Paper presented at the 52nd CFCS Annual Meeting, Guadeloupe, July 10-16, 2016 MATHEMATICAL PERSPECTIVES
SIMULATION SOFTWARE FOR THE VIABILITY ANALYSIS OF AGROECOLOGICAL TRANSITION TO SOIL PRESERVATION IN THE FRENCH WEST INDIES Anna Desilles ENSTA-Paristech (Palaiseau, France) and LASTRE (Paris, France) Keywords : viability theory, optimal control, numerical simulations, agro-economic models of small farms Abstract The purpose of this communication is to present the simulation software for long term viability study of small farms. This software was developed within the framework of ANR TOO GAIA project. The main problem that is studied is formulated in terms of the mathematical theory of viability. The goal is to determine the ability of a farm to restore soil quality to a target level, while respecting a number of economic constraints. The software is designed to enable a comprehensive global analysis of the possibilities of soil restoration as function of the current state of the soil and of the available wealth of the farm. It allows also determining the farm management strategies that the soil restoration and the viability with respect to the economic constraints. These strategies can be found for each possible initial conditions of a parcel for a given choice of time horizon to study. Main results The research previously conducted by the multidisciplinary team of the project led to the development of a dynamic model describing the evolution of the quality of the soil of a parcel as function of the choices of the crop or livestock raised on the parcel and of the agricultural practices. An economic dimension has been associated with this model. The presented software is composed of a main calculation kernel and a graphical interface to set up calculations and display the results. To provide the global evaluation of the economical and agro-ecological viability of a given parcel, the main computation kernel of the software uses some numerical set-valued algorithms based on the viability theory to compute capture basins and viability kernels. In addition, the software can determine for each initial state of a parcel the optimal global economic performance by solving an optimal control problem associated with the dynamic model. One of the essential components of this simulation software is the computation of the feedback lows (viable or optimal) together with capture basins or viability kernels. The computed feedbacks determine the control strategies guaranteeing the restoration of the soil to a given target quality. When the best economic performance is computed, the corresponding feedback low gives the optimal farm management strategies. To produce relevant results, the model implemented in software should be based on a large amount of data describing the agro-technical and economic characteristics of the different crops. In addition, it is necessary to provide for each crop the parameters of crops-soil interaction model. These parameters are crucial to define the soil quality evolution during each culture cycle. So, the data modeling for these simulations is a complex task. To facilitate the work of experts the software has a graphical user interface that allows to maintain a database of known crops and livestocks. Different graphical visualization tools was designed to facilitate the calibration process of the crops parameters. The Figure 1 shows an example of the screen for editing the parameters of a crop in the database. Using this database of known crops and livestocks, the user can easily create a model to evaluate the viability of a parcel and choose the computation parameters. The figure 2 shows the example of the visualization of computed optimal and viable farm conducting strategies obtained for a given parcel. Conclusion The simulation software developed as part of the ANR project is the first example of a complete simulation tool based on the mathematical theory of viability and dedicated to the study of agro ecological transitions for small farms. The main contribution of this tool is the possibility of global viability and capturability analysis, with respect to the starting conditions, both for soil quality for the financial health of the farm. It can be used, In particular, to the starting conditions, both for soil quality for the financial health of the farm. It can be used, In particular, to analyze the impact of financial incentives to change of the agricultural practices and transition assistance.
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