Data-driven Model Predictive Control with Matrix Forgetting Factor

• Published in: IFAC-PapersOnLine Vol. 56; no. 2; pp. 10077 - 10082
• Main Authors: Calderőn, Horacio M., Schulz, Erik, Oehlschlägel, Thimo, Werner, Herbert
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2023
• Subjects: Data-driven; Koopman operator; model predictive control; recursive least squares; model predictive control; Koopman operator; Data-driven; recursive least squares
• ISSN: 2405-8963; 2405-8971; 2405-8963
• DOI: 10.1016/j.ifacol.2023.10.877

In this paper, a model predictive control (MPC) based on the Koopman operator framework is presented. This framework, allows to obtain a model solely from data. Moreover, it can be easily updated using a recursive least squares (RLS) approach. This aids the controller to deal with inaccuracies in the model parameters. The performance of the update mechanism can be enhanced by the inclusion of forgetting techniques. One of these is the addition of a constant forgetting factor (CFF) to the update equations. However, this technique can be very sensitive to noise and if the measured signals are not persistently exciting, numerical issues can occur. To avoid the latter, the matrix forgetting factor (MFF) presented in (Bruce et al., 2020) is used. This approach combines two forgetting techniques: variable-rate and variable-direction forgetting, which leads to a higher closed loop performance of the proposed controller.