A Direct Optimization Algorithm for Input-Constrained MPC
Name
2306.15079v6.pdf
Description
Accepted version
Size
224.62 KB
Format
Adobe PDF
Checksum (MD5)
c04aa7c3498fbf5f7e7ec8b79277ee0d
Author(s)
Wu, Liang
Braatz, Richard D
Date Issued
2024
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers
Citation
L. Wu and R. D. Braatz, "A Direct Optimization Algorithm for Input-Constrained MPC," in IEEE Transactions on Automatic Control.
Version
Author's final manuscript
Abstract
Providing an execution time certificate is a pressing requirement when deploying Model Predictive Control (MPC) in real-time embedded systems such as microcontrollers. Real-time MPC requires that its worst-case (maximum) execution time must be theoretically guaranteed to be smaller than the sampling time in closed-loop. This technical note considers input-constrained MPC problems and exploits the structure of the resulting box-constrained QPs. Then, we propose a \textit{cost-free} and \textit{data-independent} initialization strategy, which enables us, for the first time, to remove the initialization assumption of feasible full-Newton interior-point algorithms. We prove that the number of iterations of our proposed algorithm is \textit{only dimension-dependent} (\textit{data-independent}), \textit{simple-calculated}, and \textit{exact} (not \textit{worst-case}) with the value ⌈log(2nϵ)−2log(2n√2n√+2√−1)⌉+1, where n denotes the problem dimension and ϵ denotes the constant stopping tolerance. These features enable our algorithm to trivially certify the execution time of nonlinear MPC (via online linearized schemes) or adaptive MPC problems. The execution-time-certified capability of our algorithm is theoretically and numerically validated through an open-loop unstable AFTI-16 example.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1109/tac.2024.3463529
