Crowd Motion Paradigm Modeled by a Bilevel Sweeping Control Problem

This article concerns an optimal crowd motion control problem in which the features a structure given by its organization into N groups (participants) each one spatially confined set. The overall consists driving ensemble of sets as close possible to point (the “exit”) while population set minimizes effort subject sweeping dynamics with controlled state dependent velocity drift. In order capture conflict between goal and those various groups, is cast bilevel optimization framework. A key challenge this bringing together two quite different paradigms: programming Necessary conditions optimality form Maximum Principle Pontryagin Gamkrelidze framework are derived. These then used solve simple illustrative example participants, emphasizing interaction them.