Two-Timescale Optimization Framework for Decentralized Linear-Quadratic Optimal Control
<|reference_start|>Two-Timescale Optimization Framework for Decentralized Linear-Quadratic Optimal Control: A $\mathcal{H}_2$-guaranteed decentralized linear-quadratic optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where several sparsity promoting functions are added, respectively, into the $\mathcal{H}_2$ cost to penalize the number of communication links among decentralized 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 weighted-$\ell_1$ sparsity promoting function is of concern, and a two-timescale algorithm is developed based on the BSUM (Block Successive Upper-bound Minimization) framework and a primal-dual splitting approach. Second, the optimization problem induced by piecewise quadratic sparsity penalty is investigated, which exhibits an accelerated convergence rate. Third, the nonconvex sparse optimization problem with $\ell_0$-penalty is studied, which can be approximated by successive coordinatewise convex optimization problems.<|reference_end|>
@article{feng2024two-timescale,
    title={Two-Timescale Optimization Framework for Decentralized Linear-Quadratic
  Optimal Control},
    author={Lechen Feng, Yuan-Hua Ni, Xuebo Zhang},
    journal={arXiv preprint arXiv:2406.11168},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.11168},
    primaryClass={math.OC cs.LG}
}