Modelling of a pH neutralization process via recurrent neural networks: stability study and possible control applications

The aim of this work is to explore and evaluate the identification capability of nonlinear dynamic systems through the use of recurrent neural networks and thus to create a clear picture of what identification techniques exploit the art Artificial Intelligence techniques. In particular way, in this thesis, the Long Short-Term Memory (LSTM) and the Echo State Network (ESN) are object of study. Some definitions and stability properties are recalled such as $\delta$Input-to-state stability (deltaISS) and Input-to-state stability (ISS) and their possible validity is studied on models obtained through recurrent neural networks. To do this, the pH neutralization process proposed by Hall and Seborg is implemented on the \textit{Simulink} simulation software, knowing a priori the equations that describe the dynamics of this system. The dynamic system under study, is highly nonlinear and it is simulated in order to obtain different datasets to train the neural networks. The structures of the ESN and LSTM networks are implemented on the Matlab software, and are subsequently trained and evaluated. The evaluation process consists of two phases: the validation phase and the testing phase. The validation phase is used to select the neural network that guarantees the best identification capability avoiding overfitting, while the testing phase is carried out using a dataset with different characteristics with respect to the training datasets, in order to guarantee the efficacy obtained during the validation. Furthermore, constraints are inserted in the training algorithm to ensure the stability properties mentioned above. Subsequently, the possible use of the ESN-based model to structure an algorithm based on advanced predictive control techniques (Model Predictive Control) is illustrated. The possible implementation of an observer is described, useful to estimate equilibrium states of the ESN networks required in the development of the controller. In conclusion, a study of less stringent constraints for the ESN training phase is recommended and the possibility of cancelling or reducing the dependence on the system's equilibria of the algorithm based on predictive control techniques is suggested. Due to the loss of generalization of the LSTM in the constrained case, a future development to study the causes of this problem and the research of possible improvements is suggested. It is also proposed, as a further development, the possibility of predicting the disturbances affecting the system, knowing its history, in order to allow better control actions.

Modellizzazione del processo di neutralizzazione del pH tramite reti neurali ricorrenti: studio di stabilità e possibili applicazioni di controllo