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Optimal control from inoculation on a continuous microalgae culture. (English) Zbl 1389.49014

Summary: The present work is centred on the problem of biomass productivity optimization of a culture of microalgae Spirulina maxima. The mathematical tools consisted of necessary and sufficient conditions for optimal control coming from the celebrated Pontryagin’s Maximum Principle (PMP) as well as the Bellman’s Principle of Optimality, respectively. It is shown that the optimal dilution rate turns to be a bang-singular-bang control. It turns out that, the experimental results are in accordance to the optimal mathematical findings.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49L20 Dynamic programming in optimal control and differential games
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
92C40 Biochemistry, molecular biology
49N90 Applications of optimal control and differential games
90C46 Optimality conditions and duality in mathematical programming
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