Data-Driven Modeling of Photosynthesis Regulation Under Oscillating Light Condition - Part I: In-Silico Exploration

TL;DR

This work addresses how to model photosynthesis regulation under oscillating light using data-driven, control-oriented methods. It first applies Best Linear Approximation (BLA) in the frequency domain to in-silico data generated by the Basic DREAM Model (BDM) to obtain local second-order transfer functions across varying DC light levels and modulation frequencies. Building on these local models, the authors construct a Linear Parameter-Varying (LPV) representation with the DC light value $u_{dc}$ as the scheduling variable, yielding a compact state-space description that interpolates across operating regimes. The combination of multisine excitation and both nonparametric FRF analysis and parametric LS/WLS fitting demonstrates good agreement between the LPV predictor and the nonlinear BDM under unseen inputs, highlighting a practical route toward control-oriented, data-driven modeling for lighting optimization in photosynthesis.

Abstract

This paper explores the application of data-driven system identification techniques in the frequency domain to obtain simplified, control-oriented models of photosynthesis regulation under oscillating light conditions. In-silico datasets are generated using simulations of the physics-based Basic DREAM Model (BDM) Funete et al.[2024], with light intensity signals -- comprising DC (static) and AC (modulated) components as input and chlorophyll fluorescence (ChlF) as output. Using these data, the Best Linear Approximation (BLA) method is employed to estimate second-order linear time-invariant (LTI) transfer function models across different operating conditions defined by DC levels and modulation frequencies of light intensity. Building on these local models, a Linear Parameter-Varying (LPV) representation is constructed, in which the scheduling parameter is defined by the DC values of the light intensity, providing a compact state-space representation of the system dynamics.

Figures (14)

• Figure 1: Spectrum of multisine signal with random phase and amplitude of $38\mu Em^{-2}s^{-1}$PintelonSchoukens2012BookSystemIdentificationSchoukens2012BookMasteringSysId.
• Figure 2: Magnitude spectrum of fluorescence in response to multisine light intensity with an amplitude of $38\mu E,m^{-2},s^{-1}$ and a DC value of $100\mu E,m^{-2},s^{-1}$. The plot distinguishes between linear and nonlinear behavior.
• Figure 3: Comparison of nonparametric and parametric (LS) models for fluorescence response to multisine light intensity (amplitude: $38\mu Em^{-2}s^{-1}$, DC value: $100\mu Em^{-2}s^{-1}$).
• Figure 4: Comparison of nonparametric and parametric (WLS) models for fluorescence response to multisine light intensity (amplitude: $38\mu Em^{-2}s^{-1}$, DC value: $100\mu Em^{-2}s^{-1}$).
• Figure 5: LPV model structure.