A direct optimization algorithm for input-constrained MPC

• URL: http://arxiv.org/abs/2306.15079v6
• Date: Sat, 30 Mar 2024 11:15:05 GMT
• Title: A direct optimization algorithm for input-constrained MPC
• Authors: Liang Wu, Richard D. Braatz,
• Abstract summary: This technical note considers input-constrained MPC problems and exploits the structure of the resulting box-constrained QPs. We prove that the number of iterations of our proposed algorithm is textitonly dimension-dependent. The execution-time-certified capability of our algorithm is theoretically and numerically validated through an open-loop unstable AFTI-16 example.
• Score: 3.0992677770545254
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\left\lceil\frac{\log(\frac{2n}{\epsilon})}{-2\log(\frac{\sqrt{2n}}{\sqrt{2n}+\sqrt{2}-1})}\right\rceil \!+ 1$, where $n$ denotes the problem dimension and $\epsilon$ 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.

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