异构变时延多智能体系统编队控制分析

实际工程应用中,异构多智能体的编队控制问题研究具有十分重要的意义。考虑现实环境影响,编队系统个体之间的通信变时延难以忽略。系统收敛速率是评价系统性能的重要依据,然而现有编队控制问题研究很少能给出相应的量化指标。针对上述情形,对包含一、二阶智能体的异构变时延系统的编队控制问题进行分析研究。首先,考虑固定有向通信拓扑情况,对领航跟随者模式下异构变时延多智能体系统提出线性一致性控制协议。然后,构建误差系统模型,利用图论与矩阵论分析方法,并结合Routh-Hurwitz定理与牛顿-莱布尼兹公式,获得系统实现编队控制的充要条件,同时得到估算系统收敛速率的不等式关系。最后,仿真算例中随机给定一种系统节点0全局可达的通信拓扑,并对不同时延情况的编队控制效果进行分析,验证一致性控制协议的正确性和有效性。     

Containment control for second-order multi-agent systems with time-varying delays

This paper considers the containment control problem for second-order multi-agent systems with time-varying delays. Both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated. Sufficient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control are given. In the case that the leaders are stationary, the Lyapunov–Razumikhin function method is used. In the case that the leaders are dynamic, the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) method are jointly used. A novel discretized Lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is, which leads to a better result on the allowed upper bound of the delays to ensure containment control. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

Containment control for second-order nonlinear multi-agent systems with intermittent communications

This article investigates the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics, under the common assumption that each agent can only obtain the relative information of its neighbours intermittently. A kind of distributed protocol based only on the relative local intermittent measurements of neighbouring agents is designed for containment control under fixed directed topology. In the absence of delays, based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee the intermittent containment control of second-order nonlinear multi-agent systems. In the presence of delays, some containment conditions are also obtained for a second-order multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Moreover, the similar results are obtained for second-order nonlinear multi-agent systems under switching directed topology. Finally, simulation examples are given to illustrate the correctness and effectiveness of the theoretical analysis.     

Distributed Containment Control of Multi-agent Systems with General Linear Dynamics and Time-delays

Containment control problems for high-order linear time-invariant multi-agent systems with fixed communication time-delays are investigated. Based on Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) method, sufcient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control of the multi-agent systems under the different containment control algorithms are given. Finally, numerical simulations are presented to demonstrate theoretical results.     

含通信延时及输入延时的线性多智能体的一致性

针对通信延时及输入延时并存的情况下,研究具有一般线性动态特性的高阶多智能体在固定且无向的网络拓扑下的一致性.通过将多智能体的特征方程分解为一系列低阶的因子,一致性问题转换为一系列低阶因子的稳定性分析问题,降低了问题的分析复杂度.进一步地,分析无延时情况下多智能体达到一致性的控制增益的取值范围,即增益的稳定区间.当从稳定区间选取一个固定的控制增益时,应用频率扫描高级聚类法分析多个因子在两延时参数空间中的稳定性,并由此获得多智能体延时无关及延时相关的一致性结论.一个说明性的例子验证了分析结论.     

Multi-stage dynamic event-triggered containment control of nonlinear multi-agent systems with input-bounded leaders and time-varying delay

This article immerses in the event-triggered containment control problem for a Lipschitz-like nonlinear multi-agent system with multiple active leaders. First, two event-triggered mechanisms with internal dynamic variables are designed in both sensor-observer (S-O) and controller-actuator (C-A) channels to monitor data transmission and reduce communication burden. Second, an observer is constructed with the aid of the output information to estimate the states that cannot be acquired directly. Then, a control protocol considering time-varying communications delays is proposed based on the observer. Third, the boundedness analysis of the containment error system is constructed by Lyapunov stability theory, the sufficient conditions are given in light of strict feasible LMIs. Finally, the validity of the proposed controller is verified by two simulations.     

Nonfragile containment control of nonlinear multi-agent systems via a disturbance observer-based approach

In this article, we consider the nonfragile containment control problem of nonlinear multi-agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer-based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques.     

组合连通拓扑下基于事件触发的多智能体快速一致性算法

针对组合连通拓扑下多智能体系统控制过程中存在通信和计算资源损耗大以及系统收敛速度慢等问题,提出一种新的具有状态预测器的事件触发一致性控制协议,通过设计状态预测器使每个智能体都能对其邻居智能体的未来状态作出预测;同时,对于智能个体给出了基于状态信息的事件触发条件,当状态误差满足该条件才触发事件.在该控制策略下多智能体系统可在节约通信和计算资源的同时具有更快的收敛速度.利用Lyapunov稳定性理论和代数图论,证明了所提事件触发控制策略能够有效实现组合连通拓扑结构下的平均一致性,且不存在Zeno行为.仿真实例进一步验证了理论结果的有效性.     

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.     

Distributed Cooperative Learning for Discrete-Time Strict-Feedback Multi Agent Systems Over Directed Graphs

This paper focuses on the distributed cooperative learning (DCL) problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs. Compared with the previous DCL works based on undirected graphs, two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric, and the derived weight error systems exist n-step delays. Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying (LTV) systems with different phenomena including the nonsymmetric Laplacian matrix and time delays. Subsequently, an adaptive neural network (NN) control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law. Then, by using two novel lemmas on the extended exponential convergence of LTV systems, estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced. The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the “mod” function and proper time series. A simulation comparison is shown to demonstrate the validity of the proposed DCL method.      

