基于事件触发的分布式优化算法

Event-triggered Distributed Optimization Algorithms

本文研究了一类分布式优化问题,其目标是通过局部信息交换使由局部成本函数之和构成的全局成本函数最小.针对无向连通图,我们提出了两种基于比例积分策略的分布式优化算法.在局部成本函数可微且凸的条件下,证明了所提算法渐近收敛到全局最小值点.更进一步,在局部成本函数具有局部Lipschitz梯度和全局成本函数关于全局最小值点是有限强凸的条件下,证明了所提算法的指数收敛性.此外,为了避免智能体之间的连续通信和减少通信负担,将所提的两种分布式优化算法与事件触发通信相结合,提出了两种基于事件触发的分布式优化算法.证明了提出的事件触发优化算法不存在Zeno行为,并且在相应条件下保持了与连续通信下分布式优化算法一样的收敛性.最后,通过数值仿真验证了上述理论结果.

This paper studies a class of distributed optimization problems,whose objective is to minimize the global cost function formed by a sum of local cost functions through local information exchanges.For undirected connected graphs,we propose two distributed optimization algorithms based on the proportional-integral feedback mechanism.Under the condition that the local cost functions are differentiable and convex,it is proved that the proposed algorithms asymptotically converge to a global minimum.For the case that the local cost functions have local Lipschitz gradient and the global cost function is strongly convex with respect to the global minimum,the exponential convergences of the two distributed optimization algorithms are established.In addition,in order to avoid continuous communication between agents and reduce communication burden,by integrating the two proposed distributed optimization algorithms with event-triggered communications,two event-triggered based distributed optimization algorithms are developed.It is shown that the two proposed event-triggered optimization algorithms are free of Zeno behavior.Moreover,the two proposed event-triggered based distributed optimization algorithms maintain the same convergence properties as the distributed optimization algorithms with continuous communications under the corresponding conditions.Finally,the above theoretical results are verified by numerical simulations.