MOCOKI: A Monte Carlo approach for optimal control in the force of a linear kinetic model

Abstract 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 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 Code Ocean capsule: https://codeocean.com/capsule/0114150 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.