Stability estimates in the problem of cloaking material bodies for Maxwell’s equations

A control problem is considered for the three-dimensional Maxwell equations in the exterior of an impenetrable body with a boundary partly covered for cloaking. The role of the control is played by the surface impedance of the covered part of the boundary, which enters into the impedance boundary condition. The solvability of the control problem is proved, and an optimality system describing necessary conditions for an extremum is derived. An analysis of the optimality system yields sufficient conditions on the initial data that ensure the uniqueness and stability of optimal solutions for a particular cost functional.