# Robust Model Predictive Control of Time-Delay Systems through System Level Synthesis

arXiv: https://arxiv.org/abs/2209.11841 · HTML: https://mlsanity.com/paper/2209.11841/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2022.

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

- [The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedback](https://mlsanity.com/paper/2305.00889/) (2023)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)

## Abstract (arXiv)

We present a robust model predictive control method (MPC) for discrete-time linear time-delayed systems with state and control input constraints. The system is subject to both polytopic model uncertainty and additive disturbances. In the proposed method, a time-varying feedback control policy is optimized such that the robust satisfaction of all constraints for the closed-loop system is guaranteed. By encoding the effects of the delayed states and inputs into the feedback policy, we solve the robust optimal control problem in MPC using System Level Synthesis which results in a convex quadratic program that jointly conducts uncertainty over-approximation and robust controller synthesis. Notably, the number of variables in the quadratic program is independent of the delay horizon. The effectiveness and scalability of our proposed method are demonstrated numerically.