Semi-Data-Driven Model Predictive Control: A Physics-Informed Data-Driven Control Approach

Abstract: Data-enabled predictive control (DeePC) has emerged as a powerful technique to control complex systems without the need for extensive modeling efforts. However, relying solely on offline collected data trajectories to represent the system dynamics introduces certain drawbacks. Therefore, we present a novel semi-data-driven model predictive control (SD-MPC) framework that combines (limited) model information with DeePC to address a range of these drawbacks, including sensitivity to noisy data, lack of robustness, and a high computational burden. In this work we focus on the performance of DeePC in operating regimes not captured by the offline collected data trajectories and demonstrate how incorporating an underlying parametric model can counteract this issue. SD-MPC exhibits equivalent closed-loop performance as DeePC for deterministic linear time-invariant systems. Simulations demonstrate the general control performance of the proposed SD-MPC for both a linear time-invariant system and a nonlinear system modeled as a linear parameter-varying system. These results provide numerical evidence of the enhanced robustness of SD-MPC over classical DeePC.