H₂-Optimal Estimation of a Class of Linear PDE Systems using Partial Integral Equations

2024/11/04 by Braghini, Danio, Shivakumar, Sachin, Peet, Matthew M. · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2411.01793

Abstract

The H₂ norm is a commonly used performance metric in the design of estimators. However, H₂-optimal estimation of most PDEs is complicated by the lack of state-space and transfer function representations. To address this problem, we 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 formulate the associated H₂-optimal estimation problem. The optimal observer synthesis problem is then recast as an LPI, and the resulting observers are validated using numerical simulation.

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