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Communication Dans Un Congrès Année : 2023

Optimal control of microalgae culture accounting for photoinhibition and light attenuation

Résumé

In a photobioreactor, due to the gradient of light, microalgae are successively exposed to conditions of low and high (inhibiting) light. This phenomenon can be captured by the Han model, which is a common mechanistic model of photoinhibition. Based on Han's description, we introduce a dynamic system of microalgae growth involving two control variables: the light intensity and the dilution rate of the reactor. This model is derived from slow/fast dynamic considerations in a chemostat system accounting for the light gradient due to absorption and scattering following the Lambert-Beer's law. Then, we formulate and study an optimal control problem in order to fully-characterize the optimal light supply and dilution strategies that maximize the harvested biomass. Our study, mainly based on Pontryagin's maximum principle (PMP), shows that singular arcs and turnpike-like behaviors appear in the optimal solution. In particular, we prove that the optimal strategy maintains the biomass at a constant level along singular arcs, and we determine its static value. The theoretical results are illustrated throughout this paper using a direct optimization method.
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hal-04251736 , version 1 (20-10-2023)

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  • HAL Id : hal-04251736 , version 1

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Ignacio Fierro, Walid Djema, Olivier Bernard. Optimal control of microalgae culture accounting for photoinhibition and light attenuation. IFAC World Congress 2023, Jul 2023, Yokohama, Japan. ⟨hal-04251736⟩
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