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The Use of the State Observer in the Simulation of the Process of the AntiAngiogenesis Therapy
# 12, December 2016
DOI: 10.7463/1216.0852798
authors: M.S. Vinogradova^{1,*}, S.B. Tkachev^{1}
 ^{1} Bauman Moscow State Technical University, Moscow, Russia 
Antiangiogenesis therapy is one of the modern and progressive methods for treatment of cancerous disease in which the growth of new vessels is suppressed. In the paper a model of cancerous tumour evolution in the framework of antiangiogenesis therapy is analyzed. Earlier a treatment for this model was developed which was determined by a distribution of medicament dose along the treatment. To reach the required result of the tumour volume reduction upto the given level the treatment requires 120 days. This result is refined using the differentialgeometric methods and the new scheme requires only 60 days. The proposed treatment schemes are based on the full state vector of the system but this can be hardly provided by measurements. Hence, the problem of observer design arises which obtains a state vector estimate from the measured tumour volume. In this note the normal form of the system is refined and an observer with high gain is designed. An estimate of the full state vector of the system obtained by the observer is used in the output feedback which stabilizes the system. An identification algorithm for parameters of the nonlinear system is also presented which is based on lower sample of the output measurement. The identification algorithm is based on using the observer. The theoretical results obtained in this work are verified by numerical simulation. References  Hahnfeldt P., Panigrahy D., Folkman J., Hlatky L. Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer research, 1999, vol. 59, iss. 19, pp. 4770–4775.
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