Crowd Motion Paradigm Modeled by a Bilevel Sweeping Control Problem

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Tan H. Cao (Author) Other; Nathalie T. Khalil (Author) Other; Boris S. Mordukhovich (Author) Other; Dao Nguyen (Author) Other; Fernando Lobo Pereira (Author) FEUP

Journal

Title: IEEE Control Systems Letters

Vol. 6

Pages: 385-390

Publisher: IEEE

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00V-19C

DOI: 10.1109/lcsys.2021.3077446

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6