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.

中文翻译：

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具有时变二次成本函数的最优资源分配的分布式连续时间算法

在本文中，我们提出了分布式连续时间算法，以解决多智能体系统中具有某些时变二次成本函数的最优资源分配问题。目的是在优化所有本地随时间变化的成本函数之和的同时分配一定数量的资源。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，我们的算法只能使用本地信息来实现。通过使用预测-校正方法和不平滑的共识思想，我们首先设计两种分布式算法来处理时变成本函数具有相同的Hessian的情况。我们进一步提出了一种基于估计器的算法，该算法使用分布式平均跟踪理论来估计某些全局信息。借助估计的全局信息，可以解决不相同的恒定黑森州情况。在每种情况下，都证明了所提出的具有某些初始条件的动力学系统的解渐近收敛到最优轨迹。我们通过仿真说明了所提出的分布式连续时间最优资源分配算法的有效性。