Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.     

Fully distributed consensus for fuzzy multiagent systems with jointly connected topology

This paper investigates the problem of fully distributed consensus for polynomial fuzzy multiagent systems (MASs) under jointly connected topologies. First, a polynomial fuzzy modeling method is presented to characterize the error dynamics that is constructed by one leader and multiple followers. Then, using the relative state information and the agents' dynamics, a distributed adaptive protocol is designed to guarantee that MASs under jointly connected topologies can achieve consensus in a fully distributed fashion. Utilizing the Lyapunov technique, a relaxed sufficient criterion is proposed to ensure consensus for fuzzy MASs under jointly connected topologies. Moreover, the adaptive coupling weights between neighboring agents can converge to certain values. The derived condition is transformed into a sum-of-squares form, which can be solved numerically. We provide an example to illustrate the proposed distributed adaptive consensus technique's validity.     

异构集群系统分布式自适应输出时变编队跟踪控制

提出了一种能够解决高阶异构集群系统输出时变编队跟踪问题的控制方法. 集群系统中的智能体分为领导者和跟随者, 领导者和跟随者的动力学模型可以完全不同. 跟随者的输出在跟踪领导者输出的同时保持时变编队实现协同运动. 考虑了领导者存在已知或未知控制输入、领导者和跟随者均存在未知扰动、有向通信拓扑存在切换等多种因素并存的情况, 结合观测器理论、自适应控制理论和滑模控制理论设计了完全分布式的输出时变编队跟踪控制协议, 摆脱了对领导者控制输入上界值、与通信拓扑相关的拉普拉斯矩阵的特征值以及时变编队函数等全局信息的依赖. 利用Lyapunov理论证明了在有向拓扑切换条件下异构集群系统的闭环稳定性. 最后通过数值仿真对理论结果的有效性进行了验证.     

Mean square leader-following consensus of heterogeneous multi-agent systems with Markovian switching topologies and communication delays

This article considers the mean square leader-following output consensus problem of heterogeneous multi-agent systems under randomly switching topologies and time-varying communication delays. By modeling the switching topologies as a time-homogeneous Markov process and taking the communication delays into consideration, a distributed observer is proposed to estimate the state of the leader. A novel distributed output feedback controller is then designed. By constructing a novel switching Lyapunov functional, an easily-verifiable sufficient condition to achieve the mean square leader-following output consensus is given. Finally, two simulation examples are presented to show the effectiveness of the proposed control scheme.     

单向通信拓扑领航者动态未知线性多智能体系统的协同迭代学习控制（英文）

This paper considers the cooperative tracking of linear multi-agent systems with a dynamic leader whose input information is unavailable to any followers. Cooperative iterative learning controllers, based on the relative state information of neighboring agents, are proposed for tracking the dynamic leader over directed communication topologies. Stability and convergence of the proposed controllers are established using Lyapunov-Krasovskii functionals. Furthermore, this result is extended to the output feedback case where only the output information of each agent can be obtained. A local observer is constructed to estimate the unmeasurable states. Then, cooperative iterative learning controllers, based on the relative observed states of neighboring agents,are devised. For both cases, it is shown that the multi-agent systems whose communication topologies contain a spanning tree can reach synchronization with the dynamic leader, and meanwhile identify the unknown input of the dynamic leader using distributed iterative learning laws. An illustrative example is provided to verify the proposed control schemes.     

单向通信拓扑领航者动态未知线性多智能体系统的协同迭代学习控制

研究单向通信拓扑领航者动态未知线性多智能体系统的协同跟踪问题.基于邻居的相对状态信息,设计了分布式迭代学习控制律实现对领航者的协同跟踪控制,采用Lyapunov-Krasovskii函数分析闭环系统的稳定性与收敛性.进而,将状态反馈结论拓展到输出反馈,通过构造局部观测器估计不可量测的状态信息,采用估计的相对状态信息设计了分布式迭代学习控制器.对于以上两种情形,多智能体系统在通讯拓扑含有生成树的条件下能够实现与领航者的状态同步,同时,所设计的分布式迭代学习律能够对领航者未知输入进行精确估计.仿真实例验证了所提方法的有效性.     

