# Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

arXiv: https://arxiv.org/abs/1909.01813 · HTML: https://mlsanity.com/paper/1909.01813/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2019.

## Built on by (most cited first, 8 of 8)

- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [Non-asymptotic System Identification for Linear Systems with Nonlinear Policies](https://mlsanity.com/paper/2306.10369/) (2023)
- [Adaptive Robust Model Predictive Control via Uncertainty Cancellation](https://mlsanity.com/paper/2212.01371/) (2022)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)

## Abstract (arXiv)

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction and stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain L2 stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example. This paper is an extended version of~[1], and contains additional details regarding the theoretical proof of Theorem~1, the numerical example, and the offline computations in Appendix~A--B.