Necessary and Sufficient Conditions for Consensus of Double-Integrator Multi-Agent Systems With Measurement Noises
Necessary and Sufficient Conditions for Consensus of Double-Integrator Multi-Agent Systems With Measurement Noises
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DOI：
10.1109/tac.2011.2139450
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发表时间：
2011-04
影响因子：
6.8
通讯作者：
L. Cheng;Z. Hou;M. Tan;Xu Wang
中科院分区：
文献类型：
--
作者：
L. Cheng;Z. Hou;M. Tan;Xu Wang
提出了平均共识协议，用于连续的双重整合器多代理系统，并在固定拓扑结构下进行测量噪声。时间变化的控制收益用于减轻噪音。因此，闭环系统是时间变化的线性随机微分方程。通过确定该闭环系统的状态过渡矩阵，可以充分描述多代理系统的动态特性。事实证明，在嘈杂的通信环境中，只有当通信拓扑是平衡且牢固地连接的图表时，可以达到平均共识，并且随时间变化的控制增益满足随机近似型型条件。在提出的协议下，每个代理的位置在均等方面收敛到一个通用随机变量，该变量的数学期望是系统中所有试剂的初始位置和初始速度的平均值，而每个代理的速度在均等方面都会收敛到一个平方。常见的随机变量，其数学期望和方差均为零。
An average consensus protocol is proposed for continuous-time double-integrator multi-agent systems with measurement noises under fixed topologies. The time-varying control gain is employed to attenuate noises. The closed-loop system is therefore a time-varying linear stochastic differential equation. By determining the state transition matrix of this closed-loop system, the dynamic characteristics of the multi-agent system can be fully described. It is proved that in the noisy communication environment the average consensus can be achieved if and only if the communication topology is a balanced and strongly connected graph, and the time-varying control gain satisfies the stochastic approximation-type conditions. Under the proposed protocol, the position of each agent is convergent in mean square to a common random variable whose mathematical expectation is the average of initial positions and initial velocities of all agents in the system, while each agent's velocity is convergent in mean square to a common random variable whose mathematical expectation and variance are both zero.