多智能体系统的一致性分析与控制
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摘要
多智能体系统是指包含大量具有动态演化特征的个体以及个体之间的局部协作和相互作用的系统,是一类典型的复杂动态系统。一致性问题是多智能体系统研究领域的热点问题,对其进行深入研究,一方面能够为自然和社会中出现的复杂现象提供合理的理论解释,另一方面又可为多机器人系统、传感器网络和人造卫星簇等领域的新技术开发与应用提供重要的理论指导。
本文研究在连续时间意义下多智能体系统的一致性问题,主要内容包括以下三个部分：
1、多智能体系统的群一致性。考虑个体模型为一阶的情况,针对群之间的信息交换不连续的情形,设计了一类混杂协议来实现多智能体系统的群一致性,得到了一系列的充分条件及代数判据。进一步,考虑到自然界中的很多个体是可以做旋转运动,用Euler-Lagrange方程来描述个体的模型,同时针对系统参数是未知的情形,为实现群一致性,设计了群协同协议和参数估计器算法,从而得到了一些充分条件。在此基础上,考虑到在动力系统演化过程中,个体间的拓扑结构是变化的,提出了切换拓扑意义下的群一致性问题,利用Barbalat-like定理,得到了该问题的充分条件。
2、二阶多智能体系统在复杂环境下的一致性。这里的复杂环境是指多智能体系统在演化过程中存在着外部干扰,使得个体不能得到邻居的即时速度信息。文中针对两种不同的情况,给出了相应的方法来克服扰动带来的影响,其一是仅知道干扰是有界的,并在其统计特征未知的前提下,为实现一致性,利用干扰的界,对邻居的速度设计了一类分布式的估计规则,从而保证整个系统实现静态一致；其二是在Leader-following的框架下,针对Leader的速度不可测,同时每个个体都具有相同的内在非线性系统的情况,设计了一类速度估计器,使得多智能系统系统实现动态一致,并且保证速度估计误差渐近地趋于0。
3、多智能体系统在合作竞争网络中的一致性。在合作竞争网络中,边的权量为正表示相应个体间的关系为合作,权量为负表示个体间的竞争关系。由于存在着竞争关系,多智能体系统一般不能实现一致性。文中采用了两种控制手段来抑制竞争带来的不利影响,其一针对一阶带有非线性项的个体模型,首先将整个网络分成合作子网和竞争子网两部分,采用时滞控制方法,将控制加到竞争子网上,得到了一系列充分条件及代数判据,在此基础上,将结论推广到全竞争网络上,即所有边的权量均为负,也得到了一些充分条件。其二针对二阶的个体模型,提出了一类时滞脉冲控制方法,利用脉冲增益矩阵与时滞量之间的关系,得到了一致性的充分条件。
最后,对全文研究内容进行总结与归纳,同时结合文中所存在的问题以及目前一致性领域的研究现状,指出了今后值得关注和进一步深入研究的方向。
A multi-agent system is always composed of many interconnected agents, in which agents represent individual elements with their own dynamics and edges represent the relationships between their dynamics. The consensus problem is one fundamental issues in the study of the distributed control of multi-agent systems, and has attracted many attentions from a variety of areas, since the research on such problem not only helps better understand the mechanisms of natural collective phenomena, but also provides useful insights to develop formation control and distributed cooperative control for the coordination between multiple mobile autonomous robots.
This thesis studies the consensus problem in networks of autonomous agents, and the main contributions of the thesis are as follows:
1. This thesis investigates a group consensus problem with discontinuous information transmissions among different groups of dynamic agents.In the group consensus problem, the agents reach more than one consistent state asymptotically where the communication network of these agents is considered undirected. Then a novel group consensus protocol, called hybrid protocol, is proposed to solve this problem. The convergence analysis is presented and the algebraic criterions are established. Then, a group consensus problem is further investigated for multiple networked agents with parametric uncertainties where all the agents are governed by the Euler-Lagrange system with uncertain parameters. A novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed for each agent in order to solve the couple-group consensus problem. It is shown that the group consensus is reachable even when the system contains the uncertain parameters. Moreover, the multi-group consensus and the group consensus with switching topology are also discussed as extensions.
