bound of the disturbances is unknown. To compensate the inherent uncertainties and disturbances, time-varying protocols are proposed by integrating time-varying technique and sliding mode method. Based on the proposed protocols, the finite-time leader-following consensus and finite-time containment are achieved under directed graph. Finally, the validation of the proposed protocols is verified by two examples.