This talk concerns an optimal control framework to support the environmentally and economically sustainable management and control of resources in a wide range of problems arising in agriculture.
Usually, in any given region, there is an environmental interdependence that necessarily cause interactions among its agricultural production units. In the quest of prosperity, not to mention, mere survival, farmers have at their disposal some controls such as irrigation level, agrochemicals (fertilizers, and pesticides which typically enable a rapid response of the system), as well as the environmentally neutral “biological control”. Their individual goal consists in maximizing the short term economic return. However, either in competitive or in non-competitive contexts, their strategies have necessarily a negative impact in the environment, in the sense that, in the long term, its state does not converge to a sustainable healthy equilibrium, (see  and references therein).
Thus, the main challenge to be presented and discussed in this talk concerns the definition of a control architecture that includes a decision-making layer at the individual production units level, and a coordination layer, that takes into account the environmental impact of each production unit as well as the required long term environment healing needs in order to define upper and lower bounds on the controls that can be used by the each one of the production units.
While, each farmer to solve an optimal control problem, [2,5], in order to maximize his/her economic return by the year end, the coordination layer will seek to ensure that such behaviors do not prevent the environment state to converge to a healthy long term natural equilibrium.
Thus, the control architecture consists of a set of two nested optimization processes in which a discrete time “infinite horizon approximating Model Predictive Control scheme, [3,4], plays a key role in planning and coordination.
There are a huge number of Mathematical challenges – well beyond those of modeling and complexity – concerning the formulation of the coordination as well as how to ensure the desired behavior of the overall system whose discussion does not fit in the talk constraints. However, we will discuss some challenges and recent results on the Pontryagin Maximum Principle for infinite horizon optimal control problems as well as on the convergence on MPC schemes for impulsive control systems.