Density Control of Interacting Agent Systems
Density Control of Interacting Agent Systems
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DOI：
10.1109/tac.2023.3271226
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发表时间：
2021-08
影响因子：
6.8
通讯作者：
Yongxin Chen
中科院分区：
文献类型：
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作者：
Yongxin Chen
在本文中，我们考虑控制大量不断相互作用的动态系统的群体行为的问题。假设这些系统具有相同的动态（例如，鸟群、无人机群），并且它们的群体行为可以通过分布进行建模。因此，这个问题可以看作是分布空间上的最优控制问题。我们提出了一种新颖的算法来计算反馈控制策略，以便当代理采用时，它们的分布将在有限时间窗口内从初始分布转换为目标分布。我们的方法建立在最优传输理论的基础上，但与该领域现有的工作有很大不同，因为我们的方法明确地模拟了代理之间的相互作用。从算法的角度来看，我们的算法基于广义近端梯度下降算法，并具有亚线性速率的收敛保证。我们进一步扩展了我们的框架，以考虑代理来自多个物种的情况。在线性二次设置中，解的特征是耦合 Riccati 方程组，可以以封闭形式求解。最后，提出了几个数值示例来说明我们的框架。
In this article, we consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., flocks of birds, UAV swarms) and their group behavior can be modeled by a distribution. Thus, this problem can be viewed as an optimal control problem over the space of distributions. We propose a novel algorithm to compute a feedback control strategy so that, when adopted by the agents, the distribution of them would be transformed from an initial one to a target one over a finite-time window. Our method is built on the optimal transport theory but differs significantly from existing work in this area in that our method models the interactions among agents explicitly. From an algorithmic point of view, our algorithm is based on the generalized proximal gradient descent algorithm and has a convergence guarantee with a sublinear rate. We further extend our framework to account for the scenarios where the agents are from multiple species. In the linear quadratic setting, the solution is characterized by a system of coupled Riccati equations, which can be solved in closed form. Finally, several numerical examples are presented to illustrate our framework.