  Controlled environment agriculture (CEA) is used for efficient food
production. Efficiency can be increased further by interconnecting different
CEA systems (e.g. plants and insect larvae or fish and larvae), using products
and by-products of one system in the other. These interconnected systems define
an overall system that can be described by models of interacting species. It is
necessary to identify system parameters (e.g. initial species concentration,
harvest rate, feed quality, etc.) such that the resources are not exhausted.
For such systems with interacting species, modelled by the Lotka-Volterra
equations, a set-based approach based on the recent results of the theory of
barriers to exactly determine the so-called admissible set (also known as
viability kernel) and the maximal robust positively invariant set is presented.
Using an example of a larvae-fish based production system, steps to obtain
special trajectories which are the boundaries of the admissible set are shown.
This admissible set is used to prevent the under and over population of the
species in the CEA. Furthermore, conditions of the system parameters are
stated, such that the existence of these trajectories can be guaranteed.
