Iterative method for estimating the robust domains of attraction of non-linear systems: Application to cancer chemotherapy model with parametric uncertainties

European Journal of Control - Tập 47 - Trang 64-73 - 2019
Rachid Riah1, Mirko Fiacchini1, Mazen Alamir1
1University Grenoble Alpes, GIPSA-lab (UMR CNRS 5216), Grenoble, F-38000, France

Tài liệu tham khảo

Aubin, 2009 Bertsekas, 1972, Infinite-time reachability of state-space regions by using feedback control, IEEE Trans. Autom. Control, 17, 604, 10.1109/TAC.1972.1100085 Bertsekas, 2009 Chesi, 2011, 415 Gilbert, 1991, Linear systems with state and control constraints: The theory and application of maximal output admissible sets, IEEE Trans. Autom. Control, 36, 1008, 10.1109/9.83532 Kolmanovsky, 1998, Theory and computation of disturbance invariant sets for discrete-time linear systems, Math. Probl. Eng., 4, 317, 10.1155/S1024123X98000866 Raković, 2005, Invariant approximations of the minimal robust positively invariant set, IEEE Trans. Autom. Control, 50, 406, 10.1109/TAC.2005.843854 Magni, 2001, A stabilizing model-based predictive control algorithm for nonlinear systems, Automatica, 37, 1351, 10.1016/S0005-1098(01)00083-8 Alamo, 2009, Convex invariant sets for discrete-time Lur’e systems, Automatica, 45, 1066, 10.1016/j.automatica.2008.11.013 Fiacchini, 2010, On the computation of convex robust control invariant sets for nonlinear systems, Automatica, 46, 1334, 10.1016/j.automatica.2010.05.007 Blanchini, 2008 Fiacchini, 2010 Fiacchini, 2012, Invariant sets computation for convex difference inclusions systems, Syst. Control Lett., 61, 819, 10.1016/j.sysconle.2012.04.012 Aubin, 2012, 264 Riah, 2015, Invariance-based analysis of cancer chemotherapy, 1111 Swan, 1990, Role of optimal control theory in cancer chemotherapy, Math. Biosci., 101, 237, 10.1016/0025-5564(90)90021-P Martin, 1992, Optimal control drug scheduling of cancer chemotherapy, Automatica, 28, 1113, 10.1016/0005-1098(92)90054-J De Pillis, 2006, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations, J. Theor. Biol., 238, 841, 10.1016/j.jtbi.2005.06.037 Matveev, 2002, Application of optimal control theory to analysis of cancer chemotherapy regimens, Syst. Control Lett., 46, 311, 10.1016/S0167-6911(02)00134-2 De Pillis, 2007, Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls, Math. Biosci., 209, 292, 10.1016/j.mbs.2006.05.003 Ledzewicz, 2008, Optimal control for combination therapy in cancer, 1537 Chareyron, 2009, Mixed immunotherapy and chemotherapy of tumors: Feedback design and model updating schemes, J. Theor. Biol., 258, 444, 10.1016/j.jtbi.2008.07.002 Alamir, 2014, Robust feedback design for combined therapy of cancer, Opt. Control Appl. Methods, 35, 77, 10.1002/oca.2057 M. Alamir, On probabilistic certification of combined cancer therapies using strongly uncertain models, arXiv:1502.06218 (2015). Afenya, 1996, Acute leukemia and chemotherapy: a modeling viewpoint, Math. Biosci., 138, 79, 10.1016/S0025-5564(96)00086-7 Afenya, 1998, Some perspectives on modeling leukemia, Math. Biosci., 150, 113, 10.1016/S0025-5564(98)10005-6 Hahnfeldt, 1999, Tumor development under angiogenic signaling a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res., 59, 4770 De Pillis, 2001, A mathematical tumor model with immune resistance and drug therapy: an optimal control approach, Comput. Math. Methods Med., 3, 79 Murray, 1994, Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle, Math. Biosci., 123, 183, 10.1016/0025-5564(94)90011-6 Riah, 2016, Domain of attraction estimation of cancer chemotherapy model affected by state proportional uncertainty, 2133 Rockafellar, 1970 Boyd, 2004