# BP-MPC: Optimizing the Closed-Loop Performance of MPC using BackPropagation

arXiv: https://arxiv.org/abs/2312.15521 · HTML: https://mlsanity.com/paper/2312.15521/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2023.

## Built on by (most cited first, 3 of 3)

- [Differentiable Nonlinear Model Predictive Control](https://mlsanity.com/paper/2505.01353/) (2025)
- [A Systematic Review and Taxonomy of Reinforcement Learning-Model Predictive Control Integration for Linear Systems](https://mlsanity.com/paper/2604.21030/) (2026)
- [Pick-to-Learn Calibration of an MPC Policy for an Origin-to-Destination Flight Problem](https://mlsanity.com/paper/2607.16084/) (2026)

## Abstract (arXiv)

Model predictive control (MPC) is pervasive in research and industry. However, designing the cost function and the constraints of the MPC to maximize closed-loop performance remains an open problem. To achieve optimal tuning, we propose a backpropagation scheme that solves a policy optimization problem with nonlinear system dynamics and MPC policies. We enforce the system dynamics using linearization and allow the MPC problem to contain elements that depend on the current system state and on past MPC solutions. Moreover, we propose a simple extension that can deal with losses of feasibility. Our approach, unlike other methods in the literature, enjoys convergence guarantees.