# A Semi-Definite Programming Approach to Robust Adaptive MPC under State Dependent Uncertainty

arXiv: https://arxiv.org/abs/1910.04378 · HTML: https://mlsanity.com/paper/1910.04378/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2019.

## 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 propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known Lipschitz constant. We use a non-parametric technique for online identification of the system uncertainty by approximating its graph via envelopes defined by quadratic constraints. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction for the closed loop system for all possible values of system uncertainty modeled by the envelope. The uncertainty envelope is refined with data using Set Membership Methods. We highlight the efficacy of the proposed framework via a detailed numerical example.