# Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality

arXiv: https://arxiv.org/abs/2604.08521 · HTML: https://mlsanity.com/paper/2604.08521/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2026.

## Built on by (most cited first, 2 of 2)

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Learning to control switching nonlinear systems with Koopman operator regression](https://mlsanity.com/paper/2607.11344/) (2026)

## Abstract (arXiv)

We study closed-loop stability and suboptimality for MPC and infinite-horizon optimal control solved using a surrogate model that differs from the real plant. We employ a unified framework based on quadratic costs to analyze both finite- and infinite-horizon problems, encompassing discounted and undiscounted scenarios alike. Plant-model mismatch bounds proportional to states and controls are assumed, under which the origin remains an equilibrium. Under continuity of the model and cost-controllability, exponential stability of the closed loop can be guaranteed. Furthermore, we give a suboptimality bound for the closed-loop cost recovering the optimal cost of the surrogate. The results reveal a tradeoff between horizon length, discounting and plant-model mismatch. The robustness guarantees are uniform over the horizon length, meaning that larger horizons do not require successively smaller plant-model mismatch.