# Optimal inflow control penalizing undersupply in transport systems with uncertain demands

## TL;DR

This paper develops optimal control strategies for transport systems with uncertain demands modeled by Ornstein-Uhlenbeck processes, introducing an undersupply penalty to improve supply-demand matching.

## Contribution

It proposes a novel control approach incorporating undersupply penalties for systems with stochastic demand modeled by Ornstein-Uhlenbeck processes.

## Key findings

- Undersupply penalty influences optimal control strategies.
- Numerical simulations demonstrate improved supply-demand alignment.
- Control strategies adapt to demand uncertainty effectively.

## Abstract

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.