Stationary consensus of heterogeneous multi-agent systems with bounded communication delays

Consensus seeking is investigated for the discrete-time heterogeneous multi-agent systems composed of first-order agents and second-order agents, and two stationary consensus algorithms are constructed for the first-order agents and the second-order agents, respectively. Based on the properties of nonnegative matrices, sufficient consensus criteria are obtained for the agents with bounded communication delays under fixed topology and switching topologies, respectively. With some prerequisites on the coupling weights and the sampling interval, the asymptotic consensus achievement of the dynamic agents is independent of the communication delay, but strictly depends on the connectedness of the interconnection topology. Simulation results illustrate the correctness of the results.     

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.     

基于事件触发非线性多智能体系统的固定时间一致性

本文研究了在有向拓扑下,带有非线性动力学多智能体系统的固定时间一致性问题.提出了一种新的基于事件触发机制的非线性控制策略,对于每个智能体给出了基于状态信息的事件触发条件,当状态误差满足所给条件时才触发事件,能有效的减小系统的能量耗散和控制器的更新频次.利用Lyapunov稳定性理论和代数图论,证明在该控制策略下,多智能体系统在固定时间能实现领导跟随一致性,且不存在Zeno行为.相较于有限时间一致性策略,采用固定时间一致性策略系统的收敛时间不再依赖于系统的初始状态.最后,仿真实例验证了理论结果的有效性.     

复杂分数阶多自主体系统的运动一致性

复杂环境中,许多自然现象的动力学特性不能应用整数阶方程描述,而只能用分数阶（非整数阶）动力学的智能个体合作行为来解释. 本文假设多自主体 系统存在个体差异,采用不同的分数阶动力学特性组成复杂分数混合阶微分方程. 应用分数阶系统的Laplace变换和频域理论,研究了有向网络拓扑下,时延分数混合阶多自主体系统的运动一致性. 由于整数阶系统是分数阶系统的特殊情况,本文的结论可以推广到整数阶与分数阶混合的多自主体系统中. 最后,应用仿真实例对本文结论进行了验证.     

Consensus tracking control for sampled-data second-order multi-agent systems with arbitrary weights under fixed communication topology

This paper focuses on the consensus tracking control problem of multi-agent systems (MASs) with arbitrary adjacency weights instead of traditional nonnegative weights in a sampling setting. First, unlike Lemma 4 in Hu and Hong [2007. Leader-following coordination of MASs with coupling time delays. Physica A: Statistical Mechanics and its Applications, 374(2), 853–863], for MASs with arbitrary weights, the global reachability of the leader node is just a necessary but not a necessary and sufficient condition to guarantee the positive stability of matrix H. Hence, it's urgent for us to establish some positive stability criteria of matrix H first, which is a necessary condition for MASs to achieve consensus tracking. Simultaneously, we also solve the following problems successfully: which nodes should have direct connection with the leader? What's the range size of the leader adjacency coefficients? Then, some sufficient consensus tracking control conditions are obtained for MASs without time-delays and with time-delays by using matrix analysis method and perturbation theory, respectively. Finally, numerical examples are given to illustrate the effectiveness of our results.     

带强连通分支的多智能体系统可控包含控制

研究有强连通子图拓扑结构的有向多智能体系统领导者选择及可控包含控制问题.根据网络拓扑结构,智能体被分为两类:单元智能体和一般智能体.首先设计强连通子图中个体组成的单元智能体的一致性协议实现各个单元的一致;后由单元智能体和一般智能体构成新的拓扑结构,结合复杂网络可控性理论与二分图最大匹配算法确定满足网络可控的最少领导者集合,并为所有智能个体设计相应的控制协议,驱使跟随者渐近收敛到多个领导者组成的动态凸包中,从而实现网络的可控包含控制.仿真结果验证了理论分析的正确性.     

基于有向图的信息拓扑独立的二阶系统一致性判据

针对可能存在拓扑切换情形的有向图, 研究了多个二阶系统在没有领航者时的一致性问题. 提出了两个使用不同合作策略的一致性算法, 并得到了若干与信息拓扑参数无关的一致性判据. 采用基于特征值分析的方法对第一个一致性算法进行了分析, 得到了该算法在固定有向图条件下一致性可达的充分必要条件. 对于第二个一致性算法, 如果切换网络拓扑的并图存在一棵有向生成树的频率足够高, 则系统仍然可以实现一致性. 利用等价模型变换将原系统转化为级联系统的方法, 给出并简化了该算法的收敛性分析. 采用同样的策略, 针对切换无向图的一致性问题进一步推导得到了一个新颖的充分必要条件. 另外, 本文还分别针对固定有向图研究了这两个算法对时延的鲁棒性. 论文最后给出了仿真示例, 验证了所得理论结果的正确性和算法的有效性.     

Finite interval tracking algorithm for nonlinear multi-agent systems with communication delays

We propose an iterative learning control (ILC) tracking strategy to solve the tracking problem of multi-agent systems with nonlinear dynamics and time-varying communication delays. The distributed tracking strategy, in which each tracking agent only utilises its own and neighbours’ information, enables the tracking agents successfully track a maneuvering target in a finite time interval although with presence of time delays. Compared with the existing related work, the quantitative relationship between the boundary of tracking errors and the estimation of time delays is derived. Furthermore, in many practical control problems, identical initialisation condition may not be satisfied, which is called initial-shift problem. Hence, a forgetting factor is introduced to deal with that problem. It is proved that the presented results are effective via conducting numerical examples.     

Consensus of second-order multi-agent systems with delayed nonlinear dynamics and aperiodically intermittent communications

In this paper, we investigate the consensus problem for second-order multi-agent systems with inherent delayed nonlinear dynamics and aperiodically intermittent communication. First, different from previous works, aperiodically intermittent communication is proposed. Moreover, two types of delay are considered. The first case is that the delay is small enough so that it is less than the minimum of communication width. The other one is that the delay is time-varying and large, and in this case, we do not restrict the delay less than the communication width. Different approaches are provided to study these two cases, and some conditions are obtained to achieve second-order consensus under a fixed strongly connected and balanced topology. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method.     

基于事件触发控制的二阶多智能体的一致性

研究二阶多智能体系统在固定有向拓扑下的一致性问题。为减少不必要的网络带宽资源的浪费,给出一种基于事件触发控制的一致性算法。该算法基于状态误差对系统中的所有个体建立事件触发函数,使得个体之间的信息通讯和控制信号更新仅在事件触发时刻进行。采用矩阵理论和模型变换思想对系统进行了分析和转化,并利用Lyapunov理论给出了系统达到渐近一致的充分条件。仿真结果验证了理论方案的有效性。