基于预设时间收敛的分布式优化算法

Distributed optimization algorithms based on predefined-time convergence

考虑一类分布式优化问题,其目标是通过局部信息交互,使得局部成本函数之和构成的全局成本函数最小.针对该类问题,通过引入时基发生器(TBG),提出两种基于预设时间收敛的分布式比例积分(PI)优化算法.与现有的基于有限/固定时间收敛的分布式优化算法相比,所提出算法的收敛时间不依赖于系统的初值和参数,且可以任意预先设计.此外,在全局成本函数关于最优值点有限强凸,局部成本函数为可微的凸函数,且具有局部Lipschitz梯度的条件下,通过Lyapunov理论证明了所提算法都能实现预设时间收敛.最后,通过数值仿真验证了所提出算法的有效性.

This paper studies a class of distributed optimization problems,which aims to minimize the global cost function consisting of the sum of local cost functions through local information exchanges.For this class of problems,by introducing a time-based generator(TBG),the paper proposes two distributed proportional-integral(PI)optimization algorithms based on predefined-time convergence.Compared to existing distributed optimization algorithms based on finite/fixed time convergence,the convergence time of the proposed algorithms does not depend on initial values and parameters of the system and it can be arbitrarily predefined.Furthermore,the proposed algorithms can converge within a predefined time based on the Lyapunov theory under the conditions that the global cost function is restricted strongly convex with respect to the global optimal point along with local cost functions being convex,differentiable,and having local Lipschitz gradient.Finally,the effectiveness of these two algorithms is verified by numerical simulation.