For this, we have to abstract a model and then use control theory or optimal theory to analyze its properties like stability. Can someone give some suggestions on the scenarios where this applies well?
For biological control of insects in agriculture this could be useful .
In my opinion, this type of analysis has been conducted a few times in horticulture and greenhouse cultivation of vegetables and fruits. An implementation example is given in Speetjens 2008, Towards Model Based Adaptive control of the Watergy greenhouse, ISBN 978-90-8504-949-4
Not so much stability is investigated, because the models (and biological systems itself) can be unstable in reality. But especially the reaction and interaction of the biological system (e.g plant mass) to external factors should be investigated, from a control point of view.
E.g tomatos in a greenhouse have a huge influence on internal climate, and their biomass increase and plant health are influenced by many factors (air temperature, Rel Humidity, O2 and CO2 concentration, light levels, nutrient concentration, root pressure, etc).
A detailed biological system (interaction) model can be used in this case, to determine optimal (economical) climate control choices.
May be epidemic models can adjust to what you are looking for. For an epidemic model you can use vaccination controls. First, choose a model with a set of subpopulations 8 i.e. , the cathegories of the various populations whose sum is the total one) , for instance, SEIR models ( susceptible, infected, infectious and removed by immunity or immune) and add to this model a vaccination control which can be constant, impulsive or designed by feedback so that the infectious subpopulation is asymptotically zeroed. Note that the epidemic models are never controllable since all the subpopulations cannot be simultaneously driven to prescribed values. Rather than this, they change of status through time. For instance, a susceptible individual then can become infected ( without symptoms) , later on infectious ( with external symptoms) and then removed by immunity.
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