Robust consensus of heterogeneous multiagent systems with switching topologies: A time-delay case

The robust leader-following consensus of heterogeneous multiagent systems under switching communication topologies is investigated in this paper. Especially, the input delay is considered in each follower. In order to access the information of leader through time-varying communication, a type of distributed dynamic compensator is proposed for every follower firstly, which get rid of the dependence on the global spectrum information and is proved that it can be viewed as a asymptotic observer of the leader. Then combined with the internal model principle, two types of distributed control law are proposed based on the compensator. By applying the truncated predictor feedback scheme to synthesize the closed-loop systems, it is proved that the consensus can be achieved by both of the control laws despite the existence of the input delay and the plant parameters perturbations. Finally, numerical simulations are illustrated to demonstrate the results.     

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders’ measurable output was designed to estimate a convex combination of the leaders’ states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders’ convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.      

Disturbance observer–based consensus tracking for nonlinear multiagent systems with switching topologies

This paper considers the leader‐follower consensus tracking problem for nonlinear multiagent systems with external disturbances and switching topologies. A distributed disturbance observer is constructed to estimate the disturbances suffered by the followers. Then, a distributed consensus protocol is proposed for the consensus tracking problem with disturbance rejection under a fixed directed topology based on the disturbance observer. Next, this result is extended to the case in which the switching communication topology only frequently but not always contains a directed spanning tree. By selecting the parameters appropriately such that the communication time satisfies various preset conditions, it is theoretically proven that the consensus tracking with disturbance rejection can also be achieved by the multiagent systems. Finally, a simulation example is presented to demonstrate the performance of the proposed control scheme.     

Finite‐time consensus tracking for harmonic oscillators using both state feedback control and output feedback control

This paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems

This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs.The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees.This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree.A distributed adaptive pole placement control sche...     

Iterative Consensus for a Class of Second-order Multi-agent Systems

In this paper, the problem of leader-following consensus for a class of multi-agent systems with double integrator dynamics is investigated based on an iterative learning approach. Consensus errors of individual agents are considered as the anticipation in time, based on which a distributed iterative learning protocol is proposed for the undirected networks with fixed topology to make the followers track the leader in finite time. The dynamic of the leader is assumed to be time-varying and the state information is available to only a portion of the followers. The sufficient condition for solving the consensus problem of the multi-agent system is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed method.     

有向图中网络Euler-Lagrange系统的自适应协调跟踪

基于一致性理论, 在有向图中研究网络 Euler-Lagrange 系统的协调跟踪控制. 所有跟随智能体的动力学模型均为 Euler-Lagrange 方程. 在仅有部分跟随智能体能获取领航智能体信息的情形下, 同时考虑系统模型的参数不确定性, 设计分布式自适应控制律实现所有跟随智能体对领航智能体的跟踪. 针对领航智能体的运动状态, 考虑以下两种情形: 1) 领航智能体为固定点; 2) 领航智能体为动态点. 对第一种情形, 设计的控制律使得所有跟随智能体渐近交会于固定点; 对第二种情形, 首先对每个跟随智能体设计分布式连续估计器, 然后提出了分布式自适应控制律. 当每个跟随智能体均能获取领航智能体的加速度信息时, 设计的控制律能实现对领航智能体的渐近跟踪, 当跟随智能体不能获取领航智能体的加速度信息时, 跟踪误差是有界的. 最后通过仿真分析验证设计的控制算法是合理有效的.     

