Closed-loop training of static output feedback neural network controllers for large systems: A distillation case study

The online implementation of model predictive control has two main disadvantages: it requires an estimate of the entire model state and an optimisation problem must be solved online. These issues have typically been treated separately. This work proposes an integrated approach for the offline training of an output feedback neural network controller in closed-loop. As the training is performed offline, the neural network can be efficiently evaluated online to find control actions given noisy measurements as inputs. In addition, as the controller is trained in closed loop we are able to train for robustness to uncertainty and also design the controller to only use a selection of measurements. The choice of measurements can greatly change the controller performance and robustness. We demonstrate that although measurements can be automatically selected by regularisation, choosing measurements based on engineering judgement is an effective alternative. The proposed method is demonstrated by extensive simulations using a non-linear distillation column model of 50 states. We show that a controller using only 4 measurements is able to control the system with a decrease in performance of only 15% compared to MPC with perfect state feedback.