不确定通信下多智能体系统的一致性
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摘要
近些年,多智能体一致性问题引起了许多研究人员的极大兴趣。所谓一致性问题是指如何基于局部信息交换的多智能体系统如何达到相同的状态。在控制领域中,多智能体系统一致性问题是协调控制的重要问题之一。实际中的多智能体系统往往处在各种复杂的环境中,多智能体之间的局部信息交换可能会受到一些不确定性的影响,比如通信网络的切换和传输时延。为克服不确定性通信对一致性的影响,本文运用代数图论、矩阵理论、控制理论、稳定性理论和马尔科夫跳变系统理论,重点研究了带不确定性通信的多智能体系统的一致性问题。本文的主要工作如下：
对于具有马尔科夫切换通信的多移动机器人系统的一致性问题进行了研究。实际中,准确知道马尔科夫链的所有转移概率是困难的事情,本文考虑转移概率矩阵中的部分概率未知的情况,对于有二阶积分特性的多移动机器人系统给出了线性一致性算法,使用随机李雅普诺夫函数分析得到系统达到均方一致的充分条件,并提出了相应的控制器优化设计方法。
对于具有马尔科夫切换拓扑结构的传感器网络的平均一致性问题进行了研究。网络拓扑是无向的马尔科夫切换的,假设在马尔科夫链的转移概率矩阵中,仅已知每一个概率的上下界而不知概率真值。就线性分布式推断算法,本文导出所有传感器状态达到平均一致的充分条件。为了取得更快的收敛速度,基于数值优化技术,我们给出了快速达到的平均一致推断参数设计方法。
在任意切换通信情况下,对带非线性耦合的多智能体系统的一致性问题进行了研究。通过收缩分析方法,获得了非线性系统达到一致性的条件。
研究了具有传输时延的线性离散时间多智能体系统的一致性。考虑到实际中往往不能量测系统的全部状态而只能得到系统的输出,本文提出了基于时变时延输出反馈的一致性算法,在马尔科夫切换通信下,分析了多智能体系统的一致性,给出了确保一致性的控制器设计方法。
研究了具有网络诱导约束(比如：丢包、传输时延和错序)的多智能体系统的一致性。运用独立多马尔科夫链建立网络诱导约束的模型,得出了多智能休系统达到均方一致的充分必要条件,并基于锥互补线性化算法,给出了控制参数的设计方法。
最后对全文进行了总结,并就未来研究工作进行了展望。
In recent years, the consensus problem of multi-agent systems has received much attention of many researchers. In the control field, the multi-agent consensus problem becomes one of the important problems in multi-agent coordination control. It is needed to design an appropriate protocol or control law such that the state of each agent converge to the same objective based on local information exchange between agents. The actual multi-agent systems are in various complex environment, therefore local information exchange between agents may be affected by uncertainties such as communication network switching and transmission delay, etc. This dissertation studies consensus problems of multi-agent systems with uncertain communication using algebra graph theory, matrix theory, control theory, stability theory and Markov jump system theory. The content of this dissertation is given in the following:
The consensus problem is studied for mobile robot with Markov communication topology. Because it is difficult to know exactly the probability for every transition; the Markov chain considered has some unknown element in its transition probability matrix. Under a linear consensus protocol, a sufficient condition is presented for mean square consensus of mobile robots. A consensus protocol design method is provided based on linear matrix inequalities, bisection search and numerical optimization.
The average consensus problem is studied in mean square sense for distributed inference in a wireless sensor network under Markovian communication topology of uncertain transition probability. A sufficient condition is presented for average consensus of linear distributed inference algorithm. Based on linear matrix inequalities and numerical optimization, a design method is provided of faster distributed inference systems.
Under switching communication topology, the consensus problem of a class of multi-agent systems with nonlinear coupling is studied. By contraction analysis, consensus conditions are obtained of these systems.
The consensus problem is studied for linear discrete time munti-agent systems with time-varying transmission delay. Markov communication topology and output feedback protocol are considered. Based on Lyapunov function, a protocol design method is given such that the multi-agent systems reach to mean square consensus.
