论文标题
对有限图的最佳控制：渐进的最佳控制和恒定常数在熵成本的情况下
Optimal control on finite graphs: asymptotic optimal controls and ergodic constant in the case of entropic costs
论文作者
论文摘要
为了在连续时间上有限图上的最佳控制问题，动态编程原理会导致以非线性普通微分方程系统为特征的价值功能。在本文中，我们考虑了熵成本的情况，由于与熵和指数之间的经典二元性链接的变量的变化，非线性微分方程可以转化为线性。连接该图后，我们表明可以通过矩阵分析的经典工具轻松地计算出渐近的最佳控制和恒定常数。
For optimal control problems on finite graphs in continuous time, the dynamic programming principle leads to value functions characterized by systems of nonlinear ordinary differential equations. In this paper, we consider the case of entropic costs for which the nonlinear differential equations can be transformed into linear ones thanks to a change of variables linked to the classical duality between entropy and exponential. When the graph is connected, we show that the asymptotic optimal control and the ergodic constant can be computed very easily with classical tools of matrix analysis.
