Sustainable use of agricultural ecosystems: an optimum control problem

Agricultural ecosystems comprise both natural and socioeconomic processes. By introducing fertilizing, harvesting or irrigation as control variables, one is led to the formulation of control problems. A main problem is the development of suitable performance criteria if both economic and ecological aspects are taken into account. The use of control theory leads to two major problems. The first concerns the choice of performance criteria. An appropriate performance criterion consists of an economic and an ecological part. In the framework of economic theory, environmental side-effects are referred to as external costs. Several approaches for including external costs are presented. The second problem concerns the definition of sustainability, which implies the derivation of long-term strategies. Time horizons are much longer. Objectives valid for one vegetation period cannot be applied to crop rotations or farming systems. Simulations show that local optimization does not lead to global sustainability. Using optimal control theory in ecology quickly leads to numerical problems. If one focuses on small, preferably linear models, analytic solutions of optimization problems are obtained by the application of known maximum principles. As ecological systems include complex nonlinear relationships, solutions can be derived by numerical optimization only. As the underlying model contains discrete and continuous model equations, the optimization results are derived by using dynamic programming.