# Two-Timescale Optimization Framework for Sparse-Feedback Linear-Quadratic Optimal Control

arXiv: https://arxiv.org/abs/2406.11168 · HTML: https://mlsanity.com/paper/2406.11168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Distributed Reinforcement Learning for Decentralized Linear Quadratic Control: A Derivative-Free Policy Optimization Approach](https://mlsanity.com/paper/1912.09135/) (2019)
- [Saddle-point dynamics: conditions for asymptotic stability of saddle points](https://mlsanity.com/paper/1510.02145/) (2015)
- [Iteration Complexity Analysis of Block Coordinate Descent Methods](https://mlsanity.com/paper/1310.6957/) (2013)
- [Optimization Landscape of Gradient Descent for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2109.13132/) (2021)
- [ADMM Penalty Parameter Selection by Residual Balancing](https://mlsanity.com/paper/1704.06209/) (2017)
- [Sparsity Invariance for Convex Design of Distributed Controllers](https://mlsanity.com/paper/1906.06777/) (2019)
- [An Accelerated Proximal Alternating Direction Method of Multipliers for Optimal Decentralized Control of Uncertain Systems](https://mlsanity.com/paper/2304.11037/) (2023)
- [Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM](https://mlsanity.com/paper/2001.00306/) (2020)
- [A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate](https://mlsanity.com/paper/2109.13467/) (2021)

## Abstract (arXiv)

A H2-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where ℓ0-penalty is added into the H2 cost to penalize the number of communication links among distributed controllers. Then, the sparse-feedback gain is investigated to minimize the modified H2 cost together with the stability guarantee, and the corresponding main results are of three parts. First, the ℓ1 relaxation sparse-feedback LQ problem is of concern, and a two-timescale algorithm is developed based on proximal coordinate descent and primal-dual splitting approach. Second, piecewise quadratic relaxation sparse-feedback LQ control is investigated, which exhibits an accelerated convergence rate. Third, sparse-feedback LQ problem with ℓ0-penalty is directly studied through BSUM (Block Successive Upper-bound Minimization) framework, and precise approximation method and variational properties are introduced.