Adaptive data-based model predictive control of batch systems

In this work, we generalize a previously developed multi-model, data-based modeling approach for batch processes to account for time-varying dynamics by incorporating online learning ability into the model. The application of the standard recursive least squares (RLS) algorithm with a forgetting factor for the model form leads to unnecessary updates for some of the models. We address this issue by developing a probabilistic RLS (PRLS) estimator (also with a forgetting factor) for each model that takes the probability of the model being representative of the current plant dynamics into account in the update. The main advantage of adopting this local update approach is adaptation tuning flexibility. Specifically, the model adaptations can be made more aggressive while maintaining better parameter precision compared to the the standard RLS algorithm. The benefits from using the PRLS algorithm for model adaptation are demonstrated via simulations of a nylon-6,6 batch polymerization reactor. The model adaptation is shown to be crucial for achieving acceptable control performance when encountering large disturbances in the initial conditions.