# American Institute of Mathematical Sciences

2015, 12(5): 1127-1139. doi: 10.3934/mbe.2015.12.1127

## 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, United States 2 Electrical Engineering and Computer Science Department, Masdar Institute of Science and Technology, Masdar City, Abu Dhabi, United Arab Emirates 3 Department of Mathematics, University of Tennessee, 1403 Circle Dr, Ayres Hall 227, Knoxville, TN, 37996-2250, United States

Received  September 2014 Revised  March 2015 Published  June 2015

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.
Citation: Gregory Zitelli, Seddik M. Djouadi, Judy D. Day. Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1127-1139. doi: 10.3934/mbe.2015.12.1127
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##### References:
 [1] New Eng J Med, 369 (2013), 840-851. Google Scholar [2] Proceedings of the $52^{nd}$ IEEE Conference on Decision and Control, Florence, Italy, December 10-13 (2013), 3373-3378. Google Scholar [3] Springer-Verlag London, Ltd., London, 1999.  Google Scholar [4] American Mathematical Society, Providence, RI, 2007.  Google Scholar [5] Math Biosci Eng, 7 (2010), 739-763. doi: 10.3934/mbe.2010.7.739.  Google Scholar [6] J Exp Med, 174 (1991), 1209-1220. Google Scholar [7] Comput. Biol. Med., 38 (2008), 339-347. Google Scholar [8] 9th International Symposium on Dynamics and Control of Process Systems, 9 (2010), 272-277. Google Scholar [9] Springer-Verlag, New York, 1990. doi: 10.1007/978-1-4757-2101-0.  Google Scholar [10] J Theor Bio, 242 (2006), 220-236. doi: 10.1016/j.jtbi.2006.02.016.  Google Scholar [11] Wiley-Interscience, Hoboken, NJ, 2006. doi: 10.1002/0470045345.  Google Scholar [12] Oxford University Press, Oxford, 2008.  Google Scholar [13] Birkhäuser Boston, Inc, Boston, MA, 1992.  Google Scholar
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