有限图上的最优控制：熵代价下的渐近最优控制和遍历常数
Optimal control on finite graphs: asymptotic optimal controls and ergodic constant in the case of entropic costs
摘要：
对于连续时间有限图上的最优控制问题，动态规划原理导致了以非线性常微分方程系统为特征的值函数。在本文中，我们考虑的情况下，熵成本的非线性微分方程可以转化为线性的，由于变量变换与熵和指数之间的经典对偶。当图是连通的时，我们证明了用经典的矩阵分析工具可以很容易地计算渐进最优控制和各态历经常数。
英文摘要：
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.
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