${\mathcal{H}}_2/{\mathcal{H}}_{\infty }$ Optimal Control with Sparse Sensing and Actuation

Abstract

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.