Optimal Inflow Control Penalizing Undersupply in Transport Systems with Uncertain Demands
We are concerned with optimal control strategies subject to uncertain demands. An Ornstein-Uhlenbeck process describes the uncertain demand. The transport within the supply system is modeled by the linear advection equation. We consider different approaches to control the produced amount at a given time to meet the stochastic demand in an optimal way. In particular, we introduce an undersupply penalty and analyze its effect on the optimal output in a numerical simulation study.
The authors are grateful for the support of the German Research Foundation (DFG) within the project “Novel models and control for networked problems: from discrete event to continuous dynamics” (GO1920/4-1) and the BMBF within the project ENets.
- 3.Göttlich, S., Korn, R., Lux, K.: Optimal control of electricity input given an uncertain demand. Preprint (2018). arXiv:1810.05480Google Scholar