Work

H∞-Optimal Estimator Synthesis for Linear 2D PDEs using Convex Optimization

Year: 2024

Type: article

Abstract: Any suitably well-posed PDE in two spatial dimensions can be represented as a Partial Integral Equation (PIE) – with system dynamics parameterized using Partial Integral (PI) operators. Furthermore, L 2 -gain analysis of PDEs with a PIE representation can be posed as a linear operator inequality, which can be solved using convex optimization. In this paper, these results are used to derive a convex-optimization-based test for constructing an H ∞ -optimal estimator for 2D PDEs. In particular, a PIE representation is first derived for arbitrary well-posed 2D PDEs with sensor measurements along boundaries of the domain. An associated Luenberger-type estimator is then parameterized using a PI operator ℒ as the observer gain. Next, it is shown that an upper bound on the H ∞ -norm of the error dynamics for the estimator can be minimized by solving a linear operator inequality on PI operator variables. Finally, an analytical formula for inversion of a sub-class of 2D PI operators is derived and used to reconstruct the Luenberger gain ℒ . Results are implemented in the PIETOOLS software suite – applying the methodology and simulating the estimator for an unstable 2D heat equation.

Source: IFAC-PapersOnLine

DOI: 10.1016/j.ifacol.2024.10.108

Authors: Declan S. Jagt, Matthew M. Peet

Institution: Arizona State University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: War on Boundary Conditions - A Control-Oriented Framework for Partial Differential Equations