Optimal Feedback Control of Microalgal Growth Based on the Slow Reduction

A state feedback law is proposed for on-line optimization of microalgal growth in a photobioreactor in the presence of non-measurable disturbances. The objective is to maximize a photosynthetic production rate (specific growth rate of microalgae) by manipulating the irradiance. The model describing the growth of microalgae is based on the mechanistic description in the form of the so-called photosynthetic factory. The reduction to a slow dynamics is used to derive analytically the approximation of the optimal feedback control. The analysis of the obtained explicit formula shows that the optimal feedback control actually performs optimal transfer to a constant optimal irradiance developed earlier but does not achieve principally better performance than the optimal control within the class of constant irradiance. Therefore, by reducing fast dynamics one can not reveal possible more complex optimal solutions. At the same time, this contradicts to a common belief in biotechnological community that the fast phenomena may be neglected. Illustrative simulations are included.