Parameter Identifiability for Nonlinear LPV Models
References
- Abbas, H.S., Tóth, R., Petreczky, M., Meskin, N. and Mohammadpour, J. (2014). Embedding of nonlinear systems in a linear parameter-varying representation, IFAC Proceedings Volumes 47(3): 6907–6913.10.3182/20140824-6-ZA-1003.02506
- Alkhoury, Z., Petreczky, M. and Mercère, G. (2017). Identifiability of affine linear parameter-varying models, Automatica 80: 62–74.10.1016/j.automatica.2017.01.029
- Anaya, J.Z. and Henrion, D. (2009). An improved Toeplitz algorithm for polynomial matrix null-space computation, Applied Mathematics and Computation 207(1): 256–272.10.1016/j.amc.2008.10.037
- Anguelova, M. (2007). Observability and Identifiability of Nonlinear Systems with Applications in Biology, PhD thesis, Chalmers University of Technology, Gothenburg.
- Anstett, F. (2006). Les systèmes dynamiques chaotiques pour le chiffrement: Synthèse et cryptanalyse, PhD thesis, Université Henri Poincaré-Nancy I, Nancy.
- Anstett, F., Bloch, G., Millérioux, G. and Denis-Vidal, L. (2008). Identifiability of discrete-time nonlinear systems: The local state isomorphism approach, Automatica 44(11): 2884–2889.10.1016/j.automatica.2008.03.019
- Anstett, F., Millérioux, G. and Bloch, G. (2006). Chaotic cryptosystems: Cryptanalysis and identifiability, IEEE Transactions on Circuits and Systems I: Regular Papers 53(12): 2673–2680.10.1109/TCSI.2006.885979
- Audoly, S., Bellu, G., D’Angiò, L., Saccomani, M.P. and Cobelli, C. (2001). Global identifiability of nonlinear models of biological systems, IEEE Transactions on Biomedical Engineering 48(1): 55–65.10.1109/10.900248
- Balsa-Canto, E., Alonso, A.A. and Banga, J.R. (2010). An iterative identification procedure for dynamic modeling of biochemical networks, BMC Systems Biology 4: 11.10.1186/1752-0509-4-11
- Beelen, H. and Donkers, T. (2017). Joint state and parameter estimation for discrete-time polytopic linear parameter-varying systems, IFAC-PapersOnLine 50(1): 9778–9783.10.1016/j.ifacol.2017.08.880
- Bellman, R. and Aström, K. J. (1970). On structural identifiability, Mathematical Biosciences 7(3): 329–339.10.1016/0025-5564(70)90132-X
- Bellu, G., Saccomani, M.P., Audoly, S. and D’Angiò, L. (2007). Daisy: A new software tool to test global identifiability of biological and physiological systems, Computer Methods and Programs in Biomedicine 88(1): 52–61.10.1016/j.cmpb.2007.07.002288853717707944
- Buchberger, B. (2006). Bruno Buchberger’s PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal, Journal of Symbolic Computation 41(3–4): 475–511.10.1016/j.jsc.2005.09.007
- Chis, O.-T., Banga, J.R. and Balsa-Canto, E. (2011). Structural identifiability of systems biology models: A critical comparison of methods, PLOS ONE 6(11): e27755.10.1371/journal.pone.0027755
- Chow, E. and Willsky, A. (1984). Analytical redundancy and the design of robust failure detection systems, IEEE Transactions on Automatic Control 29(7): 603–614.10.1109/TAC.1984.1103593
- Coll, C. and Sánchez, E. (2019). Parameter identification and estimation for stage-structured population models, International Journal of Applied Mathematics and Computer Science 29(2): 327–336, DOI: 10.2478/amcs-2019-0024.
- Dankers, A., Tóth, R., Heuberger, P. S., Bombois, X. and Van den Hof, P.M. (2011). Informative data and identifiability in LPV-ARX prediction-error identification, 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, USA, pp. 799–804.
- Denis-Vidal, L. and Joly-Blanchard, G. (1996). Identifiability of some nonlinear kinetics, 3rd Workshop on Modelling of Chemical Reaction Systems, Heidelberg, Germany, pp. 1–8.
- Denis-Vidal, L., Joly-Blanchard, G. and Noiret, C. (1999). Some results and applications about identifiability of non-linear systems, European Control Conference, ECC 1999, Karl-sruhe, Germany, pp. 1232–1237.
- Glover, K. and Willems, J. (1974). Parametrizations of linear dynamical systems: Canonical forms and identifiability, IEEE Transactions on Automatic Control 19(6): 640–646.10.1109/TAC.1974.1100711
- Joly-Blanchard, G. and Denis-Vidal, L. (1998). Some remarks about an identifiability result of nonlinear systems, Auto-matica 34(9): 1151–1152.10.1016/S0005-1098(98)00055-7
- Joubert, D. (2020). Structural Identifiability of Large Systems Biology Models, PhD thesis, Wageningen University, Wageningen.
