Robust MPC with recursive model update

Journal article

Robust constrained control of linear systems with parametric uncertainty and additive disturbance is addressed. The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism. Requirements for closed-loop stability and provable constraint satisfaction are considered separately, resulting in the use of online set-membership system identification combined with homothetic prediction tubes for robust constraint satisfaction, and an $\mathcal H_\infty$ optimal point estimate of the unknown parameters to achieve a finite closed-loop gain from the disturbance to the state. Extensions to time-varying parameters and persistently exciting inputs to guarantee parameter convergence are presented. A numerical example illustrates the proven properties and efficacy of the approach.

Authors: Lorenzen, M; Cannon, M; Allgower, F

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Automatica
• Volume: 103
• Pages: 461-471
• Publication date: 2019-03-05
• Acceptance date: 2019-01-24
• DOI: 10.1016/j.automatica.2019.02.023
• ISSN: 0005-1098
• Keywords: adaptive model predictive control; adaptive control; model predictive control; control of constrainedsystems; receding horizon control; system identification; uncertain linear systems