Bayesian Model Update in a Horizon Estimation Framework

For industrial applications of Model Predictive Control, one important and widely used model class is the class of black-box models. Black-box models are typically identified at commissioning time from step tests on the plant. However, over time, their accuracy and hence their control performance may degrade, e.g. due to changing operating conditions of the controlled plant. In this paper, we propose a Bayesian approach for updating linear state space black-box models, based on closed loop data from the plant. Using the original model as a prior, we derive Maximum a Posteriori estimators by stating nonlinear horizon estimation problems and solving them with nonlinear programming. We demonstrate the effectiveness of our approach with two applications: a simple cart control task (double integrator) and a control of a rotary cement kiln. Our results indicate that the Bayesian approach has the potential to deliver improved model updates, in particular when used with limited data and especially closed-loop data.