2. This thesis addresses a consensus problem for second-order agents with unknown but bounded (UBB for short) disturbance which may affect the measure of neighbors'velocities. In this study, the communication topology of the multi-agent system is supposed to be connected. In order to solve this consensus problem, a new velocity estimation called distributed lazy rule is firstly proposed, where each agent can estimate its neighbors'velocities one by one. Then, a group of sufficient conditions for this second-order consensus problem are presented by adopting graph theory and the well-known Barbalat lemma, and the bounded consensus protocol is taken into account due to actuator saturation. Moreover, a consensus problem is investigated for a group of second-order agents with an active leader. Here, the velocity of the leader cannot be measured, while the leader and all agents are governed by the same nonlinear intrinsic dynamics. To achieve consensus in the sense of both position and velocity, a neighbor-based estimator design approach and a pinning-controlled algorithm are proposed for each autonomous agent. It is found that all agents in the group follow the leader, and the velocity tracking errors of estimators converge to zero asymptotically, without assuming that the interaction topology is strongly connected or contains a directed spanning tree. When considering switching topologies between leader and followers, similar results are obtained.
3. This thesis investigates the consensus problem for a group of first-order agents in the cooperation-competition network, where agents can cooperate or even compete with each other, i.e., the elements in the coupling weight matrix of the graph can be either positive or negative. In order to solve this consensus problem, the whole network is firstly divided into two sub-networks, i.e., the cooperation sub-network and the competition sub-network, and then two kinds of time-delayed control schemes are designed in the competition sub-network. By combining the Lyapunov theory together with the synchronization manifold method, several effective sufficient conditions of consensus are provided, which means that the competition relationships could help the agents achieve consensus under the time-delayed control designed in the competition sub-network. Moreover, the results are also extended to the pure competition networks where all the elements in the weight matrices are either zeros or negative. Furthermore, the consensus problem of second-order multi-agent systems with switching topologies is investigated by designing a time-delayed impulsive consensus control scheme, where all the agents are governed by the same nonlinear intrinsic dynamics and they can either cooperate or compete with each other. By establishing a comparison system, a new comparison principle method is successfully applied to study such consensus problem. Then, several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree.
Finally, we review the results presented in this thesis, and outline research directions which spring from this thesis.
本文研究在连续时间意义下多智能体系统的一致性问题,主要内容包括以下三个部分：
1、多智能体系统的群一致性。考虑个体模型为一阶的情况,针对群之间的信息交换不连续的情形,设计了一类混杂协议来实现多智能体系统的群一致性,得到了一系列的充分条件及代数判据。进一步,考虑到自然界中的很多个体是可以做旋转运动,用Euler-Lagrange方程来描述个体的模型,同时针对系统参数是未知的情形,为实现群一致性,设计了群协同协议和参数估计器算法,从而得到了一些充分条件。在此基础上,考虑到在动力系统演化过程中,个体间的拓扑结构是变化的,提出了切换拓扑意义下的群一致性问题,利用Barbalat-like定理,得到了该问题的充分条件。
2、二阶多智能体系统在复杂环境下的一致性。这里的复杂环境是指多智能体系统在演化过程中存在着外部干扰,使得个体不能得到邻居的即时速度信息。文中针对两种不同的情况,给出了相应的方法来克服扰动带来的影响,其一是仅知道干扰是有界的,并在其统计特征未知的前提下,为实现一致性,利用干扰的界,对邻居的速度设计了一类分布式的估计规则,从而保证整个系统实现静态一致；其二是在Leader-following的框架下,针对Leader的速度不可测,同时每个个体都具有相同的内在非线性系统的情况,设计了一类速度估计器,使得多智能系统系统实现动态一致,并且保证速度估计误差渐近地趋于0。
3、多智能体系统在合作竞争网络中的一致性。在合作竞争网络中,边的权量为正表示相应个体间的关系为合作,权量为负表示个体间的竞争关系。由于存在着竞争关系,多智能体系统一般不能实现一致性。文中采用了两种控制手段来抑制竞争带来的不利影响,其一针对一阶带有非线性项的个体模型,首先将整个网络分成合作子网和竞争子网两部分,采用时滞控制方法,将控制加到竞争子网上,得到了一系列充分条件及代数判据,在此基础上,将结论推广到全竞争网络上,即所有边的权量均为负,也得到了一些充分条件。其二针对二阶的个体模型,提出了一类时滞脉冲控制方法,利用脉冲增益矩阵与时滞量之间的关系,得到了一致性的充分条件。
最后,对全文研究内容进行总结与归纳,同时结合文中所存在的问题以及目前一致性领域的研究现状,指出了今后值得关注和进一步深入研究的方向。
A multi-agent system is always composed of many interconnected agents, in which agents represent individual elements with their own dynamics and edges represent the relationships between their dynamics. The consensus problem is one fundamental issues in the study of the distributed control of multi-agent systems, and has attracted many attentions from a variety of areas, since the research on such problem not only helps better understand the mechanisms of natural collective phenomena, but also provides useful insights to develop formation control and distributed cooperative control for the coordination between multiple mobile autonomous robots.
