Optimal control of electromagnetic wave displacement with an unknown velocity of propagation

ABSTACT The aim of this paper is to control an electromagnetic wave that penetrates in a medium with some missing information about its physical properties. The missing value of wave velocity of propagation leads us to use averaged control notion which is recently introduced by E. Zuazua, also the boundary Dirichlet condition is unknown which requires using the notion of no-regret control introduced by J. L. Lions. In this work, we combine these two techniques where we introduce the notion of averaged no-regret control to solve our optimal control problem with missing data. The averaged no-regret control will be characterised by an optimality system.