Singular Perturbation Based Solution to Optimal Microalgal Growth Problem and Its Infinite Time Horizon Analysis

The problem of the optimal microalgal growth of the so-called photosynthetic factory (PSF) is considered here. The objective is to maximize the photosynthetic production rate (the specific growth rate of microalgae) by manipulating the irradiance. Using the singular perturbation based reduction, an analytical solution of such an optimal control problem is obtained and its infinite horizon analysis shows that the optimal solution on large time intervals tends to the optimal steady state of PSF. This is a mathematical confirmation of the hypothesis often mentioned in biotechnological literature.