具有乘性噪声的一阶多智能体系统在马尔可夫切换拓扑下的协同性

Dianqiang Li, Tao Li
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引用次数: 0

摘要

研究了具有乘性噪声的一阶领导-跟随多智能体系统在马尔可夫切换拓扑下的协同性问题。每个智能体都表现为一阶线性动态,并且在智能体之间的信息交换过程中存在乘性噪声。通信拓扑为马尔可夫交换拓扑。利用马尔可夫切换随机微分方程的稳定性理论和马尔可夫链理论,建立了领导-跟随型多智能体系统可协作的充分必要条件。条件如下:(ⅰ)系统参数与噪声强度乘积的平方小于1/2;(ⅱ)从非连通图到连通图的过渡速率应为系统参数的2倍;(ⅲ)连通图到连通图的过渡速率应小于一个常数,该常数与系统参数、乘性噪声强度、非连通图到连通图的过渡速率有关。最后,通过种群增长系统验证了控制策略的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The cooperatability of the first-order multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies
We investigate the cooperatability of the first-order leader-following multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies. Each agent exhibits first-order linear dynamics, and there are multiplicative noises along with information exchange among the agents. What is more, the communication topologies are Markov switching topologies. By utilizing the stability theory of the stochastic differential equations with Markovian switching and the Markov chain theory, we establish the necessary and sufficient conditions for the cooperatability of the leader-following multi-agent systems. The conditions are outlined below: (ⅰ) The product of the system parameter and the square of multiplicative noise intensities should be less than 1/2; (ⅱ) The transition rate from the unconnected graph to the connected graph should be twice the system parameter; (ⅲ) The transition rate from the connected graph to the unconnected graph should be less than a constant that is related to the system parameter, the intensities of multiplicative noises, and the transition rate from the unconnected graph to the connected graph. Finally, the effectiveness of our control strategy is demonstrated by the population growth systems.
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