具有最终观测值的分数阶/正态发展方程Dirichlet边界控制的时间半离散逼近
Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation
摘要：
研究了具有最终观测的分数阶/正态演化系统的最优Dirichlet边界控制.得到了该最优控制问题解的唯一存在性和一阶最优性条件。严格建立了时间半离散近似的收敛性，其中控制不显式离散，状态方程在时间上由间断Galerkin方法离散。数值结果验证了理论结果。
英文摘要：
Optimal Dirichlet boundary control for a fractional/normal evolution 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.
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