Learning model predictive control of nonlinear systems with time-varying parameters using Koopman operator

Koopman operator with numerical approximation method for modelling nonlinear systems has become a popular data-driven approach in the past five years. However, when the system contains time-varying parameters, the data-driven Koopman operator-based model produces deviations between the nominal model and the true one. It affects the control performance when it serves as the nominal model in Model Predictive Control (MPC). To solve this issue, the Koopman operator-based model learned by using a multi-step prediction autoencoder and the strategy of online updating model are proposed. In the first step, a neural network with encoder-decoder structure is trained to search for the optimal lifted functions of the corresponding nonlinear system with fixed parameters. In the second step, an online updating strategy is presented to update the Koopman operator-based model using the collected data, when the nominal model is applied in the closed loop operation of MPC. In order to reduce the additional time consumption on updating the nominal model, the matrix inversion lemma is applied and it leads the strategy of updating to be presented in a recursive form. In general, this paper proposed an iterative MPC algorithm for online updating the Koopman operator-based model in a recursive form based on the optimal lifted function using autoencoder. Numerical simulations on three nonlinear cases with time-varying parameters show good performances on tracking control using the proposed Koopman operator-based model using autoencoder and online updating strategy.