论文标题
连续时间不受约束的分布式优化的统一框架
A Unified Framework for Continuous-time Unconstrained Distributed Optimization
论文作者
论文摘要
我们引入了一类分布式非线性控制系统，称为流动轨道动力学，该系统捕获平均状态由平均控制输入控制的现象，没有单个代理可以直接访问该平均值。代理商通过非线性观察者更新平均值的估计值。我们证明，对于满足这些条件的任何分布式控制系统，利用适当的梯度反馈将导致对应的分布式优化问题的解决方案。我们表明，用于求解分布式优化的许多现有算法是这种动态的实例，因此它们的收敛属性可以从其属性遵循。从这个意义上讲，提出的方法建立了一个统一的框架，以连续时间分布式优化。此外，这种公式使我们能够通过容易地扩展这种动力学的图形理论条件来引入新的连续时间分布式优化算法。
We introduce a class of distributed nonlinear control systems, termed as the flow-tracker dynamics, which capture phenomena where the average state is controlled by the average control input, with no individual agent has direct access to this average. The agents update their estimates of the average through a nonlinear observer. We prove that utilizing a proper gradient feedback for any distributed control system that satisfies these conditions will lead to a solution of the corresponding distributed optimization problem. We show that many of the existing algorithms for solving distributed optimization are instances of this dynamics and hence, their convergence properties can follow from its properties. In this sense, the proposed method establishes a unified framework for distributed optimization in continuous-time. Moreover, this formulation allows us to introduce a suit of new continuous-time distributed optimization algorithms by readily extending the graph-theoretic conditions under which such dynamics are convergent.
