Resilient Sparse Controller Design with Guaranteed Disturbance Attenuation

TL;DR

This paper presents a novel framework for designing resilient sparse state-feedback controllers for LTI systems that guarantees a specified al performance measure, balancing sparsity, robustness, and performance.

Contribution

It introduces a new method combining non-fragile control theory with sparsification techniques to ensure performance guarantees in sparse controller design.

Findings

First framework with performance guarantees for sparse feedback gain.

Tradeoff analysis between sparsity, performance, and fragility.

Use of greedy and re-weighted al norm minimization techniques.

Abstract

We design resilient sparse state-feedback controllers for a linear time-invariant (LTI) control system while attaining a pre-specified guarantee on ${\mathcal{H}}_\infty$ performance measure. We leverage a technique from non-fragile control theory to identify a region of resilient state-feedback controllers. Afterward, we explore the region to identify a sparse controller. To this end, we use two different techniques: the greedy method of sparsification, as well as the re-weighted $\ell_1$ norm minimization. Our approach highlights a tradeoff between the sparsity of the feedback gain, performance measure, and fragility of the design. To best of our knowledge, this work is the first framework providing performance guarantees for sparse feedback gain design.