# A direct optimization algorithm for input-constrained MPC

arXiv: https://arxiv.org/abs/2306.15079 · HTML: https://mlsanity.com/paper/2306.15079/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 38 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Efficient Calibration of Embedded MPC](https://mlsanity.com/paper/1911.13021/) (2019)
- [A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control](https://mlsanity.com/paper/2109.10205/) (2021)
- [A Unifying Complexity Certification Framework for Active-Set Methods for Convex Quadratic Programming](https://mlsanity.com/paper/2003.07605/) (2020)
- [A construction-free coordinate-descent augmented-Lagrangian method for embedded linear MPC based on ARX models](https://mlsanity.com/paper/2207.06098/) (2022)

## Built on by (most cited first, 1 of 1)

- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)

## Abstract (arXiv)

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 textitcost-free and textitdata-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 textitonly dimension-dependent (textitdata-independent), textitsimple-calculated, and textitexact (not textitworst-case) with the value leftlceilfraclog(frac2nε)-2log(frac√2n√2n+√2-1)rightrceil !+ 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.