Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2016 | 26 | 4 | 803-813
Tytuł artykułu

Set-membership identifiability of nonlinear models and related parameter estimation properties

Treść / Zawartość
Warianty tytułu
Języki publikacji
Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.
Opis fizyczny
  • LAAS-CNRS, University of Toulouse, UPS, 7 avenue du Colonel Roche, 31400 Toulouse, France
  • LAAS-CNRS, University of Toulouse, UPS, 7 avenue du Colonel Roche, 31400 Toulouse, France
  • UNIHAVRE, LMAH, Normandy University, FR-CNRS-3335, ISCN, 76600 Le Havre, France
  • Alamo, T., Bravo, J.M. and Camacho, E.F. (2005). Guaranteed state estimation by zonotopes, Automatica 41(6): 1035-1043.
  • Auer, E., Kiel, S. and Rauh, A. (2013). A verified method for solving piecewise smooth initial value problems, International Journal of Applied Mathematics and Computer Science 23(4): 731-747, DOI: 10.2478/amcs-2013-0055.
  • Boulier, F. (1994). Study and Implementation of Some Algorithms in Differential Algebra, Ph.D. thesis, Université des Sciences et Technologie de Lille, Lille.
  • Bourbaki, N. (1989). Elements of Mathematics, Springer-Verlag, Berlin/Heidelberg.
  • Braems, I., Jaulin, L., Kieffer, M. and Walter, E. (2001). Guaranteed numerical alternatives to structural identifiability testing, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, pp. 3122-3127.
  • Chabert, G. and Jaulin, L. (2009). Contractor programming, Artificial Intelligence 173(11): 1079-1100.
  • Chiscii, L., Garulli, A. and Zappa, G. (1996). Recursive state bounding by parallelotopes, Automatica 32(7): 1049-1055.
  • Denis-Vidal, L., Joly-Blanchard, G. and Noiret, C. (2001a). Some effective approaches to check identifiability of uncontrolled nonlinear systems, Mathematics and Computers in Simulation 57(1-2): 35-44.
  • Denis-Vidal, L., Joly-Blanchard, G., Noiret, C. and Petitot, M. (2001b). An algorithm to test identifiability of non-linear systems, Proceedings of the 5th IFAC Symposium on Nonlinear Control Systems, St. Petersburg, Russia, Vol. 7, pp. 174-178.
  • Herrero, P., Delaunay, B., Jaulin, L., Georgiou, P., Oliver, N. and Toumazou, C. (2016). Robust set-membership parameter estimation of the glucose minimal model, International Journal of Adaptive Control and Signal Processing 30(2): 173-185.
  • Jauberthie, C., Verdière, N. and Travé-Massuyès, L. (2011). Set-membership identifiability: Definitions and analysis, Proceedings of the 18th IFAC World Congress, Milan, Italy, pp. 12024-12029.
  • Jauberthie, C., Verdière, N. and Travé-Massuyès, L. (2013). Fault detection and identification relying on set-membership identifiability, Annual Reviews in Control 37(1): 129-136.
  • Jaulin, L., Kieffer, M., Didrit, O. and Walter, E. (2001). Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics, Springer, Londres.
  • Jaulin, L. and Walter, E. (1993). Set inversion via interval analysis for nonlinear bounded-error estimation, Automatica 29(4): 1053-1064.
  • Kieffer, M., Jaulin, L. and Walter, E. (2002). Guaranteed recursive nonlinear state bounding using interval analysis, International Journal of Adaptive Control and Signal Processing 6(3): 193-218.
  • Kieffer, M., Jaulin, L., Walter, É. and Meizel, D. (2000). Robust autonomous robot localization using interval analysis, Reliable Computing 6(3): 337-362.
  • Kieffer, M. and Walter, E. (2011). Guaranteed estimation of the parameters of nonlinear continuous-time models: Contributions of interval analysis, International Journal of Adaptive Control and Signal Processing 25(3): 191-207.
  • Kolchin, E. (1973). Differential Algebra and Algebraic Groups, Academic Press, New York, NY.
  • Kurzhanski, A.B. and Valyi, I. (1997). Ellipsoidal Calculus for Estimation and Control, Nelson Thornes, Birkhäuser.
  • Lagrange, S., Delanoue, N. and Jaulin, L. (2008). Injectivity analysis using interval analysis: Application to structural identifiability, Automatica 44(11): 2959-2962.
  • Ljung, L. and Glad, T. (1994). On global identifiability for arbitrary model parametrizations, Automatica 30(2): 265-276.
  • Maiga, M., Ramdani, N. and Travé-Massuyès, L. (2013). A fast method for solving guard set intersection in nonlinear hybrid reachability, Proceedings of the 52nd IEEE Conference on Decision and Control, CDC 2013, Firenze, Italy, pp. 508-513.
  • Maiga, M., Ramdani, N., Travé-Massuyès, L. and Combastel, C. (2016). A comprehensive method for reachability analysis of uncertain nonlinear hybrid systems, IEEE Transactions on Automatic Control 61(9): 2341-2356, DOI:10.1109/TAC.2015.2491740.
  • Milanese, M., Norton, J., Piet-Lahanier, H. and Walter, É. (2013). Bounding Approaches to System Identification, Springer Science & Business Media, New York, NY.
  • Munkres, J.R. (1975). Topology-A First Course, Prentice Hall, Upper Saddle River, NJ.
  • Nelles, O. (2002). Nonlinear System Identification, Springer-Verlag, Berlin/Heidelberg.
  • Pohjanpalo, H. (1978). System identifiability based on the power series expansion of the solution, Mathematical Biosciences 41(1): 21-33.
  • Puig, V. (2010). Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies, International Journal of Applied Mathematics and Computer Science 20(4): 619-635, DOI: 10.2478/v10006-010-0046-y.
  • Raïssi, T., Ramdani, N. and Candau, Y. (2004). Set-membership state and parameter estimation for systems described by nonlinear differential equations, Automatica 40(10): 1771-1777.
  • Ravanbod, L., Verdière, N. and Jauberthie, C. (2014). Determination of set-membership identifiability sets, Mathematics in Computer Science 8(3-4): 391-406.
  • Seybold, L., Witczak, M., Majdzik, P. and Stetter, R. (2015). Towards robust predictive fault-tolerant control for a battery assembly system, International Journal of Applied Mathematics and Computer Science 25(4): 849-862, DOI: 10.1515/amcs-2015-0061.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.