Leader‐following control for multiple inertial agents

This paper investigates distributed controller design problem for a leader‐follower network in the presence of communication delays. Two main contributions are made in this work. First, the second‐order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second‐order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Coordination of networked systems on digraphs with multiple leaders via pinning control

It is well known that achieving consensus among a group of multi-vehicle systems by local distributed control is feasible if and only if all nodes in the communication digraph are reachable from a single (root) node. In this article, we take into account a more general case that the communication digraph of the networked multi-vehicle systems is weakly connected and has two or more zero-in-degree and strongly connected subgraphs, i.e. there are two or more leader groups. Based on the pinning control strategy, the feasibility problem of achieving second-order controlled consensus is studied. At first, a necessary and sufficient condition is given when the topology is fixed. Then the method to design the controller and the rule to choose the pinned vehicles are discussed. The proposed approach allows us to extend several existing results for undirected graphs to directed balanced graphs. A sufficient condition is proposed in the case where the coupling topology is variable. As an illustrative example, a second-order controlled consensus scheme is applied to coordinate the movement of networked multiple mobile robots.     

Distributed consensus of multi‐agent systems with general linear node dynamics and intermittent communications

Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi‐agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi‐agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low‐dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi‐step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi‐agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

基于一致性的小型四旋翼机群自主编队分布式运动规划

设计一种小型四旋翼无人机群起飞后自主形成正多边形编队的分布式运动规划方法.在四旋翼无人机的串级控制系统框架下,分布式编队控制器以简化agent模型为基础,同时采用平均一致性算法和有领导一致性算法,共同产生各无人机位置与偏航角的期望轨迹.讨论了达成最终协调目标队形的拓扑条件,并给出一种基于有向Hamilton环的通信拓扑设计方案.最后通过数值仿真验证了所提出算法的有效性.     

多智能体系统一致性问题的控制器与拓扑协同优化设计

本文考虑多智能体系统一致性问题的控制与拓扑协同优化设计.首先在给定的二次性能指标下,对多智能体系统的分布式一致性控制协议寻优,得到依赖于网络拓扑图拉普拉斯矩阵的最优控制器.其次,为进一步最大限度地减少拓扑之间的连边,又不降低多智能体系统的收敛速度,通过权衡系统的通信能量和控制能量,寻求网络拓扑的优化设计,给出了拓扑优化算法和多智能体系统特征值的优化方法.最后,仿真研究验证了在控制器优化的基础上进一步寻求拓扑优化,可大大提升系统的一致性性能.     

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.     

Consensus in multi‐agent systems with communication constraints

The problem of second‐order consensus is investigated in this paper for a class of multi‐agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second‐order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second‐order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays

The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

Second-order consensus of multi-agent systems with noises via intermittent control

Second-order consensus of multi-agent systems with noises via intermittent control is investigated in this paper. First, we study the mean-square consensus problem with communication noises by intermittent control. In order to reach consensus, under the strong directed interacted topology, by using the tools of graph theory and Lyapunov method, a distributed control protocol is proposed based on the noises and periodical intermittent information. The upper bound of noise strength in the sense of matrix norm and the lower bound of communication time duration are obtained. Second, a class of coupled system models which include delay-terms in their nonlinearities in the noisy environment is discussed. Under the balanced strongly connected topology, the sufficient conditions to achieve the mean-square average-consensus are obtained. Finally, simulations are given to illustrate the effectiveness of our results.     

Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.     

Solving a modified consensus problem of linear multi-agent systems

A distributed protocol is proposed for a modified consensus problem of a network of agents that have the same continuous-time linear dynamics. Each agent estimates its own state using its output information and then sends the estimated state to its neighbor agents for the purpose of reaching a consensus. The modified consensus problem requires the group decision value to be a linear function of initial states and initial estimated states of all agents in the network, and the transformation matrix associated with this linear function not to be a zero matrix. It is proved that under the proposed control protocol, the modified consensus problem can be solved if and only if the system matrices of the agent’s dynamics are stabilizable and detectable, the input matrix is not a zero matrix, and the communication topology graph has a spanning tree. The proposed protocol can also be extended to multi-agent systems where agents are described by discrete-time linear dynamics. The corresponding necessary and sufficient conditions are provided as well.     

