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Estimation of the Domain of Attraction of Free Tumor Equilibrium Point for Perturbed Tumor Immunotherapy Model | ||
| AUT Journal of Electrical Engineering | ||
| مقاله 7، دوره 50، شماره 2، اسفند 2018، صفحه 157-162 اصل مقاله (470.37 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/eej.2018.12086.5036 | ||
| نویسندگان | ||
| A. Dini؛ M.J. Yazdanpanah* | ||
| School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran | ||
| چکیده | ||
| In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We find a specific Lyapunov function in order to vanish maximum perturbation of modeling error, aging or uncertainties which exist in this system. Using this method and appropriate Lyapunov function, we demonstrate that there is an invariant polytope that for the set of perturbed initial conditions belonging to such region, the convergence to the healthy state is guaranteed. | ||
| کلیدواژهها | ||
| Nonlinear System؛ Equilibrium Point, Stability؛ Domain of Attraction؛ LMI, Lyapunov Function؛ Perturbation؛ Tumor-Free Equilibrium Point | ||
| مراجع | ||
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[1] Z. Bajzer, M. Marusic, S. Vuk-Pavlovic, “Conceptual frameworks for mathematical modeling of tumor growth dynamics,” Math. Comput. Model 23 (6) (1996) 447-455. [2] L.G. de Pillis, A.E. Radunskaya, “A mathematical tumor model with immune resistance and drug therapy: an optimal control approach,” J. Theor. Med. 3 (2001) 79-100. [3] L.G. de Pillis, A.E. Radunskaya, C.L. Wiseman, “A validated mathematical model of cell-mediated immune response to tumor growth,” Cancer Res. 65 (17) (2005) 7950-7958. [4] L.G. de Pillis, W. Gu, A.E. Radunskaya, “Mixed immunotherapy and chemotherapy of tumors: modeling applications and biological interpretations,” J. Theor. Biol. 238 (4) (2006) 841-862. [5] L.G. de Pillis, A.E. Radunskaya, “The dynamics of an optimally Controlled tumor model: A case study,” Math. Comput. Model, (37) (2003) 1221-1244. [6] A. Merola, C. Cosentino, F. Amato, “An insight into tumor dormancy equilibrium via the analysis of its domain of attraction,” Bio. 3 (2008) 212-219. [7] J.A. Spratt, D. von Fournier, J.S. Spratt, E.E. Weber, “Decelerating growth and human breast cancer,” Cancer 71 (1992) 2013-2019. [8] R. Eftimie, J.L. Bramson. D.J.D. Earn, “Interactions between immune system and cancer: a brief review of non-spatial mathematical models,” Bull. Math. Biol. 73 (2011) 2-32. [9] R. Genesio, M. Tartaglia, and A. Vicino, “On the estimation of asymptotic stability regions: State of the art and new proposals,” IEEE Transaction on Automatic Control, vol. 30, pp. 747-755, 1985. [10] H. Chiang, M. Hirsch, and F. Wu, “Stability regions of nonlinear autonomous dynamical systems,” IEEE Transactions on Automatic Control, vol. 33, pp. 16-27, 1988. [11] G. Chesi, “Estimating the domain of attraction: a light LMI technique for a class of polynomial systems,” In Proceedings of the 42nd IEEE International Conference on Decision and Control, Maui, Hawaii, 2003. [12] B. Tibken, “Estimation of the domain of attraction for polynomials systems via LMI’s,” In Proceedings of the 39th IEEE International Conference on Decision and control, Sidney, Australia, 2003. [13] G. Chesi, A. Garulli, A. Tesi, A. Vicino, “LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems,” Int. J. Nonlinear Robust Control 15 (1) (2005) 35-49. [14] G. Chesi, “Estimating the domain of attraction for non-polynomial systems via LMI optimization,” Automatica 45 (2009) 1536-1541. [15] H.K. Khalil, Nonlinear systems, 3rd ed. (2001) Prentice Hall. [16] F. Amato, C. Cosentino, A. Merola, “Estimation of the Domain of Attraction of Equilibrium Points for Quadratic Systems: Application to Tumor Stability Analysus,” American Control Conference, New York, USA, 2007, 5378-5383. | ||
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