A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation

• Published in: Journal of the Franklin Institute Vol. 361; no. 6; p. 106713
• Main Authors: Morato, Marcelo M., Cunha, Victor M., Santos, Tito L.M., Normey-Rico, Julio E., Sename, Olivier
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-04-2024; Elsevier
• Subjects: Automatic; Engineering Sciences; Linear parameter varying systems; Model predictive control; Nonlinear systems; Tracking; Zonotopes; Model predictive control; Zonotopes; Tracking; Nonlinear systems; Linear parameter varying systems; Tracking Model Predictive Control; Linear Parameter Varying Systems
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2024.106713

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques.