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.     

Leader-following consensus of stochastic dynamical multi-agent systems with fixed and switching topologies under proportional-integral protocols

With the rapid development of swarm intelligence, consensus problem for multi-agent systems (MASs) has attracted substantial attention. To deal with the leader-following consensus problems in stochastic dynamical MASs with fixed and switching topologies, this article designed proportional-integral (PI) control protocols. On the basis of algebraic graph theory and stochastic analysis techniques, by selecting appropriate Lyapunov functions, it is theoretically shown that leader-following consensus of MASs with stochastic dynamics underlying fixed and switching topologies can be achieved in mean square, respectively. Sufficient criteria are derived for selecting the PI control gains. Finally, the theoretical results are illustrated through several numerical simulations.     

Leader-following consensus of multi-agent systems under directed communication topology via distributed adaptive nonlinear protocol

In this paper, we study the leader-following consensus problem of general linear multi-agent systems under directed communication topology. To avoid using any global information, an adaptive nonlinear protocol is proposed based only on the relative state information. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem. A numerical example is provided to illustrate the effectiveness of the theoretical results.     

离散多智能体切换系统的二阶分组一致性研究

针对随机切换拓扑下离散多智能体系统的二阶分组一致性问题进行了研究。 设计了一种新颖的分组一致性协议,该协议不依赖于保守的假设条件,能全面反映系统中智能体在分组内与分组间的相互影响。引入马尔科夫链来模拟系统的随机拓扑变化, 基于矩阵理论和图论得到了在马尔科夫切换拓扑条件下,应用新协议使系统达到分组一致的充分条件。 在证明过程的结尾部分,使用线性不等式 (LMI) 工具给出了获取协议中控制参数的算法。最后,通过数字仿真实例证明了理论结果的有效性。     

Leader-following consensus for a class of second-order nonlinear multi-agent systems

This paper deals with the leader-following consensus problem for a class of multi-agent systems with nonlinear dynamics and directed communication topology. The control input of the leader agent is assumed to be unknown to all follower agents. A distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents, which achieves leader-following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent. Compared with previous results, the nonlinear functions are not required to satisfy the globally Lipschitz or Lipschitz-like condition and the adaptive consensus protocol is in a distributed fashion. A numerical example is given to verify our proposed protocol.     

Guaranteed performance consensus problems for nonlinear multi-agent systems with directed topologies

The guaranteed performance consensus problem for multi-agent systems with Lipschitz nonlinear dynamics is investigated, where the interaction topology is directed. Both switching and fixed interaction topologies are considered. By the matrix transformation method, the guaranteed performance consensus problems are transferred into guaranteed performance stabilisation problems. Then, the criteria of guaranteed performance consensus for nonlinear multi-agent systems with switching and fixed interaction topologies are obtained, respectively. For the introduced performance function, an upper bound is given. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed results.     

Cluster consensus of high-order multi-agent systems with switching topologies

This paper investigates the cluster consensus problems of generic linear multi-agent systems with switching topologies. Sufficient criteria for cluster consensus, which generalise the results in existing literatures, are derived for both state feedback and observer-based control schemes. By using an averaging method, it is shown that cluster consensus can be achieved when the union of the acyclic topologies contains a directed spanning tree within each cluster frequently enough. We also provide a principle to construct digraphs with inter-cluster cyclic couplings that promote cluster consensus regardless of the magnitude of inter-agent coupling weights. Finally, numerical examples are given to demonstrate the effectiveness of the proposed approaches.     

Stabilisability of discrete-time multi-agent systems under fixed and switching topologies

This paper studies the problem of stabilisability for general discrete-time linear multi-agent systems. For fixed topology, a necessary and sufficient graph-theoretic condition is proposed. Based on this, a general linear form of the external control input is given, and two methods to design the feedback gain matrix by Riccati equality/inequality are given. For switching topology, a sufficient graph-theoretic condition is presented, under which the stabilisability of multi-agent systems is achieved by introducing an averaging analysis approach. Additionally, both results under fixed and switching topologies are applied for solving the tracking and formation control of discrete-time multi-agent systems, and some sufficient and/or necessary conditions are presented. Finally, numerical examples are given to illustrate the theoretical results.     

Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies

In this article, we study distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. The analysis is based on graph theory and nonnegative matrix theory. We propose two kinds of consensus protocols based on the consensus protocol of first-order and second-order multi-agent systems. Some necessary and sufficient conditions that the heterogeneous multi-agent system solves the consensus problems under different consensus protocols are presented with fixed topology. We also give some sufficient conditions for consensus of the heterogeneous multi-agent system with switching topology. Simulation examples are provided to demonstrate the effectiveness of the theoretical 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.     

切换拓扑下多自主体系统的事件触发一致性控制

本文针对一阶非线性多自主体系统,考察了切换拓扑下的事件触发一致性控制问题.当切换拓扑子图的并图包含有向生成树时,基于一阶保持器提出了一种分布式事件触发一致性算法,用以降低网络的通信负载.运用迭代法和不等式法,得到了多自主体系统达到有界一致性的充分条件.此外,证明了所提事件触发机制不存在Zeno现象,并得到了触发间隔的正下界.最后,给出仿真实例,验证了所提事件触发一致性算法和理论分析结果的有效性.     

