Work

H 2 -Optimal Estimation of Linear Delayed and PDE Systems

Year: 2025

Type: conference-paper

Abstract: The H2norm is a commonly used performance metric in the design of estimators. However, H2-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 H2-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 H2-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 H2-optimal estimation problem. The resulting observers are validated using numerical simulation.

Source: IEEE Conference on Decision and Control (CDC)

DOI: 10.1109/cdc57313.2025.11312977

Authors: Danilo Braghini, Sachin Shivakumar, Matthew M. Peet

Institutions: Arizona State University, Los Alamos National Laboratory

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Collaborative Research: Robust Control of Large-Scale Networks with Variable Delays using Partial Integral Equations