Trustworthy data-driven model predictive control using a hybrid model with monitoring and adaptation of the domain of validity

The quality of the plant model is a key factor for a successful implementation of model predictive control schemes. An inaccurate process model can result in unsatisfactory dynamics of the controlled system and may lead to violations of quality and safety constraints or even instability. Building reliable models that are based on physics and chemistry can be challenging in practice due to the difficulty of accurately modeling all aspects of the real system, and there will always be discrepancies between the model and the behavior of the real plant. Recently, there has been a renewed research trend to use or incorporate data-driven models that are obtained by machine learning algorithms into model predictive control (MPC). However, developing reliable standalone data-driven models needs large sets of training data that are obtained for sufficiently rich excitation of the system which are not often available in practice. A promising direction to overcome this issue is the use of hybrid process models which combine models based on first-principles and data-based elements. In this work, we present and evaluate a nonlinear model predictive control approach based on a hybrid model that is formed of a simplified first-principles model and a data-based model to capture the dynamics that are not adequately represented in the semi-rigorous model. In order to increase the reliability of the hybrid model, the domain of validity of the data-based model element is monitored and the contribution of the data-based model component is faded out when the plant is not operated in the region where sufficient data had been collected. Moreover it is proposed to adapt the domain of validity of the data-based component based on the measured data during operation. An extensive simulation study of an industrial control problem using a faithful simulation model is performed to investigate the potential of the approach for a typical complex application. The use of the hybrid model with and without adaptation of the domain of validity is compared to conventional nonlinear model predictive control using the simplified physics-based model, and a nonlinear model predictive controller based on a standalone data-driven model for different situations regarding the available data set for model training and the operating conditions of the plant.