Optimal Dirichlet boundary control for a fractional/normal evolution equation with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The convergence of a temporally semidiscrete approximation is rigorously established, where the control is not explicitly discretized and the state equation is discretized by a discontinuous Galerkin method in time. Numerical results are provided to verify the theoretical results.

中文翻译：

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分数/正态发展方程带最终观测值的狄利克雷边界控制的时间半离散逼近

考虑具有最终观察结果的分数/正态发展方程的最佳Dirichlet边界控制。推导了该解的唯一性和最优控制问题的一阶最优性条件。严格建立时间半离散逼近的收敛，在这种情况下，没有明确离散控制，而状态方程通过不连续Galerkin方法及时离散。提供数值结果以验证理论结果。