Distributed Continuous-Time Algorithms for Optimal Resource Allocation With Time-Varying Quadratic Cost Functions
Distributed Continuous-Time Algorithms for Optimal Resource Allocation With Time-Varying Quadratic Cost Functions
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DOI：
10.1109/tcns.2020.3020972
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发表时间：
2020-12
影响因子：
4.2
通讯作者：
Bo Wang;Shan Sun;W. Ren
中科院分区：
文献类型：
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作者：
Bo Wang;Shan Sun;W. Ren
在这篇文章中，我们提出了分布式连续时间算法来解决具有一定时变二次代价函数的多智能体系统的最优资源分配问题。目标是分配一定数量的资源，同时优化所有局部时变成本函数的总和。在这里，最优解是轨迹而不是某些固定点。我们考虑了大量通过网络连接的代理，并且我们的算法可以仅使用本地信息来实现。利用预测-校正方法和非光滑一致思想，我们首先设计了两种分布式算法来处理时变代价函数具有相同Hessian值的情况。我们进一步提出了一种基于估计器的算法，该算法利用分布式平均跟踪理论来估计某些全局信息。在估计的全局信息的帮助下，讨论了不恒等恒定Hessians的情形。在每种情况下，都证明了所提出的动力系统在一定初始条件下的解渐近收敛于最优轨迹。通过仿真验证了所提出的分布式连续时间最优资源分配算法的有效性。
In this article, we propose distributed continuous-time algorithms to solve the optimal resource allocation problem with certain time-varying quadratic cost functions for multiagent systems. The objective is to allocate a quantity of resources while optimizing the sum of all the local time-varying cost functions. Here, the optimal solutions are trajectories rather than some fixed points. We consider a large number of agents that are connected through a network, and our algorithms can be implemented using only local information. By making use of the prediction–correction method and the nonsmooth consensus idea, we first design two distributed algorithms to deal with the case when the time-varying cost functions have identical Hessians. We further propose an estimator-based algorithm which uses distributed average tracking theory to estimate certain global information. With the help of the estimated global information, the case of nonidentical constant Hessians is addressed. In each case, it is proved that the solutions of the proposed dynamical systems with certain initial conditions asymptotically converge to the optimal trajectories. We illustrate the effectiveness of the proposed distributed continuous-time optimal resource allocation algorithms through simulations.