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

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arxiv 2406.11168 v4 pith:KETNWRFA submitted 2024-06-17 math.OC cs.LG

Lechen Feng , Yuan-Hua Ni , Xuebo Zhang This is my paper · ORCID
classification math.OCcs.LG
keywords sparse-feedbackcontrolmathcalcostframeworkinvestigatedlinear-quadraticoptimal
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abstract

A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to penalize the number of communication links among distributed controllers. Then, the sparse-feedback gain is investigated to minimize the modified $\mathcal{H}_2$ cost together with the stability guarantee, and the corresponding main results are of three parts. First, the $\ell_1$ 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 $\ell_0$-penalty is directly studied through BSUM (Block Successive Upper-bound Minimization) framework, and precise approximation method and variational properties are introduced.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Convex Optimization Approach to Model-Free Inverse Optimal Control with Provable Convergence

    math.OC 2025-07 reject novelty 5.0 of 10

    A single-trajectory model-free inverse LQR method is reformulated as a convex conic feasibility problem and solved by BSUM with an O(1/k) sublinear convergence rate claim.

  2. Nonconvex Optimization Framework for Group-Sparse Feedback Linear-Quadratic Optimal Control: Penalty Approach

    math.OC 2025-07 reject novelty 5.0 of 10

    A penalty-based PALM algorithm solves a group-ℓ0 regularized LQ problem and converges to a critical point under explicit parameter conditions.

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