# Bounded-Regret MPC via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity

arXiv: https://arxiv.org/abs/2210.12312 · HTML: https://mlsanity.com/paper/2210.12312/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2022.

## Built on by (most cited first, 16 of 16)

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- [Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batching](https://mlsanity.com/paper/2601.10418/) (2026)
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## Abstract (arXiv)

We study Model Predictive Control (MPC) and propose a general analysis pipeline to bound its dynamic regret. The pipeline first requires deriving a perturbation bound for a finite-time optimal control problem. Then, the perturbation bound is used to bound the per-step error of MPC, which leads to a bound on the dynamic regret. Thus, our pipeline reduces the study of MPC to the well-studied problem of perturbation analysis, enabling the derivation of regret bounds of MPC under a variety of settings. To demonstrate the power of our pipeline, we use it to generalize existing regret bounds on MPC in linear time-varying (LTV) systems to incorporate prediction errors on costs, dynamics, and disturbances. Further, our pipeline leads to regret bounds on MPC in systems with nonlinear dynamics and constraints.