多个体切换网络中带有时延通信的分布式次梯度优化算法

Distributed Subgradient Optimization Algorithm with Communication Delays for Multi-agent Switched Networks

在一般的非平衡有向切换网络中,网络中的个体间可能存在通信时延现象。针对该情况,文中提出了多个体切换网络中带有时延通信的分布式次梯度优化算法。在该算法中,通过对通信网络进行扩维,将存在通信时延的无约束凸优化问题转化为无时延的无约束凸优化问题进行解决。利用非二次李雅普诺夫函数法证明了只要非平衡有向切换网络是周期强连通的以及通信时延有上界,那么基于时延通信的分布式次梯度优化算法就是收敛的。由于集中考虑了网络拓扑与通信时延,该算法更贴合实际情况。最后通过仿真实验验证了算法的有效性。

In the general non-balanced directional switching network,there may be communication delays among agents in networks.In light of this,this paper proposed a distributed subgradient optimization algorithm with communication delays for multi-agent switched networks.In this method,the unconstrained convex optimization problem with communication delays is converted into the unconstrained convex optimization problem without communication delays by augmenting delay nodes in communication network.The convergence of the multi-agent distributed subgradient optimization algorithm with communication delays is proved by using the non-quadratic Lyapunov function method,as long as the non-balanced directional switching network is periodical strong connectivity and the communication delays are upper bounded.Because the network topology conditions and communication delay are both intensively considered,this algorithm is more general and practical.Finally,a simulation example was given to demonstrate the effectiveness of the proposed algorithm.