Sparse Actuation for LPV Systems with Full-State Feedback in ${\mathcal{H}}_2\mathrm{/}{\mathcal{H}}_{\mathrm{\infty }}$ Framework

This paper addresses the sparse actuation problem for nonlinear systems represented in the Linear Parameter-Varying (LPV) form. We propose a convex optimization framework that concurrently determines actuator magnitude limits and the state-feedback law that guarantees a user-specified closed-loop performance in the ${\mathcal{H}}_2\mathrm{/}{\mathcal{H}}_{\mathrm{\infty }}$ sense. We also demonstrate that sparse actuation is achieved when the actuator magnitude-limits are minimized in the $l_1$ sense. This is the first paper that addresses this problem for LPV systems. The formulation is demonstrated in a vibration control problem for a flexible wing.