Wen-Hua, Chen;
Yan, Yunda;
(2024)
New Stability Theory of Model Predictive Control: Modified Stage Cost Approach.
International Journal of Systems Science
, 56
(4)
pp. 808-826.
10.1080/00207721.2024.2409846.
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Abstract
This paper presents a promising new approach to establish the stability of finite receding horizon control with a terminal cost. Departing from the traditional approaches of using the property of the terminal cost or relaxed Lyapunov inequalities, this paper establishes its stability based on the property of a modified stage cost. First, we rotate the stage cost with the terminal cost. Then a one-step optimisation problem is defined based on this augmented stage cost. It is shown that a slightly modified Model Predictive Control (MPC) algorithm is stable if the value function of the augmented one-step cost (OSVF) is a Control Lyapunov Function (CLF). Stability for MPC algorithms with zero terminal cost or even negative terminal cost can be unified with this new approach. Combining it with the existing MPC stability theories, we are able to significantly relax the stability requirement on MPC and extend the stabilising MPC design space to the region that no existing MPC stability theories can cover. The proposed stage cost-based approach will help to further reduce the gap between stability theory and practical applications of MPC and other optimisation-based control methods.
| Type: | Article |
|---|---|
| Title: | New Stability Theory of Model Predictive Control: Modified Stage Cost Approach |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/00207721.2024.2409846 |
| Publisher version: | https://www.tandfonline.com/journals/TSYS |
| Language: | English |
| Additional information: | This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. |
| Keywords: | Finite horizon; optimisation; stability; model predictive control; constraints |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10197594 |
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