$H_2$-Optimal Estimation of Linear Delayed and PDE Systems
Abstract
The norm is a commonly used performance metric in the design of estimators. However, -optimal estimation of most PDEs is complicated by the lack of transfer function and state-space representations. To address this problem, we first re-characterize the -norm in terms of a map from initial condition to output. We then leverage the Partial Integral Equation (PIE) state-space representation of systems of linear PDEs coupled with ODEs to recast this characterization of -norm as a convex optimization problem defined in terms of Linear Partial Integral (LPI) inequalities. We then parameterize a class of PIE-based observers and solve the associated -optimal estimation problem. The observer synthesis problem is then recast as an LPI, and the resulting observers are validated using numerical simulation.
Cite
@article{arxiv.2411.01793,
title = {$H_2$-Optimal Estimation of Linear Delayed and PDE Systems},
author = {Danio Braghini and Sachin Shivakumar and Matthew M. Peet},
journal= {arXiv preprint arXiv:2411.01793},
year = {2026}
}