This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents. Only using the local information, a novel continuous-time distributed algorithm based on proportional-integral-differential (PID) control strategy is proposed. Under the assumption that the global utility function is strictly convex and local utility functions have locally Lipschitz gradients, the exponential convergence of the proposed algorithm is established with undirected and connected graph among these agents. Finally, numerical simulations are presented to illustrate the effectiveness of theoretical results.

本文研究了分布式凸优化问题，其中全局效用函数是与各个代理相关的局部成本函数的总和。仅利用局部信息，提出了一种基于比例-积分-微分(PID)控制策略的新型连续时间分布式算法。在全局效用函数严格凸且局部效用函数具有局部Lipschitz梯度的假设下，提出算法的指数收敛建立在这些代理之间的无向和连通图上。最后，通过数值模拟来说明理论结果的有效性。