Detectability and global observer design for 2D Navier–Stokes equations with uncertain inputs

Sergiy Zhuk*, Mykhaylo Zayats, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present simulation friendly detectability conditions for 2D Navier–Stokes Equation (NSE) with periodic boundary conditions, and describe a generic class of “detectable” observation operators: it includes pointwise evaluation of NSE's solution at interpolation nodes, and spatial average measurements. For “detectable” observation operators we design a global infinite-dimensional observer for NSE with uncertain possibly destabilizing inputs: in our numerical experiments we illustrate H1-sensitivity of NSE to small perturbations of initial conditions, yet the observer converges for known and uncertain inputs.

Original languageEnglish
Article number111043
JournalAutomatica
Volume153
DOIs
StatePublished - Jul 2023

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