Output consensus control of multi-agent systems with nonlinear non-minimum phase dynamics

This paper considers the output consensus problem in non-minimum phase nonlinear multi-agent systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, a consensus protocol consisting of two terms is proposed. The first term is a linear function of the states of each agent employed in order to overcome the non-minimum phase dynamics, and the second term is a function of the output of neighbouring agents which provides coupling among agents and guarantees output consensus in the network. The asymptotic stability of output consensus errors and the boundedness of the states of agents are also studied. A numerical example is presented to show the effectiveness of the proposed approach.     

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.     

Adaptive Consensualization for Lipschitz Nonlinear-type Multi-agent Networks with Fixed Topologies

Adaptive consensualization problems for Lipschitz nonlinear-type multi-agent networks with fixed topologies are addressed. By using the state errors of the neighboring agents, an adaptive consensus protocol is proposed to deal with the consensualization problems. To eliminate the impacts of the Lipschitz nonlinear dynamics, the structure property of a transformation matrix and the Laplacian matrix, and the Lipschitz condition are well utilized. In the Lyapunov function, a scaling constant is introduced to eliminate the impacts of eigenvalues of the Laplacian matrix, which are the global information of the whole multi-agent networks. Then, an completely distributed consensualization criterion is presented in terms of the linear matrix inequality. Furthermore, an explicit expression of the consensus function and its initial state of this multi-agent network are presented. In the Final, a numerical example is shown to verify the validity of theoretical results.     

基于公共邻居的MHK一致性协议及其稳定性分析

如何增强多智能体系统一致性收敛是其一致性研究的重要问题。提出了一种新的MHK（multi-agent-based Hegselmann-Krause）一致性协议,该协议将智能体间的公共邻居作为切换网络下多智能体分布式协作的重要调控因素。针对该协议下的多智能体系统设计了能量函数,分析并证明了该系统具有李雅普诺夫意义下的稳定性,将收敛为一个或多个子观点集群。数值仿真采用增量分析方法考察了系统所收敛的观点集群数量与初始拓扑区间长度的关系;实验表明,该协议使多智能体系统收敛为数量更少的观点集群。所提出的基于公共邻居的MHK一致性协议能够有效提高切换网络的连通性,从而增强系统的一致性收敛,并能为观点演化模型的控制与优化提供理论支撑。     

Consensus of high-order multi-agent systems with large input and communication delays

We study in this paper the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays in both the communication network and inputs. Provided that the open-loop dynamics of the agents is not exponentially unstable, but may be polynomially unstable, and the communication topology contains a directed spanning tree, a truncated predictor feedback approach is established to solve the consensus problem. It is shown that, if the delays are constant and exactly known, the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays. If it is further assumed that the open-loop dynamics of the agents only contains zero eigenvalues, the delays are allowed to be time-varying and unknown. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches.     

Adaptive consensus tracking for linear multi‐agent systems with heterogeneous unknown nonlinear dynamics

This paper considers the consensus tracking control problem for general linear multi‐agent systems with unknown dynamics in both the leader and all followers. Based on parameterizations of the unknown dynamics of all agents, two decentralized adaptive consensus tracking protocols, respectively, with dynamic and static coupling gains, are proposed to guarantee that the states of all followers converge to the state of the leader. Furthermore, this result is extended to the robust adaptive consensus tracking problem in which there exist parameter uncertainties and Lipschitz‐type disturbances in the network. It is also shown that the parameter estimation errors converge to zero based on contradiction method and Lyapunov function approach. Finally, a simulation example is provided to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

A novel gain design method to improve the consensus performance of output-feedback multi-agent systems

