A Monte Carlo framework for solving optimal control problems governed by kinetic models is presented. The focus is on a kinetic model with Keilson-Storer linear collision term and the control mechanism is an external space-dependent force. The purpose of this control is to drive an ensemble of particles to acquire a desired mean velocity and position and to reach a desired final configuration in phase space. For this purpose, a gradient-based computational strategy in the framework of Monte Carlo methods is developed. Results of numerical experiments successfully validate the proposed control framework.

Program summary

Program title: MOCOKI

CPC Library link to program files: https://doi.org/10.17632/6cb8fggwm2.1

Licensing provisions: GNU General Public License 3

Programming language: C/C++/Python

Nature of problem: In many applications involving gases or plasma, it is not possible to assume a continuum and therefore models and methods that work at the mesoscopic level are needed. In this framework, kinetic models and Monte Carlo techniques play a central role. On the other hand, many present and envisioned application require to design control strategies by external forces that drive the evolution of these systems. For this purpose, it is necessary to implement optimal control techniques consistent with kinetic structures and Monte Carlo schemes. The novel methodology presented in this paper, although focusing on a linear kinetic model and a low-dimensional setting, can be extended in principle to nonlinear models and high-dimensional problems.

Solution method: The proposed computational framework solves ensemble optimal control problems governed by linear kinetic models with a control-in-the-force mechanism. This framework combines transport techniques and Monte Carlo schemes for collision with numerical optimization methods.

中文翻译：

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MOCOKI：蒙特卡洛方法，用于线性动力学模型力的最佳控制

提出了解决动力学模型控制的最优控制问题的蒙特卡洛框架。重点是带有Keilson-Storer线性碰撞项的动力学模型，控制机制是与外部空间有关的力。该控制的目的是驱动粒子集合以获取所需的平均速度和位置，并在相空间中达到所需的最终配置。为此，在蒙特卡洛方法的框架内开发了一种基于梯度的计算策略。数值实验结果成功验证了所提出的控制框架。

计划摘要

节目名称： MOCOKI

CPC库链接到程序文件： https : //doi.org/10.17632/6cb8fggwm2.1

许可条款： GNU通用公共许可证3

编程语言： C / C ++ / Python

问题的性质：在涉及气体或等离子体的许多应用中，不可能假设连续体，因此需要在介观水平上起作用的模型和方法。在此框架中，动力学模型和蒙特卡洛技术起着核心作用。另一方面，许多当前和预期的应用都需要通过驱动这些系统发展的外力来设计控制策略。为此，有必要实施与动力学结构和蒙特卡洛方案一致的最佳控制技术。本文介绍的新颖方法论虽然关注线性动力学模型和低维设置，但原则上可以扩展到非线性模型和高维问题。

解决方法：所提出的计算框架通过力控制机制解决了由线性动力学模型控制的整体最优控制问题。该框架结合了用于碰撞的运输技术和蒙特卡洛方案以及数值优化方法。