Infinite Horizon Optimal Control for Resources Management in Agriculture

This article concerns an optimal control based framework for the optimization of resources in agriculture taking into account the environment sustainability. A decentralized, adaptive, hierarchic architecture to support long term coordinated decision-making strategies is required in order to achieve the common long term desired equilibrium in the environment state, and, at the same time, allow the economic sustainability of a number of distributed farm producers with, possibly conflicting, short term economic goals. The overall coordination is achieved by an adaptive Model Predictive Control structure that, on the one end hand, promotes the long term common good by approximating the solution to an infinite horizon optimal control problem, and, on the other hand, provides agro-chemical indicators to each one of the local farmers. We will emphasize on the importance of optimality results for infinite horizon optimal control problems of the Mayer type depending on the state at the final time while satisfying constraints at both trajectory endpoints.