Decentralised regulation of nonlinear multi-agent systems with directed network topologies

This paper aims to address the leader–follower regulation problem of multi-agent systems with directed network topologies, where the agents are described by feedforward nonlinearities with the growth rate being unknown a priori. Both the state feedback regulation protocol and the output feedback regulation protocol are delicately constructed such that all the states of followers can converge to the leader state globally. In this paper, a model transformation is firstly performed and the leader–follower regulation problem can be transformed into a general regulation problem. Then, by introducing an appropriate state transformation, the regulation problem can be changed into a parameter determined problem. It is proved that the parameter can be determined by both the properties of M-matrices and the estimates of nonlinear terms. Finally, a numerical example is presented to show the feasibility of designed protocols.     

有向网络下非线性多智能体系统的协调跟踪

基于一致性理论,在有向拓扑结构下研究非线性多智能体系统的协调跟踪控制问题．考虑智能体动力学模型为一般且仅满足Lipschitz条件的非线性系统,在仅有部分跟随智能体能获取领航智能体信息的情形下,当领航智能体与跟随智能体之间的拓扑结构具有有向生成树,即存在领航智能体到所有跟随智能体的有向路径时,所设计的分布式控制律可实现所有跟随智能体对领航智能体的跟踪,并指出该拓扑结构是系统实现跟踪的一个必要条件．最后,仿真实验验证了所设计控制算法的有效性．     

Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader

This paper investigates the distributed consensus tracking problem for multi-agent systems with Lipschitz-type dynamics under a reference leader. It is assumed that the leader state information is only available to a subset of followers, while the bounded reference input of the leader’s is unavailable to any follower. To achieve consensus tracking, a class of discontinuous protocols based on the relative information between the neighbouring agents are proposed. Furthermore, as extensions of the former result, the robust and adaptive consensus tracking problems are studied for the case where there exist parameter uncertainties and external disturbances in the network. Finally, the effectiveness of the theoretical result is demonstrated through a network of single-link manipulators.     

Event‐triggered tracking control of heterogeneous multiagent systems based on two kinds of observers with asymmetric delay

In this paper, we consider the output tracking problem of a multiagent system with asymmetric delays and a switching topology. The multiagent system contains a leader and some followers, the dynamics of which are heterogeneous, and the output of the leader is available to only a subset of followers. We propose two types of observers to estimate states of the leader and reduce communication cost. For the informed followers that can directly obtain information of the leader, a common observer is given to reduce the complexity of observer design. Meanwhile, for the rest of the followers, a distributed observer with asymmetric communication delays for each follower is designed. The observer error system is transformed into a switched system. Through designing the average dwell‐time switching law and constructing multiple Lyapunov functionals, some sufficient conditions for stability of the observer error system are obtained. Furthermore, a distributed controller for followers based on the relative information is developed to track the output of the leader. Finally, an example is given to validate the effectiveness of the proposed results.     

Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation

This paper investigates the leader-following fixed-time output feedback consensus problem for second-order multi-agent systems with input saturation. By combing fixed-time control technique and bi-limit homogeneous systems theory, a class of bounded fixed-time consensus protocols are developed for leader-following multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the followers are measurable, a state feedback consensus protocol is designed to achieve fixed-time consensus. Then, when the velocity information is unmeasurable, an observer-based fixed-time consensus protocol is proposed. With the help of Lyapunov stability theorem and the property of a homogeneous function, it is theoretically shown that the states of all followers can track that of the leader in fixed-time in the presence of input saturation. Finally, numerical simulation is carried out to illustrate the effectiveness of theoretical results.     

The leader-following attitude control of multiple rigid spacecraft systems

In this paper, we consider the leader-following consensus problem for a multiple rigid spacecraft system whose attitude is represented by the unit quaternion. Most results on this problem rely on the assumption that every follower can access the state of the leader and are obtained via a decentralized control manner. By developing a nonlinear distributed observer for the leader system, we can solve this problem via a distributed control scheme under the mild assumptions that the state of the leader can reach every follower through a path and that the communication between followers is bidirectional. Moreover, our result can accommodate a class of desired angular velocities generated by a marginally stable linear autonomous system.     

Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical results.