论文标题
HJB方程和希尔伯特空间半空间上的随机控制
HJB equations and stochastic control on half-spaces of Hilbert spaces
论文作者
论文摘要
在本文中，我们研究了Hilbert空间中HJB方程的轻度解理论的第一个扩展，当时该域不是整个空间的情况。更确切地说，我们将半空间视为域，而半线性的汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程。我们的主要目标是建立对此类HJB方程的解决方案的存在和独特性，这些方程在空间变量中是不断差异的。我们还将结果应用于退出时间最佳控制问题，我们表明，相应的值函数是半连接HJB方程的独特解决方案，具有足够的规律性，可以以反馈形式表达最佳控制。最后，我们举了一个说明性的例子。
In this paper we study a first extension of the theory of mild solutions for HJB equations in Hilbert spaces to the case when the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear Hamilton-Jacobi-Bellman (HJB) equation. Our main goal is to establish the existence and the uniqueness of solutions to such HJB equations, that are continuously differentiable in the space variable. We also provide an application of our results to an exit time optimal control problem and we show that the corresponding value function is the unique solution to a semilinear HJB equation, possessing sufficient regularity to express the optimal control in feedback form. Finally, we give an illustrative example.
