Optimal growth by dynamic programming approach for reduced system for the microalgae culture

The optimal microalgae growth problem of the photosynthetic factory (PSF) is studied here. The objective is to maximize the photosynthetic production rate (related proportionally to the specific growth rate of microalgae) by manipulating the irradiance. Since microalgae growth is affected by slow and fast dynamics, an optimal control on the well known reduced model is shown. Since the optimal control obtained does not depend on the states of the system but only in the time, it can be assumed as an open loop control. This is an important result because measure cost can be omitted.