多智能体系统的多步近似次梯度随机投影优化算法

Multi-step approximate subgradient random projection optimizationalgorithm for multi-agent system

基于切换网络下带有随机时延和随机通讯噪声的多智能体系统模型,提出分布式多步近似次梯度随机投影算法,并对算法的收敛性进行分析.首先,利用网络扩维的方法将含随机时延的通讯网络转化为无时延网络;其次,提出近似次梯度概念,并设计多步近似次梯度随机批量投影算法,批量随机投影可以避免在实际问题中整体约束集合不易获得而导致投影算子不易执行等情况;最后,通过数值仿真表明即使存在随机噪声,所提出的算法较一般的分布式多步次梯度算法具有更好的收敛效果,同时还分析了随机投影集合个数和随机噪声对收敛效果的影响.

Based on a multi-agent system model with random delay and random communication noise under a switched network,a distributed multi-step approximate subgradient random projection algorithm is proposed,and the algorithm convergence analysis is performed.Firstly,we convert a network with random communication delay into a network without delay by using a network expansion method.Then,we propose the concept of approximate subgradient,and design a multi-step approximate subgradient batch random projection algorithm.A batch random projection method is used to deal with the executive problem of projection operators when the overall constraint set is not easy to obtain in practical problems.Finally,the numerical simulations show that the proposed algorithm has better convergence effects than the general distributed multi-step subgradient algorithm even if there exists random noise.And the effect of the number of random projection sets and random noise are also discussed.