论文标题
部分可观测时空混沌系统的无模型预测
Optimality conditions and Lipschitz stability for non-smooth semilinear elliptic optimal control problems with sparse controls
论文作者
论文摘要
本文涉及一阶和二阶的最佳条件以及非平滑度半线性最佳控制问题的稳定性，涉及成本功能中控制的$ l^1 $ norm。 除了出现$ l^1 $ norm的外观，导致了目标的非差异性并促进了最佳控制的稀疏性，状态方程中非线性系数的不平滑度也会导致控制对状态操作员的相同属性。利用正规化方案，我们为任何本地最佳控制提供了$ c $ -Stationality条件。在关联状态的结构假设下，我们定义了曲线功能，而不包括$ l^1 $ - norm norm norm norm norm norm norm norm norm norm norm norm的二阶必需和充分最佳条件的目标。此外，在对上述状态施加的更严格的结构假设下，建立了曲率的明确配方，因此说明了显式的二阶最佳条件。最后，显示了局部溶液相对于稀疏参数的Lipschitz稳定性。
This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the appearance of the $L^1$-norm leading to the non-differentiability of the objective and promoting the sparsity of the optimal controls, the non-smoothness of the nonlinear coefficient in the state equation causes the same property of the control-to-state operator. Exploiting a regularization scheme, we derive $C$-stationarity conditions for any local optimal control. Under a structural assumption on the associated state, we define the curvature functional for the part not including the $L^1$-norm of controls of the objective for which the second-order necessary and sufficient optimality conditions are shown. Furthermore, under a more restrictive structural assumption imposed on the mentioned state, an explicit formulation of the curvature is established and thus the explicit second-order optimality conditions are stated. Finally, the Lipschitz stability of local solutions with respect to the sparsity parameter is shown.