This paper considers the consensus problem of a group of homogeneous agents. These agents are governed by a general linear system and can only directly measure the output, instead of the state. In order to achieve the consensus goal, each agent estimates its state through a Luenberger observer, exchanges its estimated state with neighbors, and constructs the control input with the estimated states of its own and neighbors. Due to the existence of observation and process noises, only practical consensus, instead of asymptotical consensus, can be achieved in such multi-agent systems. The performance of the achieved practical consensus can be measured by the ultimate mean square deviation of the states of agents. That performance is closely related to the observation gains of the state observers and the control gains of agents. This paper proposes a method to optimize such performance with respect to the concerned observation and control gains. That method starts with a set of feasible observation and control gains and formulates a group of linear matrix inequalities (LMIs). Solving these LMIs gives some intermediate matrix variables. By perturbing observation and control gains, and the intermediate matrix variables, the original LMIs yield another group of LMIs, which can be solved to provide a descent direction of observation and control gains. Moving along that descent direction, observation and control gains can be improved to yield better performance and work as the starting point of the next iteration. By iteratively repeating this procedure, we can hopefully improve the consensus performance of the concerned multi-agent system. Simulations are done to demonstrate the effectiveness of the proposed method.     

Consensus of networked multi-agent systems with communication delays based on the networked predictive control scheme

The consensus problem of discrete-time networked multi-agent systems (NMASs) with a communication delay is investigated in this article, where the dynamics of agents described by discrete-time linear time-invariant systems can be either uniform or non-uniform. For the NMASs with a directed topology and constant delay, a novel protocol based on the networked predictive control scheme is proposed to compensate for communication delay actively. Using algebraic graph theories and matrix theories, necessary and/or sufficient conditions of achieving consensus are obtained, which indicates that, under the proposed protocol, the consensus is independent of the network delay and only dominated by agents' dynamics and communication topology. Meanwhile, the protocol design and consensus analysis are also presented in the case of no network delay. Simulation results are further presented to demonstrate the effectiveness of theoretical results.     

Non-linear protocols for optimal distributed consensus in networks of dynamic agents

We consider stationary consensus protocols for networks of dynamic agents with fixed topologies. At each time instant, each agent knows only its and its neighbors’ state, but must reach consensus on a group decision value that is function of all the agents’ initial state. We show that the agents can reach consensus if the value of such a function is time-invariant when computed over the agents’ state trajectories. We use this basic result to introduce a non-linear protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents’ initial states. As a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value. We use a Lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time-invariant undirected network. Finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles.     

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.     

Reaching a consensus in networks of high-order integral agents under switching directed topologies

Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent’s full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent’s (estimated) state and the gain vector associated with the relative (estimated) states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. Also, the convergence of the transformed first-order integral agent’s state indicates the convergence of the original high-order integral agent’s state, if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative (estimated) states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be ‘uniformly jointly quasi-strongly connected’, which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach.     

Data rate for output feedback consensus of uncertain nonlinear multiagent systems

This article considers the data rate problem for output feedback consensus of uncertain nonlinear multiagent systems. Each agent is modeled by an nth order integrator with unknown nonlinear dynamics and unmeasurable states. An (n+2)th order extended state observer (ESO) is first designed to estimate the unmeasurable agent states and the unknown nonlinear dynamics. Based on the output of the ESO and a dynamic encoding and decoding scheme, a distributed consensus protocol is proposed. It is shown that, for a connected undirected network with nth order uncertain nonlinear agents, consensus can be guaranteed with merely one bit information exchange between each pair of adjacent agents at each time step.     

不确定通信拓扑下多智能体系统鲁棒一致性

本文研究一类具有通信不确定的多智能体系统鲁棒一致性问题.本文提出基于标称通信拓扑有向生成树的线性变换方法,将线性多智能体系统的状态一致性问题转化为相应线性系统的鲁棒部分变元渐近稳定性问题.首先采用基于有向生成树关联矩阵的线性变换,将多智能体系统网络的全局状态方程转化为一个降阶子系统;其次,将拉普拉斯矩阵的摄动部分进行分解,利用降阶系统设计鲁棒二次镇定控制器,推导出所有智能体状态达到渐近一致的充分条件.在此基础上将控制协议的参数设计转化为求解线性矩阵不等式的可行解.最后,通过数值仿真验证了所提出的一致性协议分析与设计方法的可行性和有效性.     

