论文标题
分布式不受约束的优化和时间变化的成本功能
Distributed Unconstrained Optimization with Time-varying Cost Functions
论文作者
论文摘要
在本文中，我们为分布式不受约束的优化问题提出了一种新的解决方案，其中总成本是组网络代理的时变局部成本功能的总和。目的是跟踪最佳轨迹，以最大程度地减少每次瞬间的总成本。我们的方法由两个阶段的动态组成，其中第一个样本将定期的第一和第二个衍生物定期构建对最佳轨迹的下降方向的估计，而第二个则使用此估算和共识术语，将当地国家驱动到时间变化的解决方案，同时达成共识。第一部分是通过在离散时间框架中实现加权平均共识算法进行的，第二部分是通过连续时间动力学执行的。使用Lyapunov稳定性分析，获得了总成本梯度上的上限，该梯度已渐近地达到。该约束的特征是当地成本的特性。为了证明所提出的方法的性能，进行了一个数值示例，该示例研究了调整算法的参数及其对局部状态与最佳轨迹的影响的影响。
In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal trajectory that minimizes the total cost at each time instant. Our approach consists of a two-stage dynamics, where the first one samples the first and second derivatives of the local costs periodically to construct an estimate of the descent direction towards the optimal trajectory, and the second one uses this estimate and a consensus term to drive local states towards the time-varying solution while reaching consensus. The first part is carried out by the implementation of a weighted average consensus algorithm in the discrete-time framework and the second part is performed with a continuous-time dynamics. Using the Lyapunov stability analysis, an upper bound on the gradient of the total cost is obtained which is asymptotically reached. This bound is characterized by the properties of the local costs. To demonstrate the performance of the proposed method, a numerical example is conducted that studies tuning the algorithm's parameters and their effects on the convergence of local states to the optimal trajectory.
