A combined observer and filter based approach for the determination of unknown parameters

International Journal of Systems Science

Volumn 40, Issue 3, 2009, Pages 213-221

  Robenack, Klaus ^a   Goel, Pranay ^b  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^b NATIONAL INSTITUTE OF DIABETES AND DIGESTIVE AND KIDNEY DISEASES   (United States)

Author keywords

Filter; Non linear observer; Parameter dependent systems

Indexed keywords

ADAPTIVE SYSTEMS; PARAMETER ESTIMATION;

CELL MODELS; DESIGN PROCEDURES; FILTER; FILTER-BASED; NON-LINEAR; NON-LINEAR OBSERVER; NON-LINEAR PARAMETERS; ON-LINE ESTIMATIONS; PARAMETER-DEPENDENT SYSTEMS; PERSISTENCE OF EXCITATIONS; REDUCED ORDERS; SIMULTANEOUS RECONSTRUCTION; SPECIAL CLASS; STATE VECTORS; TWO STAGES; UN-KNOWN INPUT OBSERVERS; UNKNOWN PARAMETERS;

OBSERVABILITY;

EID: 61549136621     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720802298715     Document Type: Article

References (54)

1. Amicucci, G.L., and Monaco, S. (1998), "On Nonlinear Detectability," Journal of the Franklin Institute, 335B(6), 1105-1123.
2. Axon (1993), in The Axon CNS Guide to Electrophysiology and Biophysics Laboratory Techniques, ed. R Shermar-Gold, Union City, CA: Molecular Devices.
3. Bastina, G., and Gevers, M.R. (1988), "Stable Adaptive Observers for Nonlinear Time-Varying Systems," IEEE Transactions on Automatic Control, 33(7), 650-658.
4. Bertram, R., and Sherman, A. (2004), "A Calcium-based Phantom Bursting Model for Pancreatic Islets," Bulletin of Mathematical Biology, 66, 1313-1344.
5. Besançon, G. (2000), "Remarks on Non-linear Adaptive Observer Design," Systems & Control Letters, 41, 271-280.
6. Besançon, G., Zhang, Q., and Hammouri, H. (2004), "High-gain Observer Based State and Parameter Estimation in Non-linear Systems," Preprint 6th IFAC-Symposium on Nonlinear Control Systems (NOLCOS 2004), Germany: Stuttgart, September, pp. 471-476.
7. Dayan, P., and Abbott, L.F. (2001), Theoretical Neuroscience, Cambridge, MA: MIT Press.
8. de Jager, B. (1991), "Symbolic Calculation of Zero Dynamics for Non-linear Control Systems," in Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, Bonn, Germany, July, pp. 321-322.
9. Denbig, P. (1998), System Analysis & and Signal Processing, Harlow, Essex: Addison-Wesley.
10. Dochain, D. (2003), "State and Parameter Estimation in Chemical and Biochemical Processes: A tutorial," Journal of Process Control, 13(8), 801-818.
11. Eskinat, E., Johnson, S.H., and Luybense, W.L. (1991), "Use of Hammerstein Models in Identification of Non-linear Systems," AIChE Journal, 37(2), 255-268.
12. Feldmann, U. (1995), Synchronization of Chaotic Systems, Dissertation: Technische Universität Dresden, Fakultät Elektrotechnik.
13. Feldmann, U., Hasler, M., and Schwarz, W. (1995), "On the Design of a Synchronizing Inverse of a Chaotic System," in Proceedings European Circuit Theory Design (ECCTD) (Vol. 1), Istanbul, Turkey: Auguest, pp. 479-482.
14. -(1996), "Communication by Chaotic Signals: The Inverse System Approach," International of Journal of Circuit Theory and Applications, 24(5), 551-579.
15. Finkel, A.S., and Gage, P.W. (1985), in Voltage and Patch Clamping with Microelectrodes, (eds.) Smith, et al, Baltimore, USA: William & Wilkins, pp. 47-94.
16. Fortell, H. (1994), "Calculation of Zero Dynamics using the Ritt Algorithm," in Proceedings 33rd Conference Decision Control (CDC'94) (Vol. 4), Florida, USA: Lake Buena Vista, December, pp. 3271-3276.
17. Gauthier, J.P., Hammouri, H., and Othman, S. (1992), "A Simple Observer for Nonlinear Systems - Application to Bioreactors," IEEE Transactions on Automatic Control, 37(6), 875-880.
