Model for Photosynthesis and Photoinhibition: Parameter Identification Based on the Harmonic Irradiation $O_{2}$ Response Measurement

A method for parameter identification of a model describing the growth of the algae is presented. The method is based on the description in the form of the so-called photosynthetic factory. The experimental data are gained by measuring the steady-state photosynthetic production when the input of the photosynthetic factory (light intensity) is a harmonic signal. Estimation of parameters is based on a sufficient number of experiments compared with simulated data via the least-squares technique. As the input signal is harmonic and the dynamics of the unforced system is exponentially stable, the resulting asymptotical steady-state trajectory of the photosynthetic factory is also periodic and can be computed via determining an appropriate center manifold graph by solving the corresponding first-order partial differential equation. The latter is performed by the finite-element method. The application of the proposed method is demonstrated on an example using real experimental data.