Sparse Sensing and Optimal Precision: Robust $\mathcal{H}_{\infty}$ Optimal Observer Design with Model Uncertainty

TL;DR

This paper develops a robust $ ext{H}_ ext{infty}$ optimal observer design framework that balances sparse sensor placement, minimal precision, and robustness against model uncertainties using convex optimization.

Contribution

It introduces a convex optimization approach for designing robust $ ext{H}_ ext{infty}$ observers with sparse sensors and minimal precision, accounting for structured and unstructured uncertainties.

Findings

Effective observer design with guaranteed performance under uncertainties.

Reduction in sensor count and precision without compromising robustness.

Numerical simulations validate the theoretical framework.

Abstract

We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the $\mathcal{H}_{\infty}$ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and unstructured uncertainties. The objective is to design an observer with a given $\mathcal{H}_{\infty}$ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible uncertainties. The problem is posed as a convex optimization problem subject to linear matrix inequalities. Numerical simulations demonstrate the application of the theoretical results presented in this work.