# Robust adaptive model predictive control with persistent excitation conditions

arXiv: https://arxiv.org/abs/2211.09275 · HTML: https://mlsanity.com/paper/2211.09275/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2022.

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

- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets](https://mlsanity.com/paper/2406.00574/) (2024)

## Abstract (arXiv)

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop control actions are introduced for a set-membership parameter identification scheme. The algorithm requires the online solution of a convex program, satisfies constraints robustly, and ensures recursive feasibility and input-to-state stability. Almost sure convergence to the actual system parameters is demonstrated under assumptions on stabilizability, reachability, and tight disturbance bounds.