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As has been reviewed in Sect. 2.3, the optimal control \(U^*(\cdot )\) of Problem (SLQ) admits the feedback law (1.11) with the help of \(\mathcal{P}(\cdot )\) and \(\eta (\cdot )\) (see (1.9) and (1.10)). In comparison to Chap. 3, both terminal problems on (1.9) and (1.10) are deterministic—a relevant property that we may now benefit from in a numerical discretization of Problem (SLQ): a canonical strategy therefore is now to approximate \(U^*(\cdot )\) by first discretizing (1.9) and (1.10) with the help of tools from deterministic numerics; and to finally insert it into SPDE (1.2) thanks to (1.11), and to then solve it numerically to get an approximation of \(X^*(\cdot )\) .

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Discretization Based on the Closed-Loop Approach

  • 章节

  • 发表日期：

    2026年

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  • Andreas Prohl,
  • Yanqing Wang

摘要

As has been reviewed in Sect. 2.3, the optimal control \(U^*(\cdot )\) of Problem (SLQ) admits the feedback law (1.11) with the help of \(\mathcal{P}(\cdot )\) and \(\eta (\cdot )\) (see (1.9) and (1.10)). In comparison to Chap. 3, both terminal problems on (1.9) and (1.10) are deterministic—a relevant property that we may now benefit from in a numerical discretization of Problem (SLQ): a canonical strategy therefore is now to approximate \(U^*(\cdot )\) by first discretizing (1.9) and (1.10) with the help of tools from deterministic numerics; and to finally insert it into SPDE (1.2) thanks to (1.11), and to then solve it numerically to get an approximation of \(X^*(\cdot )\) .