Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen

Gregory  Zitelli; Seddik M.  Djouadi; Judy D.  Day

doi:10.3934/mbe.2015.12.1127

Article Contents

2015, Volume 12, Issue 5: 1127-1139. Doi: 10.3934/mbe.2015.12.1127

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Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen

1.
Department of Mathematics, University of California, Irvine, 340 Rowland Hall, Bldg #400, Irvine, CA 92697-3875
2.
Electrical Engineering and Computer Science Department, Masdar Institute of Science and Technology, Masdar City, Abu Dhabi
3.
Department of Mathematics, University of Tennessee, 1403 Circle Dr, Ayres Hall 227, Knoxville, TN, 37996-2250

Received: August 31, 2014

Revised: February 28, 2015

Published: May 2015

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Abstract

The inflammatory response aims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen. In cases of acute systemic inflammation, the possibility of collateral tissue damage arises, which leads to a necessary down-regulation of the response. A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present results on the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.

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Mathematics Subject Classification: Primary: 92C50, 93C15; Secondary: 93C83.

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