This paper investigates the distributed convex optimization problem (DCOP) based on continuous-time multiagent systems under a state-dependent graph. The objective is to optimize the sum of local cost functions, each of which is only known by the corresponding agent. First, a piecewise continuous distributed optimization algorithm is proposed, such that all agents reach consensus in finite time and reach the optimal point of the total cost function asymptotically under a time-invariant graph. Then, another distributed optimization algorithm is presented to preserve the initial edges and make the agents solve DCOP on a state-dependent graph. In particular, any pair of agents can exchange information with each other when their geometry distance is less than a certain range. Finally, several simulations are given to verify the effectiveness of the proposed algorithms.

中文翻译：

---

状态相关无向图上的分布凸优化：齐次技术

本文研究了状态依赖图下基于连续时间多智能体系统的分布式凸优化问题。目的是优化局部成本函数之和，每个局部函数仅由相应的代理知道。首先，提出了一种分段连续分布的优化算法，使得在时间不变的情况下，所有主体在有限的时间内达到共识，并渐近地达到总成本函数的最优点。然后，提出了另一种分布式优化算法，以保留初始边缘并使代理在状态依赖图上求解DCOP。特别地，当任何一对代理的几何距离小于特定范围时，它们可以彼此交换信息。最后，