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首页> 外文OA文献 >HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Optimal Feedbacks and Approximations
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HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Optimal Feedbacks and Approximations

机译：具有时滞的微分方程最优控制的HJB方程   延迟和状态约束，II：最佳反馈和近似

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摘要

This paper, which is the natural continuation of a previous paper by the sameauthors, studies a class of optimal control problems with state constraintswhere the state equation is a differential equation with delays. This classincludes some problems arising in economics, in particular the so-called modelswith time to build. The problem is embedded in a suitable Hilbert space H andthe regularity of the associated Hamilton-Jacobi-Bellman (HJB) equation isstudied. Therein the main result is that the value function V solves the HJBequation and has continuous classical derivative in the direction of thepresent. The goal of the present paper is to exploit such result to findoptimal feedback strategies for the problem. While it is easy to defineformally a feedback strategy in classical sense the proof of its existence andof its optimality is hard due to lack of full regularity of V and to theinfinite dimension. Finally, we show some approximation results that allow usto apply our main theorem to obtain epsilon-optimal strategies for a widerclass of problems.
机译：本文是同一作者先前论文的自然延续，研究了一类具有状态约束的最优控制问题，其中状态方程是带时滞的微分方程。该类包括一些在经济学中引起的问题，尤其是所谓的具有建立时间的模型。该问题被嵌入到合适的希尔伯特空间H中，并研究了相关的汉密尔顿-雅各比-贝尔曼（HJB）方程的正则性。其中的主要结果是值函数V求解HJBequation，并在当前方向上具有连续的经典导数。本文的目的是利用这种结果来找到针对该问题的最佳反馈策略。虽然很容易从形式上正式定义一种反馈策略，但由于V的完全规则性和无穷大的尺寸，很难证明其存在和最优性。最后，我们显示了一些近似结果，这些结果使我们可以应用主定理来获得针对更广泛问题的epsilon最优策略。

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