Coupling geometric analysis and viability theory for system exploration: Application to a living food system |
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Affiliation: | 1. Orange Labs, 38-40, rue du General Leclerc, 92130 Issy-les-Moulineaux, France;2. LiSSi - University of Paris Est Creteil (UPEC): 122, rue Paul Armangot, 94400 Vitry Sur Seine, France;3. Sorbonne Universites, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606: 4 place Jussieu Paris 75005, France |
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Abstract: | This paper addresses the issue of studying a food complex system in a reverse engineering manner with the aim of identifying the set of all possible actions that makes it reach a quality target with respect to manufacturing constraints. Once the set of actions is identified, several criteria can be considered to identify interesting trajectories and control policies. A viability approach, coupling the viability theory and a geometric approach of robustness, is proposed to study complex dynamical systems. It can be implemented for several types of systems, from linear to non linear or hybrid systems. The proposed framework was adapted to a living food system: a ripening model of Camembert cheese to identify the set of states and actions (capture basin) from which it is possible to reach a predefined quality target. Within the set of viable trajectories, particular trajectories that improve the Camembert cheese ripening process are identified using the proposed approach. The results are applied at a pilot scale and are discussed in this paper. |
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Keywords: | Model exploration Viability Geometric analysis Food system Optimal control Dynamical system |
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