论文标题
$ l^1 $最佳控制问题的时空放松
A space-time relaxation for $L^1$ optimal control problems
论文作者
论文摘要
我们引入了一种垂直类型的放松，以解决最佳的控制问题，该问题仅具有$ l^1 $ - 驾驶控制。通常，此类问题同时具有浓度和振荡效应。我们建议在时空中的一个相关问题放松，其中可以将控件视为$ l^\ infty $的界限，从而大大简化了任何分析。在这种放松中，浓度转化为垂直部分，可以使用年轻测量来处理振荡。该技术可以扩展到无限维空间上的类似问题。
We introduce a vertical type relaxation for optimal control problems which only have $L^1$-coercivity for their controls. Usually such problems feature both concentration and oscillation effects at the same time. We propose relaxing to an associated problem in space-time, where the controls can be considered bounded in $L^\infty$, greatly simplifying any analysis. In this relaxation, concentrations are transformed into vertical parts and oscillations can be dealt with using Young-measures. This technique can be extended to similar problems on infinite-dimensional spaces.
