This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks (MANs) with nonuniform gradient gains. A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function. First, based on the local information of each agent’s neighborhood, a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed, where these gains only have relations with agents’ own states. And then, the original closed-loop system is changed into an equivalent one by taking a coordination transformation. Moreover, it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given. By the theory of Lyapunov stability, it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically. Finally, the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.

本文解决了梯度增益不均匀的二阶多主体网络（MAN）上的分布式自适应优化问题。选择由局部可微凸函数之和组成的一般凸函数作为团队目标函数。首先，基于每个智能体邻域的局部信息，设计了一种新的具有非均匀梯度增益的分布式自适应优化算法，其中这些增益仅与智能体自身的状态有关。然后，通过协调转换将原始的闭环系统更改为等效系统。此外，证明了通过构造一个Lyapunov函数，只要给出初始值，就可以限制包括所有主体的位置和速度在内的状态。根据李雅普诺夫稳定性理论，结果表明，所有主体最终都能达成共识，他们的职位状态渐近收敛于团队目标函数的最优解。最后，通过几个仿真实例证明了所获得理论结果的有效性。