Adaptive data-driven Koopman model predictive control for spatiotemporal biological processes

This study proposes a data-driven Koopman model predictive control (MPC) framework for intervention in spatiotemporal biological processes. First, the system model governed by nonlinear partial differential equations (PDEs) is lifted into a higher-dimensional observable space using extended dynamic mode decomposition (EDMD), which yields a Koopman linear surrogate model constructed purely from simulation data. This linear representation then enables the formulation of a computationally efficient MPC scheme that drives the spatiotemporal biological system to exhibit a desired behaviour, while adhering to safety constraints imposed on system inputs, states, and outputs. Because almost all biological processes are subject to parameter variations or dynamic changes, a recursive least squares (RLS)-based online adaptation mechanism is proposed to update the Koopman model for enhanced robustness. We evaluate the control performance of the adaptive data-driven Koopman MPC on the FitzHugh–Nagumo model and the spatiotemporal epidemic model.