间歇通信下具有双层拓扑结构的多智能体系统一致性研究

本文研究了在间歇通信机制下具有两层网络拓扑结构的多智能体系统一致性问题.首先,提出了一种在间歇通信机制下的一致性控制协议,通过建立网络结构模型和误差系统模型,将一致性问题等效转化为线性时滞系统的渐近稳定性问题.其次,利用Lyapunov-Krasovskii泛函分析方法,导出了多智能体网络在间歇通信机制下达到一致性的充分条件,结论以一组 LMI形式给出.最后,通过仿真算例验证了该方法的有效性.     

含时变时延的多智能体的包容控制器设计

针对一类含时变通讯时延的多智能体系统,基于时滞依赖法提出了其在有向网络拓扑下的一类包容控制器设计的方法,该设计能有效地驱使多智能体系统中所有跟随者的状态渐近一致地收敛到领导者运动过程中形成的几何凸包．结合李亚普诺夫稳定性理论和线性矩阵不等式（LMI）方法,推导了多智能体系统包容控制率存在的充分条件,并将包容控制器的设计最终转化成求解线性矩阵不等式可行解的问题．结果表明,该方法对多智能体系统中的时变通讯时延具有良好的补偿效果．最后通过仿真算例验证了此方法的有效性和可行性．     

Tracking Control of Multi-Agent Systems Using a Networked Predictive PID Tracking Scheme

With the rapid development of network technology and control technology, a networked multi-agent control system is a key direction of modern industrial control systems, such as industrial Internet systems. This paper studies the tracking control problem of networked multi-agent systems with communication constraints, where each agent has no information on the dynamics of other agents except their outputs. A networked predictive proportional integral derivative(PPID) tracking scheme is proposed t...     

Consensus of single integrator multi-agent systems with directed topology and communication delays

In this paper, a distributed control scheme has been developed for consensus of single integrator multi-agent systems with directed fixed communication topology for arbitrarily large constant, time-varying or distributed communication delays. It is proved that the closed loop control system can reach consensus with an exponential convergence rate if and only if the topology is quasi-strongly connected. Simulation results are also provided to demonstrate the effectiveness of the proposed controller.     

Distributed formation‐containment control with Euler‐Lagrange systems subject to input saturation and communication delays

This paper is concerned with the problem of formation‐containment on networked systems, with interconnected systems modeled by the Euler‐Lagrange equation with bounded inputs and time‐varying delays on the communication channels. The main results are the design of control algorithms and sufficient conditions to ensure the convergence of the network. The control algorithms are designed as distributed dynamic controllers, in such a way that the number of neighbors of each agent is decoupled from the bound of the control inputs. That is, in the proposed approach the amplitude of the input signal does not directly increase with the number of neighbors of each agent. The proposed sufficient conditions for the asymptotic convergence follow from the Lyapunov‐Krasovskii theory and are formulated in the linear matrix inequalities framework. The conditions rely only on the upper bound of delays and on a subset of the controller parameters, but they do not depend on the model of each agent, which makes it suitable for networks with agents governed by distinct dynamics. In order to illustrate the effectiveness of the proposed method we present numerical examples and compare with similar approaches existing in the literature.     

输出饱和多智能体系统的迭代学习趋同跟踪控制

针对带有输出饱和的多智能体系统有限时间趋同跟踪控制问题,提出了一种分布式迭代学习控制算法.首先假设多智能体系统具有固定拓扑结构,且仅有部分智能体可获取到期望轨迹信息.基于输出约束条件构造一致性跟踪误差,在此基础上设计了P型迭代学习控制率.然后采用压缩映射方法给出了一个算法收敛的充分条件,并在理论上证明了跟踪误差的收敛性.最后,将理论结果推广至具有随机切换拓扑结构的多智能体系统中.仿真结果验证了所提出算法的有效性.     

具有干扰的多领航者系统的群集运动的快速收敛

针对具有多领航者网络化系统的离散时间群集运动问题,提出了一阶/二阶网络化系统的包容控制算法。运用现代控制理论、代数图论和线性矩阵不等式等分析工具对所提出的控制算法进行理论分析,得到了具有干扰的多领航者网络化系统在离散时间情况下有限时间内实现群集运动的收敛条件。最后,利用LMI工具箱数值仿真求得正定矩阵范围,进而确定线性系统的稳定性。系统仿真验证了所得结论的正确性。     

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.     

一类多时变时延异质多智能体系统的组一致性

研究了一类由一阶和二阶智能体组成的异质多智能体系统的组一致性问题．首先,在多时变时延异质系统中设计了实现静态组一致的控制算法;其次,运用稳定性理论和线性矩阵不等式,分别给出了无时延、同时具有通信与输入时延的异质多智能体系统实现组一致性的充分条件;再次,通过求解一组可行的线性矩阵不等式,得到了输入时延的容许上界,并得出了通信时延与异质多智能体系统的组一致性无关的结论;最后,仿真结果验证了理论结果的有效性．