Entropic model predictive optimal transport over dynamical systems
Entropic model predictive optimal transport over dynamical systems
复制标题
熵模型预测动力系统上的最佳传输
DOI：
10.1016/j.automatica.2023.110980
复制
发表时间：
2023
期刊：
影响因子：
6.4
通讯作者：
Kashima Kenji
中科院分区：
文献类型：
--
作者：
Ito Kaito;Kashima Kenji
我们考虑了在无限范围内将主体种群引导到期望分布的最优控制问题。这是一个动态系统上的最优运输问题，由于其较高的计算成本而具有挑战性。本文利用熵正则化方法，提出了一种结合了模型预测控制(MPC)和所谓的Sinkhorn算法的动态传输算法SinkhornMPC。该方法的显著特点是通过同时执行控制和运输规划来实现实时的低成本运输，数值例子说明了这一点。此外，在对集成在预测控制中的Sinkhorn算法的迭代次数作了一定的假设的情况下，利用熵正则化，我们揭示了Sinkhorn预测控制的全局收敛性质。此外，在没有上述假设的情况下，聚焦于二次控制代价，我们证明了Sinkhorn预测控制的最终有界性和局部渐近稳定性。
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational cost. In this paper, by using entropy regularization, we proposeSinkhorn MPC, which is a dynamical transport algorithm integrating model predictive control (MPC) and the so-called Sinkhorn algorithm. The notable feature of the proposed method is that it achieves cost-effective transport in real time by performing control and transport planning simultaneously, which is illustrated in numerical examples. Moreover, under some assumption on iterations of the Sinkhorn algorithm integrated in MPC, we reveal the global convergence property for Sinkhorn MPC thanks to the entropy regularization. Furthermore, focusing on a quadratic control cost, without the aforementioned assumption we show the ultimate boundedness and the local asymptotic stability for Sinkhorn MPC.