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arXiv · 2406.11168

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

Lechen Feng·Yuan-Hua Ni·Xuebo Zhang
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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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Lechen Feng, Yuan-Hua Ni, Xuebo Zhang. 2024-06-17. Two-Timescale Optimization Framework for Sparse-Feedback Linear-Quadratic Optimal Control. https://arxiv.org/abs/2406.11168

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