# State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?

arXiv: https://arxiv.org/abs/2203.15471 · HTML: https://mlsanity.com/paper/2203.15471/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2022.

## Built on by (most cited first, 6 of 6)

- [Learning with Imperfect Models: When Multi-step Prediction Mitigates Compounding Error](https://mlsanity.com/paper/2504.01766/) (2025)
- [Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees](https://mlsanity.com/paper/2405.01292/) (2024)
- [Deep Learning Model Predictive Control for Deep Brain Stimulation in Parkinson's Disease](https://mlsanity.com/paper/2504.00618/) (2025)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing](https://mlsanity.com/paper/2607.18164/) (2026)

## Abstract (arXiv)

This paper contrasts recursive state space models and direct multi-step predictors for linear predictive control. We provide a tutorial exposition for both model structures to solve the following problems: 1. stochastic optimal control; 2. system identification; 3. stochastic optimal control based on the estimated model. Throughout the paper, we provide detailed discussions of the benefits and limitations of these two model parametrizations for predictive control and highlight the relation to existing works. Additionally, we derive a novel (partially tight) constraint tightening for stochastic predictive control with parametric uncertainty in the multi-step predictor.