Observability and controllability analysis of blood flow network

Chun Zong; Gen Qi Xu

doi:10.3934/mcrf.2014.4.521

Article Contents

2014, Volume 4, Issue 4: 521-554. Doi: 10.3934/mcrf.2014.4.521

This issue Previous Article Multivariable boundary PI control and regulation of a fluid flow system Next Article

Observability and controllability analysis of blood flow network

Chun Zong^1, and
Gen Qi Xu^1,

1.
Department of Mathematics, Tianjin University, Tianjin, 300072

Received: August 31, 2013

Revised: December 31, 2013

Published: November 2014

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Abstract

In this paper, we consider the initial-boundary value problem of a binary bifurcation model of the human arterial system. Firstly, we obtain a new pressure coupling condition at the junction based on the mass and energy conservation law. Then, we prove that the linearization system is interior well-posed and $L^2$ well-posed by using the semigroup theory of bounded linear operators. Further, by a complete spectral analysis for the system operator, we prove the completeness and Riesz basis property of the (generalized) eigenvectors of the system operator. Finally, we present some results on the boundary exact controllability and the boundary exact observability for the system.

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Mathematics Subject Classification: Primary: 93B05, 93B07; Secondary: 76Z05, 93B60.

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