# Indirect-adaptive Model Predictive Control for Linear Systems with Polytopic Uncertainty

arXiv: https://arxiv.org/abs/1509.07170 · HTML: https://mlsanity.com/paper/1509.07170/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2015.

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

- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [Adaptive Robust Model Predictive Control via Uncertainty Cancellation](https://mlsanity.com/paper/2212.01371/) (2022)

## Abstract (arXiv)

We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but unknown. Robust constraint satisfaction is obtained by constraints enforcing a robust control invariant. The terminal cost and set are constructed from a parameter-dependent Lyapunov function and the associated control law. The proposed design ensures robust constraint satisfaction and recursive feasibility, is input-to-state stable with respect to the parameter estimation error and it only requires the online solution of quadratic programs.