Instantaneous control of interacting particle systems in the mean-field limit

JOURNAL OF COMPUTATIONAL PHYSICS

卷:405

Article

Burger, Martin¹  Pinnau, Rene²  Totzeck, Claudia²  Tse, Oliver³  Roth, Andreas² 

[1] Friedrich Alexander Univ Erlangen Nurnberg, Erlangen, Germany

[2] TU Kaiserslautern, Kaiserslautern, Germany

[3] Tech Univ Eindhoven, Eindhoven, Netherlands

关键词: Interacting particle systems;    Mean-field limit;    Instantaneous control;    Numerics;   

DOI  :  10.1016/j.jcp.2019.109181

来源: Elsevier

【 摘 要 】

Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle system into a certain spatial region by repulsive forces from a few external agents, which might be interpreted as shepherd dogs leading sheep to their home. We introduce an appropriate mathematical model and the corresponding optimization problem. In particular, we are interested in the interaction of numerous particles, which can be approximated by a mean-field equation. Due to the high-dimensional phase space this will require a tailored optimization strategy. The arising control problems are solved using adjoint information to compute the descent directions. Numerical results on the microscopic and the macroscopic level indicate the convergence of optimal controls and optimal states in the mean-field limit, i.e., for an increasing number of particles. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free