ABSTRACT This paper fully studies distributed optimal consensus problem in undirected dynamical networks. We consider a group of networked agents that are supposed to rendezvous at the optimal point of a collective convex objective function. Each agent has no knowledge about the global objective function and only has access to its own local objective function, which is a portion of the global one, and states information of agents within its neighbourhood set. In this setup, all agents coordinate with their neighbours to seek the consensus point that minimises the network's global objective function. In the current paper, we consider agents with single-integrator and double-integrator dynamics. Further, it is supposed that agents' movements are limited by some convex inequality constraints. In order to find the optimal consensus point under the described scenario, we combine the interior-point optimisation algorithm with a consensus protocol and propose a distributed control law. The associated convergence analysis based on Lyapunov stability analysis is provided.

中文翻译：

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具有一阶和二阶动力学的多智能体系统中的约束最优共识

摘要 本文充分研究了无向动态网络中的分布式最优共识问题。我们考虑一组网络代理，它们应该在集体凸目标函数的最佳点会合。每个代理不知道全局目标函数，只能访问自己的局部目标函数，这是全局目标函数的一部分，并说明其邻域集中代理的信息。在此设置中，所有代理与其邻居协调以寻求最小化网络全局目标函数的共识点。在当前的论文中，我们考虑具有单积分器和双积分器动态的代理。此外，假设代理人的运动受到一些凸不等式约束的限制。为了在所描述的场景下找到最佳共识点，我们将内点优化算法与共识协议相结合，并提出了分布式控制律。提供了基于李雅普诺夫稳定性分析的相关收敛分析。