Distributed estimation for a class of nonlinear systems with application to Navier‐Stokes flow estimation

Park, Derek; Guay, Martin

doi:10.1002/cjce.22090

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…To address this challenge, closed‐loop AFC systems based on ROMs must incorporate observers (or estimators), which are capable of generating estimates of the unmeasurable states using direct sensor measurements. () The theoretical design of nonlinear observers for flow systems is further complicated by the fact that the mathematical form of the sensor measurement equation is in a nonstandard form. Due, in part, to these practical challenges, the design of suitable closed‐loop AFC methods remains a challenging task.…”

Section: Introductionmentioning

confidence: 99%

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Kidambi

Ramos-Pedroza

MacKunis

et al. 2018

Intl J Robust & Nonlinear

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Summary Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO.

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Section: Introductionmentioning

confidence: 99%

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Kidambi

Ramos-Pedroza

MacKunis

et al. 2018

Intl J Robust & Nonlinear

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show abstract

“…There has been some work on developing observers for Navier-Stokes based systems. The papers [35,20,28] work with finite dimensional approximations of the PDE involved whereas we work with the full PDE itself. A completely different approach based on developing observers using appropriate continuous time limits of discrete time 3D-var or Kalman filter is developed in a series of papers [22,24,8] and also in [7,2,1,27,18,4].…”

mentioning

confidence: 99%

Observers for Compressible Navier--Stokes Equation

Apte¹,

Auroux²,

Ramaswamy³

2018

SIAM J. Control Optim.

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We consider a multi-dimensional model of a compressible fluid in a bounded domain. We want to estimate the density and velocity of the fluid, based on the observations for only velocity. We build an observer exploiting the symmetries of the fluid dynamics laws. Our main result is that for the linearised system with full observations of the velocity field, we can find an observer which converges to the true state of the system at any desired convergence rate for finitely many but arbitrarily large number of Fourier modes. Our one-dimensional numerical results corroborate the results for the linearised, fully observed system, and also show similar convergence for the full nonlinear system and also for the case when the velocity field is observed only over a subdomain.

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Distributed estimation for a class of nonlinear systems with application to Navier‐Stokes flow estimation

Cited by 2 publications

References 27 publications

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Observers for Compressible Navier--Stokes Equation

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