Integrating autoencoder with Koopman operator to design a linear data-driven model predictive controller

Abstract

Non-linear model predictive control (NMPC) is increasingly seen as a promising tool to tackle the problem of handling process nonlinearity and achieve optimal operation. One roadblock to NMPC implementation, however, is the lack of a good model, whether a first-principles-based or a non-linear data-driven-based model such as artificial neural networks (ANN). This manuscript proposes a data-driven modelling approach that integrates an autoencoder-like network and dynamic mode decomposition (DMD) methods to result in a non-linear modelling technique where the non-linearity in the model stems from the modelling of the measured variables. The proposed method results in a semi-linear state-space model where the mapping between the model state and outputs are non-linear (via the autoencoder-like network) while the model dynamics are linear. In the subsequent model predictive controller (MPC) implementation, the autoencoder translates setpoints and outputs to the states of a state space model. The proposed approach is illustrated using a continuously stirred tank reactor simulation example. For comparison, a linear MPC and non-linear MPC based on a traditional neural network (NN) model, a classic Koopman operator-based MPC, and (to benchmark) a perfect model-based NMPC are implemented and tested on several setpoint tracking tasks. The proposed MPC design outperforms the other data driven MPCs, and has similar performance as the first-principles-based NMPC while requiring less computational time and without requiring first principles knowledge.