Offset-free Nonlinear Model Predictive Control with LSTM neural networks

The aim of this thesis is to investigate how LSTM neural network models can be exploited in the design of advanced control schemes, such as nonlinear Model Predictive Control (MPC). LSTM neural networks have been successfully employed in the analysis and forecast of time-series, but in the literature there exist only few theoretical results about their use in the control design. In particular the convergence of LSTM based MPC have been studied only in the nominal case, i.e. under the assumption that the plant behaves exactly as its model. But in real world applications model-plant mismatch and disturbances are almost always present. If the MPC is designed only regarding the nominal case it is possible to have a degradation of performances when it is applied to the real plant. To solve this problem there exist specific techniques, that can be applied also for the LSTM based MPC. In this thesis an offset-free nonlinear MPC is obtained by augmenting with a constant disturbance the output equation of the LSTM model. To facilitate the control design and to obtain a closed loop system with desirable properties, it is convenient to rely on models satisfying particular stability properties. For this reason in the scope of this thesis the control algorithms are based on LSTM networks whose weights are constrained to provide Incrementally Input-to-State Stable (δISS) models. In particular it is presented how it is possible to design a converging observer for the states of the augmented δISS LSTM, a reference calculator and an MPC based on the LSTM model. The convergence of such closed-loop system to the reference is proven in formal way. The performances of the control system are numerically tested on a pH neutralization process, where the properties of the proposed MPC algorithm are evident both for tracking and for disturbance rejection.