This thesis studies the consensus problem in networks of autonomous agents, and the main contributions of the thesis are as follows:
1. This thesis investigates a group consensus problem with discontinuous information transmissions among different groups of dynamic agents.In the group consensus problem, the agents reach more than one consistent state asymptotically where the communication network of these agents is considered undirected. Then a novel group consensus protocol, called hybrid protocol, is proposed to solve this problem. The convergence analysis is presented and the algebraic criterions are established. Then, a group consensus problem is further investigated for multiple networked agents with parametric uncertainties where all the agents are governed by the Euler-Lagrange system with uncertain parameters. A novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed for each agent in order to solve the couple-group consensus problem. It is shown that the group consensus is reachable even when the system contains the uncertain parameters. Moreover, the multi-group consensus and the group consensus with switching topology are also discussed as extensions.
2. This thesis addresses a consensus problem for second-order agents with unknown but bounded (UBB for short) disturbance which may affect the measure of neighbors'velocities. In this study, the communication topology of the multi-agent system is supposed to be connected. In order to solve this consensus problem, a new velocity estimation called distributed lazy rule is firstly proposed, where each agent can estimate its neighbors'velocities one by one. Then, a group of sufficient conditions for this second-order consensus problem are presented by adopting graph theory and the well-known Barbalat lemma, and the bounded consensus protocol is taken into account due to actuator saturation. Moreover, a consensus problem is investigated for a group of second-order agents with an active leader. Here, the velocity of the leader cannot be measured, while the leader and all agents are governed by the same nonlinear intrinsic dynamics. To achieve consensus in the sense of both position and velocity, a neighbor-based estimator design approach and a pinning-controlled algorithm are proposed for each autonomous agent. It is found that all agents in the group follow the leader, and the velocity tracking errors of estimators converge to zero asymptotically, without assuming that the interaction topology is strongly connected or contains a directed spanning tree. When considering switching topologies between leader and followers, similar results are obtained.
3. This thesis investigates the consensus problem for a group of first-order agents in the cooperation-competition network, where agents can cooperate or even compete with each other, i.e., the elements in the coupling weight matrix of the graph can be either positive or negative. In order to solve this consensus problem, the whole network is firstly divided into two sub-networks, i.e., the cooperation sub-network and the competition sub-network, and then two kinds of time-delayed control schemes are designed in the competition sub-network. By combining the Lyapunov theory together with the synchronization manifold method, several effective sufficient conditions of consensus are provided, which means that the competition relationships could help the agents achieve consensus under the time-delayed control designed in the competition sub-network. Moreover, the results are also extended to the pure competition networks where all the elements in the weight matrices are either zeros or negative. Furthermore, the consensus problem of second-order multi-agent systems with switching topologies is investigated by designing a time-delayed impulsive consensus control scheme, where all the agents are governed by the same nonlinear intrinsic dynamics and they can either cooperate or compete with each other. By establishing a comparison system, a new comparison principle method is successfully applied to study such consensus problem. Then, several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree.
Finally, we review the results presented in this thesis, and outline research directions which spring from this thesis.
引文
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