论文标题
汉密尔顿 - 雅各比 - 贝尔曼方程的弱势解决方案在无限的地平线上
Weak epigraphical solutions to Hamilton-Jacobi-Bellman equations on infinite horizon
论文作者
论文摘要
在本文中，我们显示了汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程在无限范围内的弱叙事解决方案的唯一性结果，该方程在无限范围内消失的一类低半连续功能消失了。 HJB方程的弱层流溶液，具有时间测量的数据和光纤传感器，从经典的意义上讲是粘度解决方案 - 每当它们是局部Lipschitz的连续时。在这里，我们将局部绝对连续的管的概念扩展到具有局部界限变化的连续铭文的设置值图。这个新的概念符合哈密顿量相对于纤维的Fenchel变换的均匀下限。考虑可控性假设。
In this paper we show a uniqueness result for weak epigraphical solutions of Hamilton-Jacobi-Bellman (HJB) equations on infinite horizon for a class of lower semicontinuous functions vanishing at infinity. Weak epigraphical solutions of HJB equations, with time-measurable data and fiber-convex, turn out to be viscosity solutions - in the classical sense - whenever they are locally Lipschitz continuous. Here we extend the notion of locally absolutely continuous tubes to set-valued maps with continuous epigraph of locally bounded variations. This new notion fits with the lack of uniform lower bound of the Fenchel transform of the Hamiltonian with respect to the fiber. Controllability assumptions are considered.
