On the regional tracking problem of the bilinear wave equation subject to bounded controls

Abstract

This research focuses on a regional optimal control problem of a bilinear wave equation evolving on a spatial domain Ω⊂Rd, where d≥1. The equation is excited by bounded controls that act on the velocity term. The main objective of this study is to minimize a functional cost, which involves tracking a desired state within a subregion ω of Ω and the energy term over the time interval [0,T]. We successfully prove the existence of an optimal control that we characterize as a solution to an optimality system. Additionally, an algorithm for the computation of such a control is given and successfully illustrated through simulations.