# Linear tracking MPC for nonlinear systems Part II: The data-driven case

arXiv: https://arxiv.org/abs/2105.08567 · HTML: https://mlsanity.com/paper/2105.08567/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2021.

## Built on by (most cited first, 7 of 7)

- [Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations](https://mlsanity.com/paper/2311.05360/) (2023)
- [The Neuron as a Direct Data-Driven Controller](https://mlsanity.com/paper/2401.01489/) (2024)
- [Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning](https://mlsanity.com/paper/2205.15703/) (2022)
- [Urban traffic congestion control: a DeePC change](https://mlsanity.com/paper/2311.09851/) (2023)
- [The Benefit of Noise-Injection for Dynamic Gray-Box Model Creation](https://mlsanity.com/paper/2310.01517/) (2023)
- [Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach](https://mlsanity.com/paper/2511.09242/) (2025)
- [Data-driven generalized perimeter control: Z"urich case study](https://mlsanity.com/paper/2603.16599/) (2026)

## Abstract (arXiv)

We present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parametrization provided by the Fundamental Lemma of Willems et al. We use new input-output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the Fundamental Lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor.