On the Solvability of Some Ergodic Control Problems in ℝd
On the Solvability of Some Ergodic Control Problems in ℝd
复制标题
ℝd 中一些遍历控制问题的可解性
DOI：
10.1137/140953903
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Marco Cirant
中科院分区：
文献类型：
--
作者：
Marco Cirant
本文研究状态空间和控制空间均为$\mathbb{R}^d$的随机遍历控制问题。我们感兴趣的固定漂移，成本函数和拉格朗日函数，足以合成反馈型最优控制的条件。为了获得这样的条件，我们提出了一种方法，结合了李雅普诺夫方法和有界集上的问题与反射的扩散在边界上的近似。我们首先开发了一个一般的框架，然后研究特定的情况下，显示如何李雅普诺夫函数可以构造的近似问题的解决方案。
This paper is concerned with stochastic ergodic control problems where both the state and the control space are $\mathbb{R}^d$. We are interested in giving conditions on the fixed drift, the cost function, and the Lagrangian function that are sufficient for synthesizing an optimal control of feedback type. In order to obtain such conditions, we propose an approach that combines the Lyapunov method and the approximation of the problem on bounded sets with reflection of the diffusions at the boundary. We first develop a general framework, and then study particular cases which show how Lyapunov functions can be constructed from the solutions of the approximating problems.