A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem

In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature sweeping process involving truncated normal cone. By bilevel, it is meant that the optimization of upper level carried out over solution set lower problem.This instance arises in structured crowd motion problems confined space. We establish corresponding necessary optimality conditions Gamkrelidze’s form. The analysis relies on smooth approximation system, thereby dealing with resulting lack Lipschitzianity respect to state variable inherent process, and flattening structure via an exact penalization technique. Necessary form are applied standard approximating penalized single-level problem, main result article obtained by passing limit.