Optimal control of electricity input given an uncertain demand

Optimal Inflow Control Penalizing Undersupply in Transport Systems with Uncertain Demands

“…In this work, we tackle the challenging question of when to feed how many goods into a supply system to meet the stochastic demand. We use the framework of [3], where a corresponding stochastic optimal control problem is set up in the context of electricity injection and extend it by introducing a penalty term into the cost function. This term penalizes a production not leading to demand satisfaction, i.e.…”

“…2 Stochastic optimal control model for transport systems An analysis of optimal control strategies for a supply problem in a deterministic demand setting can be found in [1,2]. Here, we focus on the stochastic nature of the demand and start from the stochastic optimal control framework originally set up in [3]. We consider a supply system consisting of only one production line.…”

“…The uncertainty about the height and timing of the orders entails the stochasticity of Y t . As in [3], we assume that the demand process fluctuates around a given timedependent mean demand level µ(t). The latter can be seen as a forecast that is based on historical demand data.…”

“…We refer the reader to [3] for more details on the demand process and the possibility to include jumps in the demand.…”

“…In [3], a possible choice of an objective function as a tracking-type function OF track (Y s ,t 0 , y t 0 , y(s)) = E (Y s − y(s)) 2 |Y t 0 = y t 0 has been introduced. The loss is measured in terms of the quadratic deviation between output at the end of the line and the actual demand.…”