带有时延和乘性量测噪音的离散时间多自主体系统的趋同控制

Consensus control of discrete-time multi-agent systems with time-delays and multiplicative measurement noises

本文研究带有时延和乘性量测噪音的离散时间多自主体系统的随机趋同控制.利用图论、矩阵论和概率论中的分析工具,将随机趋同问题转化成离散时间随机时延系统的随机稳定性问题.通过建立随机稳定性准则,给出了多自主体系统达到趋同所需的关于控制增益的充分条件.针对一阶多自主体系统,在平衡拓扑条件下证明对任何有界时延和任意强度的噪音,都可以通过选取合适的控制增益来达到均方和几乎必然强趋同.针对二阶多自主体系统,在无向拓扑条件下给出了均方和几乎必然趋同的充分条件,并证明对任意有界时延和任意强度的噪音,都可以通过选取合适的控制增益来实现位移分量弱趋同和速度分量强趋同.这些结果被进一步推广到具有领导者的情形.

This work is concerned with stochastic consensus conditions of discrete-time multi-agent systems with time-delays and multiplicative measurement noises. By the algebraic graph theory and the matrix theory, the stochastic consensus problem is converted into the stochastic stability problem of discrete-time stochastic delayed systems driven by multiplicative noises. Then by establishing the stochastic stability criteria for discretetime stochastic delayed systems, the stochastic consensus conditions are deduced. For the case with first-order dynamics, the sufficient conditions for the mean square and the almost sure strong consensus are deduced under balanced digraphs. For the case with second-order dynamics, the consensus analysis is given under undirected graphs, and it is proved that for any given bounded time-delay and noise intensity, the stochastic weak consensus for the position and stochastic strong consensus for the velocity can be achieved by carefully choosing the control gains. These consensus results are further extended to the leader-following case.