Robust tube-based model predictive control of LPV systems subject to adjustable additive disturbance set

• Published in: Automatica (Oxford) Vol. 129; p. 109672
• Main Authors: Heydari, Reza, Farrokhi, Mohammad
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2021
• Subjects: Adjustable disturbance set; Linear parameter varying systems; Robust control; Tube model predictive control; Robust control; Adjustable disturbance set; Tube model predictive control; Linear parameter varying systems
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2021.109672

This paper proposes a robust tube-based model predictive control for polytopic linear parameter varying systems subject to bounded additive disturbances. In the proposed method, the future scheduling evolutions are described by a known nominal trajectory and some constant uncertainty sets around the nominal signals. Then, by using the notion of polar dual set, a cross-section varying tube parameterization is constructed to robustly satisfy the state and control constraints. Additionally, in contrast to the classical robust MPC problems with a priory known and fixed disturbance set, the shape and size of the additive disturbance set is maximized online through the MPC optimization problem. Therefore, at each time step, the control sequence and the largest allowable disturbance set can be computed simultaneously by solving a single constrained optimal control problem. Numerical simulation demonstrates the efficacy of the proposed approach.