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.