This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of a weak space-time variational formulation for the optimality system and the forward problem are proved by deriving inf-sup and sup-sup conditions. Using the inf-sup and sup-sup conditions, we derive guaranteed, sharp, and fully computable bounds of the approximation error for the optimal control problem and the forward problem in the functional type a posteriori estimation framework. We present here the first computational results on the derived estimates.

翻译：本文提出了多谐波分析，并推导了分布式涡流最优控制问题及其状态方程在时-周期设定下的泛函型后验估计。通过推导inf-sup和sup-sup条件，证明了最优性系统和正问题在弱时-空变分形式下的存在唯一性。基于inf-sup和sup-sup条件，我们在泛函型后验估计框架下，推导了最优控制问题和正问题近似误差的保证性、尖锐性及完全可计算界限。本文首次给出了所推导估计的计算结果。