- Khare, S.R., Pillai, H.K. and Belur, M.N. (2010). Algorithm to compute minimal nullspace basis of a polynomial matrix, 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010, Budapest, Hungary, pp. 219–224.
- Kwiatkowski, A., Boll, M.-T. and Werner, H. (2006). Automated generation and assessment of affine LPV models, 45th IEEE Conference on Decision and Control, CDC 2006, San Diego, USA, pp. 6690–6695.
- Lee, L.H. and Poolla, K. (1997). Identifiability issues for parameter-varying and multidimensional linear systems, ASME 1997 Design Engineering Technical Conferences, Sacramento, USA.10.1115/DETC97/VIB-4240
- Ljung, L. and Glad, T. (1994). On global identifiability for arbitrary model parametrizations, Automatica 30(2): 265–276.10.1016/0005-1098(94)90029-9
- Nômm, S. and Moog, C. (2004). Identifiability of discrete-time nonlinear systems, IFAC Proceedings Volumes 37(13): 333–338.10.1016/S1474-6670(17)31245-4
- Němcová, J. (2010). Structural identifiability of polynomial and rational systems, Mathematical Biosciences 223(2): 83–96.10.1016/j.mbs.2009.11.00219913563
- Nijmeijer, H. and Van der Schaft, A. (1990). Nonlinear Dynamical Control Systems, Springer, New York.10.1007/978-1-4757-2101-0
- Ohtake, H., Tanaka, K. and Wang, H.O. (2003). Fuzzy modeling via sector nonlinearity concept, Integrated Computer-Aided Engineering 10(4): 333–341.10.3233/ICA-2003-10404
- Ollivier, F. (1990). Le problème de l’identifiabilité structurelle globale: Approche théorique, méthodes effectives et bornes de complexité, PhD thesis, Ecole Polytechnique, Palaiseau.
- Peeters, R.L. and Hanzon, B. (2005). Identifiability of homogeneous systems using the state isomorphism approach, Automatica 41(3): 513–529.10.1016/j.automatica.2004.11.019
- Petreczky, M. and Mercère, G. (2012). Affine LPV systems: Realization theory, input-output equations and relationship with linear switched systems, 51st Annual Conference on Decision and Control, CDC 2012, Maui, USA, pp. 4511–4516.
- Pohjanpalo, H. (1978). System identifiability based on the power series expansion of the solution, Mathematical Biosciences 41(1–2): 21–33.10.1016/0025-5564(78)90063-9
- Saccomani, M.P. (2011). An effective automatic procedure for testing parameter identifiability of HIV/AIDS models, Bulletin of Mathematical Biology 73(8): 1734–1753.10.1007/s11538-010-9588-2
- Saccomani, M.P., Audoly, S., Bellu, G., Cobelli, C. (1997). Global identifiability of nonlinear model parameters, IFAC Proceedings Volumes 30(11): 233–238.10.1016/S1474-6670(17)42852-7
- Srinivasarengan, K., Ragot, J., Maquin, D. and Aubrun, C. (2016). Takagi–Sugeno model based nonlinear parameter estimation in air handling units, 4th IFAC International Conference on Intelligent Control and Automation Sciences, ICONS 2016, Reims, France, pp. 188–193.
- Tunali, E. T. and Tarn, T.-J. (1987). New results for identifiability of nonlinear systems, IEEE Transactions on Automatic Control 32(2): 146–154.10.1109/TAC.1987.1104544
- Vajda, S. and Rabitz, H. (1989). State isomorphism approach to global identifiability of nonlinear systems, IEEE Transactions on Automatic Control 34(2): 220–223.10.1109/9.21105
- Verdière, N., Denis-Vidal, L., Joly-Blanchard, G. and Domurado, D. (2005). Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor, International Journal of Applied Mathematics and Computer Science 15(4): 517–526.
- Villaverde, A.F. and Banga, J.R. (2017). Structural properties of dynamic systems biology models: Identifiability, reachability, and initial conditions, Processes 5(2): 29.10.3390/pr5020029
- Villaverde, A.F., Barreiro, A. and Papachristodoulou, A. (2016). Structural identifiability of dynamic systems biology models, PLOS Computational Biology 12(10): e1005153.10.1371/journal.pcbi.1005153508525027792726
- Walter, E. and Lecourtier, Y. (1982). Global approaches to identifiability testing for linear and nonlinear state space models, Mathematics and Computers in Simulation 24(6): 472–482.10.1016/0378-4754(82)90645-0
- Xia, X. and Moog, C.H. (2003). Identifiability of nonlinear systems with application to HIV/AIDS models, IEEE Transactions on Automatic Control 48(2): 330–336.10.1109/TAC.2002.808494
Language: English
Page range: 255 - 269
Submitted on: May 13, 2021
Accepted on: Feb 2, 2022
Published on: Jul 4, 2022
Published by: Sciendo
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© 2022 Krishnan Srinivasarengan, José Ragot, Christophe Aubrun, Didier Maquin, published by Sciendo
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