A data-driven framework integrating Lyapunov-based MPC and OASIS-based observer for control beyond training domains

Due to their predictive capabilities and computational efficiency, data-driven models are often employed in model predictive controller (MPC) design. These models offer precise predictions within their training domains, which aids in effective process control. However, real-world processes frequently experience operational changes, requiring control under new conditions that can lie beyond the training domains of existing data-driven models. Developing new models for these scenarios is challenging due to limited historical data. To address this limitation, we develop a novel data-driven control framework integrating an adaptive modeling approach called operable adaptive sparse identification of systems (OASIS) with the Luenberger observer. Firstly, we train the OASIS model and identify its domain of applicability (DA) using a support vector machine-based classifier. Subsequently, we formulate a Lyapunov-based MPC that relies on the OASIS model within the DA and the OASIS-based observer model beyond the DA. Additionally, we establish theoretical guarantees on the input-to-state stability of the observer, along with analyzing the stabilizability and recursive feasibility of the designed LMPC. The developed framework enhances the applicability of data-driven process control in diverse operating conditions. We highlighted its effectiveness using a chemical reactor example.