System Level Synthesis-based Robust Model Predictive Control through Convex Inner Approximation

TL;DR

This paper introduces a convex optimization-based robust MPC method using System Level Synthesis, which reduces conservatism and maintains computational efficiency for uncertain linear systems.

Contribution

It develops a convex quadratic program for robust control via SLS, with proven recursive feasibility and stability, improving over existing methods.

Findings

Reduces conservatism compared to existing SLS and tube-based MPC.

Ensures recursive feasibility and input-to-state stability.

Maintains low computational complexity.

Abstract

We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty. In our method, at each time step we solve a finite time robust optimal control problem (OCP) which jointly searches over robust linear state feedback controllers and bounds the deviation of the system states from the nominal predicted trajectory. By leveraging the System Level Synthesis (SLS) framework, the proposed robust OCP is formulated as a convex quadratic program in the space of closed-loop system responses. When an adaptive horizon strategy is used, we prove the recursive feasibility of the proposed MPC controller and input-to-state stability of the origin for the closed-loop system. We demonstrate through numerical examples that the proposed method considerably reduces conservatism when compared with existing SLS-based and tube-based robust MPC methods, while also enjoying low computational complexity.