Robust Model Predictive Control via System Level Synthesis

In this paper, we consider the robust model predictive control (MPC) problem of a linear time-variant (LTV) system with both norm-bounded disturbances and model uncertainty. In robust MPC, a series of constrained optimal control problems (OCPs) are solved. Solving these robust OCPs is challenging since disturbances can cause deviation from the predicted states and model uncertainty can render the closed-loop system unstable. A trade-off between the numerical tractability and conservativeness of the solutions is often required. We use the System Level Synthesis (SLS) framework to reformulate the robust OCP as an optimization problem over closed-loop system responses. Our contributions are: (i) solve robust MPC problems with model uncertainty and additive disturbances by synthesizing a robust state feedback controller through SLS, and (ii) significantly reduce the conservativeness in the solutions to the robust OCPs compared with existing SLS-based relaxation methods by exploiting the structure of the closed-loop responses. We conclude with numerical examples demonstrating the performance of our method.