$\mathcalH_2/\mathcalH_\infty$ Optimal Control with Sparse Sensing and Actuation
<|reference_start|>$\mathcalH_2/\mathcalH_\infty$ Optimal Control with Sparse Sensing and Actuation: In this paper, we present novel convex optimization formulations for designing full-state and output-feedback controllers with sparse actuation that achieve user-specified $\mathcal{H}_2$ and $\mathcal{H}_\infty$ performance criteria. For output-feedback control, we extend these formulations to simultaneously design control laws with sparse actuation and sensing. The sparsity is induced through the minimization of a weighted $\ell_1$ norm, promoting the efficient use of sensors and actuators while maintaining desired closed-loop performance. The proposed methods are applied to a nonlinear structural dynamics problem, demonstrating the advantages of simultaneous optimization of the control law, sensing, and actuation architecture in realizing an efficient closed-loop system.<|reference_end|>
@article{deshpande2024$\mathcal{h}_2/\mathcal{h}_\infty$,
    title={$\mathcal{H}_2/\mathcal{H}_\infty$ Optimal Control with Sparse Sensing
  and Actuation},
    author={Vedang M. Deshpande and Raktim Bhattacharya},
    journal={arXiv preprint arXiv:2409.09596},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.09596},
    primaryClass={eess.SY cs.SY math.OC}
}