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arXiv · 2411.01793

$H_2$-Optimal Estimation of Linear Delayed and PDE Systems

Danio Braghini·Sachin Shivakumar·Matthew M. Peet
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Abstract

The $H_2$ norm is a commonly used performance metric in the design of estimators. However, $H_2$-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 $H_2$-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 $H_2$-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 $H_2$-optimal estimation problem. The observer synthesis problem is then recast as an LPI, and the resulting observers are validated using numerical simulation.

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Danio Braghini, Sachin Shivakumar, Matthew M. Peet. 2024-11-04. $H_2$-Optimal Estimation of Linear Delayed and PDE Systems. https://doi.org/10.1109/cdc57313.2025.11312977

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