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Optimal control on finite graphs: asymptotic optimal controls and ergodic constant in the case of entropic costs

Olivier Gu\'eant
Nov 2020
摘要
For optimal control problems on finite graphs in continuous time, the dynamicprogramming principle leads to value functions characterized by systems ofnonlinear ordinary differential equations. In this paper, we consider the caseof entropic costs for which the nonlinear differential equations can betransformed into linear ones thanks to a change of variables linked to theclassical duality between entropy and exponential. When the graph is connected,we show that the asymptotic optimal control and the ergodic constant can becomputed very easily with classical tools of matrix analysis.
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