Learning-based rigid tube model predictive control

Conference item

This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an algorithm incorporating online learning that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using disturbance realisations. A key novelty is that the parameterisation of these quantified disturbance sets enjoys desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems is discussed. Numerical simulations are provided to demonstrate the effectiveness of our proposed algorithm and compare with conventional robust MPC algorithms.

Authors: Gao, Y; Yan, S; Zhou, J; Cannon, M; Abate, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: PMLR
• Host title: Proceedings of the 6th Annual Learning for Dynamics & Control Conference
• Pages: 492-503
• Series: Proceedings of Machine Learning Research
• Series number: 242
• Publication date: 2024-10-01
• Acceptance date: 2025-04-23
• Event title: 6th Annual Learning for Dynamics & Control Conference (L4DC 2024)
• Event location: University of Oxford, Oxford, UK
• Event website: https://l4dc.web.ox.ac.uk/home
• Event start date: 2024-07-15
• Event end date: 2024-07-17
• EISSN: 2640-3498
• Language: English
• Keywords: rigid tube MPC; learning uncertainty; scenario approach