论文标题
最佳控制问题中最佳值的塞萨罗和亚伯的线性编程估计值
Linear Programming Estimates for Cesaro and Abel Limits of Optimal Values in Optimal Control Problems
论文作者
论文摘要
我们考虑无限的地平线最佳控制问题随时间平均和时间打折标准，并在依赖初始条件的情况下对其最佳值的塞萨罗和亚伯限制进行估计。我们确定这些限制是通过某个无限维（ID）线性编程（LP）问题的最佳值限制的，并且它们是通过相应双重问题的最佳值从下面界定的。 （这些估计值特别表明，如果没有二元性差距，则塞萨罗和亚伯限制存在，并且彼此相等）。此外，我们为长期平均最佳控制问题获得了基于IDLP的最佳条件，并以示例说明了这些条件。
We consider infinite horizon optimal control problems with time averaging and time discounting criteria and give estimates for the Cesaro and Abel limits of their optimal values in the case when they depend on the initial conditions. We establish that these limits are bounded from above by the optimal value of a certain infinite dimensional (ID) linear programming (LP) problem and that they are bounded from below by the optimal value of the corresponding dual problem. (These estimates imply, in particular, that the Cesaro and Abel limits exist and are equal to each other if there is no duality gap). In addition, we obtain IDLP-based optimality conditions for the long run average optimal control problem, and we illustrate these conditions by an example.
