Integrating dynamic neural network models with principal component analysis for adaptive model predictive control

This work addresses one aspect of the overparameterization problem in using artificial/recurrent neural networks (ANN/RNN) based dynamic models for model predictive control (MPC) implementations. The manuscript presents an approach to handle situations where the training data may not be sufficiently rich, and in particular, for handling historical data with correlated inputs. Two approaches are proposed. The key idea in the first method is to perform principal component analysis (PCA) on input space and then utilize the scores to build a PCA-RNN model. Next, a PCA-RNN-based MPC is designed to compute the optimal values of scores and subsequently determined the manipulated inputs. An alternative solution is proposed in the second approach by proposing a new constraint on squared prediction error (SPE) statistic in the RNN-based MPC to make prescribed inputs follow the PCA model constructed for training input data. Finally, an approach is presented that allows to break the correlation in the MPC implementation while maintaining model validity. This is done by first generating richer closed-loop data by implementing the SPE based MPC with slightly relaxed constraints (thus compromising only slightly on the closed loop performance). Then the new data is utilized to re-identify the model, and for use in the MPC. The efficacy of the proposed approaches to handle the problem of set-point tracking is evaluated using a chemical reactor example. The results are compared with a nominal MPC design, and the superior performance under the proposed formulations demonstrated.