تقرير
Crowd motion paradigm modeled by a bilevel sweeping control problem
| العنوان: | Crowd motion paradigm modeled by a bilevel sweeping control problem |
|---|---|
| المؤلفون: | Cao, Tan H., Khalil, Nathalie T., Mordukhovich, Boris S., Nguyen, Dao, Pereira, Fernando Lobo |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control |
| الوصف: | This article concerns an optimal crowd motion control problem in which the crowd features a structure given by its organization into N groups (participants) each one spatially confined in a set. The overall optimal control problem consists in driving the ensemble of sets as close as possible to a given point (the 'exit') while the population in each set minimizes its control effort subject to its sweeping dynamics with a controlled state dependent velocity drift. In order to capture the conflict between the goal of the overall population and those of the various groups, the problem is cast as a bilevel optimization framework. A key challenge of this problem consists in bringing together two quite different paradigms: bilevel programming and sweeping dynamics with a controlled drift. Necessary conditions of optimality in the form of a Maximum Principle of Pontryagin in the Gamkrelidze framework are derived. These conditions are then used to solve a simple illustrative example with two participants, emphasizing the interaction between them. Comment: 6 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2104.09673 |
| رقم الأكسشن: | edsarx.2104.09673 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |