论文标题
偶然受限的最佳供应系统的最佳流入控制系统不确定需求不确定
Chance-constrained optimal inflow control in hyperbolic supply systems with uncertain demand
论文作者
论文摘要
在本文中，我们解决了制定最佳生产计划的任务，考虑到不确定的需求。能量系统由双曲线偏微分方程（PDE）的系统表示，不确定的需求流由Ornstein-Uhlenbeck过程捕获。我们根据生产者的风险偏好确定最佳流入。最终的输出旨在最佳地匹配给定风险标准的随机需求。我们使用不确定性量化来适应不同的风险规避水平。更确切地说，我们使用两种类型的机会限制来在规定的概率水平上制定需求满意度的要求。在数值分析中，我们分析了电报方程的机会约束优化问题和现实世界中耦合的气体对功率网络。
In this paper, we address the task of setting up an optimal production plan taking into account an uncertain demand. The energy system is represented by a system of hyperbolic partial differential equations (PDEs) and the uncertain demand stream is captured by an Ornstein-Uhlenbeck process. We determine the optimal inflow depending on the producer's risk preferences. The resulting output is intended to optimally match the stochastic demand for the given risk criteria. We use uncertainty quantification for an adaptation to different levels of risk aversion. More precisely, we use two types of chance constraints to formulate the requirement of demand satisfaction at a prescribed probability level. In a numerical analysis, we analyze the chance-constrained optimization problem for the Telegrapher's equation and a real-world coupled gas-to-power network.
