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

Published 24 Jan 2024 in math.OC, cs.SY, and eess.SY | (2401.13762v2)

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 $\mathcal{O}(N2 ( n_x3 +n_u3))$ for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to $103$ compared to general-purpose commercial solvers.

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