# Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM

arXiv: https://arxiv.org/abs/2001.00306 · HTML: https://mlsanity.com/paper/2001.00306/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2020.

## Built on by (most cited first, 2 of 2)

- [Two-Timescale Optimization Framework for Sparse-Feedback Linear-Quadratic Optimal Control](https://mlsanity.com/paper/2406.11168/) (2024)
- [Douglas-Rachford Splitting for Group-Sparse Feedback Linear-Quadratic Control](https://mlsanity.com/paper/2507.19895/) (2025)

## Abstract (arXiv)

The H2 guaranteed cost decentralized control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational effectiveness. A comprehensive analysis is given on the application of the approach in solving the optimal decentralized control problem; and subsequently, the preserved decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed optimization approach.