离散时间多智能体系统的一致性

研究了离散时间高维线性系统的一致性问题. 所考虑的系统可视为包含多个个体的多智能体系统, 每个个体的动力学行为与其他个体不同并受其他个体状态的影响. 本文建立了系统具有一致性的若干充分必要条件. 如果一致性函数存在, 文章给出了该函数的显式表达. 文末用一个数值例子说明了所得的理论结果.     

基于事件触发的非线性多智能体系统的固定时间分群一致性

结合事件触发控制方法研究非线性多智能体系统的固定时间分群一致性问题.提出一种非线性分布式事件触发分群一致性控制协议,并给出状态信息触发控制器更新的条件.该控制协议不受入度平衡条件限制,且只需自身状态信息与邻居智能体进行通信即可在固定时间内快速实现分群一致性.系统收敛时间与智能体的初始状态无关,可有效降低系统控制器更新频率和系统的资源消耗.结合代数图论、矩阵分析及Lyapunov稳定性理论,证明在所提出协议作用下,多智能体系统在固定时间内能够实现分群一致性,且不存在Zeno行为.最后,通过仿真实例检验了理论结果的可行性.     

Adaptive event-triggered consensus of singular multi-agent systems based on asynchronous data sampling

This paper is devoted to the problem of event-triggered consensus for a class of singular multi-agent systems with nonlinear dynamics. Firstly, in consideration of the impossibility to reach all agents in some case, an observer is designed to access these agents' states. Secondly, a novel adaptive event-triggered scheme is proposed based on asynchronous data sampling. In this scheme, the trigger parameter can be adjusted dynamically in order to reduce information transmissions among agents. Thirdly, by employing Lyapunov stability theory, a sufficient condition on the consensus of singular multi-agent systems is obtained. Then, the control protocol and event-triggering scheme are designed by solving a linear matrix inequality condition. Finally, an example is given to illustrate the proposed results.     

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.     

具有时延和切换拓扑的高阶离散时间多智能体系统鲁棒保性能一致性

研究存在参数不确定性的高阶离散时间多智能体系统在时延和联合连通切换通信拓扑条件下的鲁棒保性能一致性问题,给出一种线性一致性协议的设计方法.1）引入高阶离散时间不确定多智能体系统的鲁棒保性能一致性问题,定义基于智能体邻居状态误差和控制输入的保性能函数;2）通过构造合适的Lyapunov函数并利用离散时间系统稳定性理论,推导出一个使高阶离散时间不确定多智能体系统在该条件下获得保性能一致性的线性矩阵不等式（Linear matrix inequality,LMI）充分条件,并给出相应的保性能上界;3）以一致性序列的形式给出参数不确定条件下的高阶离散时间多智能体系统的一致性收敛结果;4）数值仿真验证了本文理论的正确性和有效性.     

基于牵制控制的异质多智能体系统的群一致性研究

为了研究由线性的一阶智能体、二阶智能体和非线性的EL （Euler-Lagrange）结构智能体组成的异质多智能体系统的群一致性,并实现同一个子群中智能体状态趋于期望的状态,针对无向的固定拓扑情况,提出了基于牵制控制的分布式控制协议。并通过代数图论、李雅普诺夫函数和拉塞尔不变集原理证明了控制协议的可行性。数值仿真结果表明:在所提控制协议作用下能够实现包含非线性EL结构的异质多智能体系统的群一致性,与未引入牵制控制的群一致性算法相比各个子群能够趋于期望的状态。     

Sum‐of‐squares–based consensus verification for directed networks with nonlinear protocols

In this paper, we investigate the consensus verification problem of nonlinear agents in a fixed directed network with a nonlinear protocol. Inspired by the classical Lipschitz‐like condition, we introduce a more relax condition for the dynamics of the nonlinear agents. This condition is motivated via the construction of general Lyapunov functions for achieving asymptotic consensus. Especially, for agents where dynamics are described by polynomial function of the states, our consensus criterion can be converted to a sum of squares (SOS) programming problem, solvable via semidefinite programming tools. Of interest is that the scale of the resulting SOS programming problem does not increase as the size of the network increases, and thus, the applicability to analyze consensus of large‐scale networks is promising. Finally, an example is given to illustrate the effectiveness of our theoretical results.