Designing Zero-Gradient-Sum Protocols for Finite-Time Distributed Optimization Problem
本文在多智能体系统中采用零梯度之和框架，研究分布式有限时间和固定时间优化问题，提出基本协议使网络系统在有限时间内协同找到全局目标的最优解，并针对时变拓扑引入改进算法保持网络连通性。
In this article, the distributed finite-time and fixed-time optimization problems are investigated by adopting the zero-gradient-sum (ZGS) framework in multiagent systems. Specifically, when the local convex functions are nonquadratic, a basic optimization protocol is proposed to obtain a finite-time convergence, such that the networked system can cooperatively seek the optimal solution of the global objective, the sum of local objective, in a limited time. By utilizing the property of quadratic functions, a reduced algorithm can remove the dependence of initial conditions in the estimation of the upper bound of settling time and achieve a fixed-time result. Besides, the problem with time-varying topologies is studied by introducing a modified algorithm with an artificial potential function to preserve the network connectivity. Finally, the validity of the protocols is demonstrated via some example simulations.