Intermittent observer-based consensus control for multi-agent systems with switching topologies

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach.     

Fuzzy adaptive iterative learning coordination control of second-order multi-agent systems with imprecise communication topology structure

In this paper, we investigate the perfect consensus problem for second-order linearly parameterised multi-agent systems (MAS) with imprecise communication topology structure. Takagi-Sugeno (T–S) fuzzy models are presented to describe the imprecise communication topology structure of leader-following MAS, and a distributed adaptive iterative learning control protocol is proposed with the dynamic of leader unknown to any of the agent. The proposed protocol guarantees that the follower agents can track the leader perfectly on [0,T] for the consensus problem. Under alignment condition, a sufficient condition of the consensus for closed-loop MAS is given based on Lyapunov stability theory. Finally, a numerical example and a multiple pendulum system are given to illustrate the effectiveness of the proposed algorithm.     

Consensus of Multi-slave Bilateral Teleoperation System with Time-Varying Delays

This paper studies the consensus problem for teleoperation system over communication networks. Compared with previous work, both multi-slave configuration and time variable delays are considered. According to the topology structure of slave robots, centralized and distributed consensus controllers are respectively designed, where a leader-following strategy is adopted. During the design process of distributed controllers, min-weighted rigid graph is used to optimize the topology structure of slave robots. With the optimized topology, the amount of communication links and energy dissipations in slave site can be reduced. Moreover, the sufficient stability conditions are presented to show the consensus controllers can stabilize the master-slave system under variable time delay. Finally, simulation results are performed to show the effectiveness of the main results.     

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

This paper presents a novel distributed adaptive control algorithm for uncertain higher‐order nonlinear multiagent systems subject to output constraints and unknown control directions. Regarding the latter, a generic class of cases is considered, allowing completely unknown and even nonidentical control directions. Furthermore, the communication topology is only required to contain a fixed directed spanning tree. To guarantee the output constraints and address the asymmetric directed communication topology, a new reference output using the transformation strategy is introduced for each agent, benefiting from which the consensus problem of the multiagent system is recast as local tracking control problems of single agents. Then, the distributed control algorithm is recursively established based on the backstepping technique and the Nussbaum‐type function. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that, under the proposed distributed algorithm, uniform boundedness of all closed‐loop signals can be ensured, and asymptotic consensus is achieved without violation of the output constraints. Finally, simulation studies on the angle control of single‐link robots are given to verify the effectiveness of the proposed algorithm.     

Delay-optimal quorum consensus for distributed systems

Given a set of nodes S, a coterie is a set of pairwise intersecting subsets of S. Each element in a coterie is called a quorum. Mutual exclusion in a distributed system can be achieved if each request is required to gel consensus from a quorum of nodes. This technique of quorum consensus is also used for replicated distributed database systems, and bicoteries and wr-coteries have been defined to capture the requirements of read and write operations in user transactions. The author is interested in finding coteries, bicoteries, and wr-coteries with optimal communication delay. The protocols take into account the network topology. They design delay-optimal quorum consensus protocols for network topologies of trees, rings, and clustered networks     

Distributed dynamic consensus under quantized communication data

Distributed dynamic average consensus is investigated under quantized communication data. We use a uniform quantizer with constant quantization step‐size to deal with the saturation caused by the dynamic consensus error and propose a communication feedback‐based distributed consensus protocol suitable for directed time‐varying topologies to make the internal state of each agent's encoder consistent with the output of its neighbors' decoder. For the case where the communication topology is directed, balanced and periodically connected, it is shown that if the difference of the reference inputs satisfies some boundedness condition, then the designed quantized dynamic consensus protocol can ensure the states of all the agents achieve dynamic average consensus with arbitrarily small steady state error by properly choosing system parameters. The lower bound of the required quantization levels and the method to choose the system parameters are also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

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.