In order to predict achievable productivities in the so called raceway culturing system, the dynamics of photosynthesis has to be taken into account. In particular, the dynamical effect of inhibition by an excess of light (photoinhibition) must be represented. We propose a model considering both photosynthesis and growth dynamics. This model involves three different time scales. We study the response of this model to fluctuating light with different frequencies by slow fast approximations. Therefore, we identify three different regimes for which a simplified expression for the model can be derived. These expressions give a hint on productivity improvement which can be expected by stimulating photosynthesis with a faster hydrodynamics.

 In this paper, the design of an interval observer with an adaptive dynamical gain is presented. The observer is formulated in the framework of robust state estimation of uncertain dynamical systems, where an interval that encloses the unknown state variables is provided. Here the observer is based on a change of coordinate that involves a time varying gain. We introduce a dynamics for the gain, whose trajectory converges toward a predefined optimal value (which maximizes the convergence rate of the observer). The observer performance is illustrated with the estimation of microalgal oil in the framework of biofuel production. The proposed observer design, when applied to experimental data of Isochrysis affinis galbana, appears to be a suitable robust estimation technique.

 In this paper, a mathematical reduction method named Homotopy is applied to the Anaerobic Digestion Model No. 1 or ADM1, cf. (Batstone et al., 2002), a complex model of bioprocess describing the anaerobic digestion. The proposed method neglects the slow dynamics keeping only the fastest ones in using the technique of eigenvalue-state association. This transformation is described by the Homotopy matrix H. Simulations show that both the initial and the reduced models exhibit similar steady states while reduction using balancing of empirical gramians ensure the same input-output behavior of the reduced model compared with regard to the original one.

 This paper is devoted to the minimal time control problem for fed-batch bioreactors, in presence of an inhibitory product, which is released by the biomass proportionally to its growth. We first consider a growth rate with substrate saturation and product inhibition, and we prove that the optimal strategy is fill and wait (bang-bang). We then investigate the case of the Jin growth rate which takes into account substrate and product inhibition. For this type of growth function, we can prove the existence of singular arc paths defining singular strategies. Several configurations are addressed depending on the parameter set. For each case, we provide an optimal feedback control of the problem (of type bang-bang or bang-singular-bang). These results are obtained gathering the initial system into a planar one by using conservation laws. Thanks to Pontryagin maximum principle, Green's theorem, and properties of the switching function, we obtain the optimal synthesis.

 In the framework of environment preservation, microalgae biotechnology appears to be a promising alternative for CO2 mitigation. Implementation of advanced control strategies can be further considered to improve potential performances of these organisms. In this context, this paper proposes the implementation of predictive control combined with an on-line estimation of the Chlorella vulgaris biomass, using Total Inorganic Carbon measurements. The elaboration of interval observers for biomass estimation is first detailed. This estimation is further included in a Nonlinear Model Predictive Control (NMPC) framework considered to regulate the biomass concentration. Finally experimental results are presented which validate the proposed theoretical developments.