Bioremediation of natural water resources via optimal control techniques

We study minimal time strategies for the treatment of pollution in large water volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists of feeding the bioreactor from the resource, with clean output returning to the resource with the same flow rate. We first recall recent characterizations of optimal policies among feedback controls under the assumption of a uniform concentration in the resource, in which the optimal flow rate decreases with time. Then, we introduce a dead zone in the resource, considering two measurement points. With the help of the Pontryagin Maximum Principle, we show that this variant has no influence on the optimal control law. This study advises decision makers to focus on simple models