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System Level Synthesis (SLS) enables improved robust MPC formulations byallowing for joint optimization of the nominal trajectory and controller. Thispaper introduces a tailored algorithm for solving the corresponding disturbancefeedback optimization problem. The proposed algorithm builds on a recentlyproposed joint optimization scheme and iterates between optimizing thecontroller and the nominal trajectory while converging q-linearly to an optimalsolution. We show that the controller optimization can be solved throughRiccati 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 numericalexample, the proposed algorithm exhibits computational speedups of order $10$to $10^3$ compared to general-purpose commercial solvers.

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