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

TL;DR

This paper introduces a convex optimization approach to design sparse actuator configurations for LPV systems, ensuring specified $ ext{H}_2/ ext{H}_ extinfty$ performance, demonstrated on a flexible wing vibration control case.

Contribution

It is the first to address sparse actuation design for LPV systems within the $ ext{H}_2/ ext{H}_ extinfty$ framework using convex optimization.

Findings

Achieved sparse actuation with minimized actuator magnitude limits.

Guaranteed closed-loop performance in $ ext{H}_2/ ext{H}_ extinfty$ norms.

Validated approach on a flexible wing vibration control problem.

Abstract

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 $\mathcal{H}_2/\mathcal{H}_\infty$ 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.