A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded uncertainty under a uniformly strongly connected network. Firstly, a distributed lower bounding procedure is developed, which is based on an outer iterative approximation of the DRCO through the discretization of the compact uncertainty set into a finite number of points. Secondly, a distributed upper bounding procedure is proposed, which is based on iteratively approximating the DRCO by restricting the constraints right-hand side with a proper positive parameter and enforcing the compact uncertainty set at finitely many points. The lower and upper bounds of the global optimal objective for the DRCO are obtained from these two procedures. Thirdly, two distributed termination methods are proposed to make all agents stop updating simultaneously by exploring whether the gap between the upper and the lower bounds reaches a certain accuracy. Fourthly, it is proved that all the agents finite-time converge to a feasible consensus solution that satisfies global optimality within a certain accuracy. Finally, a numerical case study is included to illustrate the effectiveness of the distributed algorithm.

翻译：针对均匀强连通网络下带界不确定性约束的分布式鲁棒凸优化问题（DRCO），本文提出一种新型分布式算法，可在有限时间内收敛至满足全局最优性及指定精度的可行共识解。首先，通过将紧致不确定性集离散化为有限个点，基于外迭代逼近方法提出分布式下界计算过程；其次，通过采用适定正参数约束右端项并在有限点处强化紧致不确定性集，提出基于迭代近似的分布式上界计算过程。由上述两过程分别获得DRCO全局最优目标值的上下界；再次，通过探测上下界间隙是否达到指定精度，提出两种分布式终止方法使所有智能体同步停止更新；复次，证明所有智能体能在有限时间内收敛至满足指定精度全局最优性的可行共识解；最后通过数值算例验证该分布式算法的有效性。