Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions

TL;DR

This paper presents a fast, scalable algorithm for robust model predictive control using system level synthesis, leveraging Riccati recursions to significantly improve computational efficiency for linear time-varying systems.

Contribution

It introduces a tailored Riccati recursion-based algorithm for disturbance feedback optimization in robust MPC, achieving linear convergence and substantial speedups over general solvers.

Findings

Achieves up to 1000x speedup in computation.

Demonstrates linear convergence of the proposed algorithm.

Scales efficiently with horizon, state, and input dimensions.

Abstract

System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of $\mathcal{O}(N^2 ( n_x^3 +n_u^3))$ for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to $10^3$ compared to general-purpose commercial solvers.