切换拓扑一阶积分器网络量化趋同控制

针对数字信道中传输的是经过量化和编码后的数据,研究了切换拓扑情况下连续时间一阶积分器网络中的量化趋同问题.通过均匀量化器,每个智能体将量化后的状态传输给邻居,并利用所得信息设计协议,实现量化趋同.在所提出的量化趋同协议下,所有状态将在有限时间内进入包含状态均值的量化层中.特别地,对于通信拓扑是时不变的情况,给出了实现量化趋同所需时间的上界.仿真结果验证了所提出算法的有效性.     

Leader-following consensus of multi-agent systems under fixed and switching topologies

The leader-following consensus problem of higher order multi-agent systems is considered. In the system, the dynamics of each agent and the leader is a linear system. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented for both fixed and switching interaction topologies, which describe the information exchange between the multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and Lyapunov inequality. Simulations indicate the capabilities of the algorithms.     

具有时延和不确定拓扑的二阶多智能体系统的平均一致性

首先,通过模型变换的方法将原系统分解为多个简单的子系统;然后,利用Lyapunov-Krasovskii的方法,以线性矩阵不等式的形式给出了带有多时变时滞的二阶多智能体系统达到平均一致性的充分条件,且只要求其通讯拓扑结构是联合连通的.最后,用仿真实验验证了本理论的正确性和有效性.     

Passivity-based consensus for linear multi-agent systems under switching topologies

This paper studies the passivity-based consensus analysis and synthesis problems for a class of stochastic multi-agent systems with switching topologies. Based on Lyapunov methods, stochastic theory, and graph theory, new different storage Lyapunov functions are proposed to derive sufficient conditions on mean-square exponential consensus and stochastic passivity for multi-agent systems under two different switching cases, respectively. By designing passive time-varying consensus protocols, the solvability conditions for the passivity-based consensus protocol synthesis problem, i.e., passification, are derived based on linearization techniques. Numerical simulations are provided to illustrate the effectiveness of the proposed methods.     

Leader-following consensus of nonlinear multi-agent systems with switching topologies and unreliable communications

In this paper, distributed leader-following consensus for a class of nonlinear multi-agent systems with switching topologies and unreliable communications is studied. Each possible topology contains a directed spanning tree rooted at the leader. Agents share the information only with their neighbors on some disconnected time intervals due to the unreliable communications. By designing suitable distributed controllers, all follower nodes asymptotically synchronize to the leader node if the communication rate is larger than a threshold value for each time interval. By using multiple Lyapunov functions theory and linear matrix inequalities technique, some sufficient conditions are given to guarantee the consensus. Moreover, based on the theoretical results, the admissible communication rate and convergence rate of the whole systems are adjusted by the feedback gain matrix, which provides helpful design guidelines in practical applications. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

线性多智能体系统在固定和切换拓扑下的领航跟随控制

研究线性多智能体系统的领航跟随一致性问题. 假设每个多智能体系统只能得到其邻域的输出测量信息, 在此条件下, 讨论多智能体在有向固定网络拓扑和无向切换网络拓扑两种情况下的一致性问题. 针对这两种情况, 提出含有一种分布式观测器的一致性控制算法. 应用Lyapunov 稳定性理论证明了若单个多智能体系统是可镇定和可检测的, 且网络连接拓扑只需满足简单的结构, 则系统能够达到领航跟随一致性. 仿真结果验证了理论分析的正确性.     

Quantized consensus over directed networks with switching topologies

This paper studies the quantized consensus problem for a group of agents over directed networks with switching topologies. We propose an effective distributed protocol with an adaptive finite-level uniform quantized strategy, under which consensus among agents is guaranteed with weaker communication conditions. In particular, we analytically prove that each agent sending 5-level quantized information to each of its neighbors, together with 3-level quantized information to itself at each time step, which suffices for attaining consensus with an exponential convergence rate as long as the duration of all link failures in the directed network is bounded. By dropping the typical common left eigenvector requirement for the existence of common quadratic Lyapunov function, we conduct the convergence analysis based on the notion of input-to-output stability. The proposed quantized protocol has favorable merits of requiring little communication overhead and increasing robustness to link unreliability, and it fits well into the digital network framework.     

Event-based consensus of multi-agent systems with general linear models

In this paper, the event-based consensus problem of general linear multi-agent systems is considered. Two sufficient conditions with or without continuous communication between neighboring agents are presented to guarantee the consensus. The advantage of the event-based strategy is the significant decrease of the number of controller updates for cooperative tasks of multi-agent systems involving embedded microprocessors with limited on-board resources. The controller updates of each agent are driven by properly defined events, which depend on the measurement error, the states of its neighboring agents and an arbitrarily small threshold. It is shown that the controller updates for each agent only trigger at its own event time instants. A simulation example is presented to illustrate the theoretical results.     

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.