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

TL;DR

This paper introduces a robust MPC approach for discrete-time linear systems with delays, uncertainties, and constraints, using System Level Synthesis to ensure robustness and scalability.

Contribution

It develops a convex quadratic program for robust control of delayed systems that is independent of delay horizon, enhancing scalability and robustness.

Findings

Effective handling of time delays and uncertainties.

Convex quadratic program with delay horizon-independent variables.

Numerical demonstrations confirm scalability and robustness.

Abstract

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.