Mean consensus problem is studied for a class of discrete time multi-agent systems in which information exchange is subjected to some network-induced constraints. These constraints include package dropout, time delay and package disorder. Using Markov jump system method, the necessary and sufficient condition of mean square consensus is obtained and a design procedure is presented such that multi-agent systems reach mean square consensus.
对于具有马尔科夫切换通信的多移动机器人系统的一致性问题进行了研究。实际中,准确知道马尔科夫链的所有转移概率是困难的事情,本文考虑转移概率矩阵中的部分概率未知的情况,对于有二阶积分特性的多移动机器人系统给出了线性一致性算法,使用随机李雅普诺夫函数分析得到系统达到均方一致的充分条件,并提出了相应的控制器优化设计方法。
对于具有马尔科夫切换拓扑结构的传感器网络的平均一致性问题进行了研究。网络拓扑是无向的马尔科夫切换的,假设在马尔科夫链的转移概率矩阵中,仅已知每一个概率的上下界而不知概率真值。就线性分布式推断算法,本文导出所有传感器状态达到平均一致的充分条件。为了取得更快的收敛速度,基于数值优化技术,我们给出了快速达到的平均一致推断参数设计方法。
在任意切换通信情况下,对带非线性耦合的多智能体系统的一致性问题进行了研究。通过收缩分析方法,获得了非线性系统达到一致性的条件。
研究了具有传输时延的线性离散时间多智能体系统的一致性。考虑到实际中往往不能量测系统的全部状态而只能得到系统的输出,本文提出了基于时变时延输出反馈的一致性算法,在马尔科夫切换通信下,分析了多智能体系统的一致性,给出了确保一致性的控制器设计方法。
研究了具有网络诱导约束(比如：丢包、传输时延和错序)的多智能体系统的一致性。运用独立多马尔科夫链建立网络诱导约束的模型,得出了多智能休系统达到均方一致的充分必要条件,并基于锥互补线性化算法,给出了控制参数的设计方法。
最后对全文进行了总结,并就未来研究工作进行了展望。
In recent years, the consensus problem of multi-agent systems has received much attention of many researchers. In the control field, the multi-agent consensus problem becomes one of the important problems in multi-agent coordination control. It is needed to design an appropriate protocol or control law such that the state of each agent converge to the same objective based on local information exchange between agents. The actual multi-agent systems are in various complex environment, therefore local information exchange between agents may be affected by uncertainties such as communication network switching and transmission delay, etc. This dissertation studies consensus problems of multi-agent systems with uncertain communication using algebra graph theory, matrix theory, control theory, stability theory and Markov jump system theory. The content of this dissertation is given in the following:
The consensus problem is studied for mobile robot with Markov communication topology. Because it is difficult to know exactly the probability for every transition; the Markov chain considered has some unknown element in its transition probability matrix. Under a linear consensus protocol, a sufficient condition is presented for mean square consensus of mobile robots. A consensus protocol design method is provided based on linear matrix inequalities, bisection search and numerical optimization.
The average consensus problem is studied in mean square sense for distributed inference in a wireless sensor network under Markovian communication topology of uncertain transition probability. A sufficient condition is presented for average consensus of linear distributed inference algorithm. Based on linear matrix inequalities and numerical optimization, a design method is provided of faster distributed inference systems.
Under switching communication topology, the consensus problem of a class of multi-agent systems with nonlinear coupling is studied. By contraction analysis, consensus conditions are obtained of these systems.
The consensus problem is studied for linear discrete time munti-agent systems with time-varying transmission delay. Markov communication topology and output feedback protocol are considered. Based on Lyapunov function, a protocol design method is given such that the multi-agent systems reach to mean square consensus.
Mean consensus problem is studied for a class of discrete time multi-agent systems in which information exchange is subjected to some network-induced constraints. These constraints include package dropout, time delay and package disorder. Using Markov jump system method, the necessary and sufficient condition of mean square consensus is obtained and a design procedure is presented such that multi-agent systems reach mean square consensus.
引文
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