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 the solution 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与函数型后验估计的推导，针对时间周期设定下的分布涡流最优控制问题及其状态方程。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解的存在唯一性。基于这些inf-sup和sup-sup条件，我们在函数型后验估计框架内，推导出最优控制问题和正问题近似误差的可保证、精确且完全可计算的界。本文首次展示了所推导估计的计算结果。