# Optimality Conditions for Model Predictive Control: Rethinking Predictive Model Design

arXiv: https://arxiv.org/abs/2412.18268 · HTML: https://mlsanity.com/paper/2412.18268/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2024.

## Built on by (most cited first, 4 of 4)

- [Bi-Level Reinforcement Learning Pathway for Sim-to-Real Optimality](https://mlsanity.com/paper/2510.17709/) (2025)
- [Mission-Aligned Learning-Informed Control of Autonomous Systems: Formulation and Foundations](https://mlsanity.com/paper/2507.04356/) (2025)
- [CORL: Reinforcement Learning of MILP Policies Solved via Branch and Bound](https://mlsanity.com/paper/2512.11169/) (2025)
- [Learning to control switching nonlinear systems with Koopman operator regression](https://mlsanity.com/paper/2607.11344/) (2026)

## Abstract (arXiv)

Optimality is a critical aspect of Model Predictive Control (MPC), especially in economic MPC. However, achieving optimality in MPC presents significant challenges, and may even be impossible, due to inherent inaccuracies in the predictive models. Predictive models often fail to accurately capture the true system dynamics, such as in the presence of stochasticity, leading to suboptimal MPC policies. In this paper, we establish the necessary and sufficient conditions on the underlying prediction model for an MPC scheme to achieve closed-loop optimality. Interestingly, these conditions are counterintuitive to the traditional approach of building predictive models that best fit the data. These conditions present a mathematical foundation for constructing models that are directly linked to the performance of the resulting MPC scheme.