Control theory and optimization applied to ecological problems
Jean-Luc Gouzé
COMORE Project, INRIA,
BP 93, 06902 Sophia-Antipolis Cedex, France
gouze@sophia.inria.fr
Control theory is a mathematical theory that studies dynamical systems with outputs and inputs. It is well known and applied in the engineering field, but seldom appears in the ecological problems (except for optimal control). The goal of this session is to point out the relevance of this theory for ecological problems, and to offer some applications of the theory within different fields.
The main concepts of the theory are the concept of system, inputs (the actions on the system) and outputs (the measures available). Some problems can be, for example:
- Is it possible, with the inputs, to regulate the system around a reference point?
- Is it possible, with the outputs, and the knowledge of the model, to estimate the (unmeasured) state variables?
In particular, control theory applies very well to managing renewable resources (fisheries, harvesting,...), and to modelling and studying biological systems in a controlled environment (bioreactors, ...). The theory has numerous ramifications (optimal control, game theory,...) that can also be applied to living systems, for problems concerning optimal management, optimal strategies, ...