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Controlled environment agriculture (CEA) is used for efficient foodproduction. Efficiency can be increased further by interconnecting differentCEA systems (e.g. plants and insect larvae or fish and larvae), using productsand by-products of one system in the other. These interconnected systems definean overall system that can be described by models of interacting species. It isnecessary 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-Volterraequations, a set-based approach based on the recent results of the theory ofbarriers to exactly determine the so-called admissible set (also known asviability kernel) and the maximal robust positively invariant set is presented.Using an example of a larvae-fish based production system, steps to obtainspecial trajectories which are the boundaries of the admissible set are shown.This admissible set is used to prevent the under and over population of thespecies in the CEA. Furthermore, conditions of the system parameters arestated, such that the existence of these trajectories can be guaranteed.

Sustainability Analysis of Interconnected Food Production Systems via Theory of Barriers