18. Griewank, A. (2000), Evaluating Derivatives - Principles and Techniques of Algorithmic Differentiation (Vol. 19), Philadelphia, SIAM: Frontiers in Applied Mathematics.
19. Guillaume, D., Rouchon, P., and Rudolph, J. (1997), "Two Simple Observers for a Class of Polymerization Reactors," Proceedings of 4th European Control Conference (ECC'97), Brüssel, Belgium, July.
20. Haber, R. (1999), Nonlinear System Identification: Input-Output Modeling Approach, Dordrecht, the Netherlands: Springer.
21. Halme, A. (1981), "Recursive Identification of Non-linear Systems by the Direct Method and Orthogonal Expansions," in Third IMA Conference on Control Theory, (eds.) J.E. Marshall, ' W.D. Collins, & C.J. Harris, London, England: Academic Press.
22. Hunter, I.W., and Korenberg, M.J. (1986), "The Identification of Non-linear Biological Systems: Wiener and Hammerstein Cascade Models," Biological Cybernetics, 55(2-3), 135-144.
23. Isermann, R. (1992), Identifikation dynamischer Systeme I (2nd ed.), Berlin: Springer.
24. Isidori, A. (1995), Nonlinear Control Systems: An Introduction (3rd ed.), London: Springer.
25. Johnston, D., and Wu, S.M. (1994), Foundations of Cellular Neurophysiology, July, Cambridge, MA: The MIT Press.
26. Koch, C, and Segev, 1. (eds.), (1998), Methods in Neuronal Modelling: From Ions to Networks, Cambridge, MA: MIT Press.
27. Kreisselmeier, G. (1977), "Adaptive Observers with Exponential Rate of Convergence," IEEE Transactions on Automatic Control, 22(1), 2-8.
28. Krener, A.J., and Isidori, A. (1983), "Linearization by Output Injection and Non-linear Observers," Systems & Control Letters, 3, 47-52.
29. Krstic, M., Kanellakopoulos, I., and Kokotovic, P. (1995), Nonlinear and Adaptive Control Design, New York: Wiley.
30. Kugi, A., Schlacher, K., and Novaki, R. (1999), "Symbolic Computation for the Analysis and Synthesis of Nonlinear Control Systems," in Software for Electrical Engineering, Analysis and Design IV, (eds.) A. Konrad, & C.A. Brebbia, Southampton: WIT-Press, pp. 255-264.
31. Kwatny, H.G., and Blankenship, G.L. (2000), Nonlinear Control and Analytical Mechanics: A Computational Approach, Boston: Birkhäuser.
32. Lee, J., Smaill, B., and Smith, N. (2006), "Hodgkin-Huxley Type Ion Channel Characterisation: An Improved Method of Voltage Clamp Experiment Parameter Estimation," Journal Theoretical Biology, 242(1), 123-134.
33. Ljung, L. (1999), System Identification: Theory for the User (2nd ed.), Englewood Cliffs: Prentice-Hall.
34. -(2007), System Identification Toolbox 7 User's Guide, Natick, MA, USA: The Mathworks, Inc.
35. Marino, R. (1990), "Adaptive Observers for Single Output Nonlinear Systems," IEEE Transactions on Automatic Control, 35(9), 1054-1058.
36. Marino, R., and Tomei, P. (1995), "Adaptive Observers with Arbitrary Exponential Rate of Convergence for Nonlinear Systems," IEEE Transactions on Automatic Control, 40(7), 1300-1304.
37. -(1995), Nonlinear Control Design: Geometric, Adaptive and Robust, Englewood Cliffs: Prentice Hall.
38. Mastorocostas, P.A., and Theocharis, J.B. (2002), "A Recurrent Fuzzy-neural Model for Dynamic System Identification," IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 32(2), 176-190.
39. Moreno, J. (2000), "Unknown Input Observers for SISO Non-linear Systems," in Proceedings 39th Conference Decision and Control (CDC 2000) (Vol. 1), Sydney, Australia: December, p. 790.
40. Moreno, J., and Rocha-Cózatl, E. (2000), "Pasivizatión y Existencia De Observadores Con Entradas Desconocidas Para Sistemas No Lineales SISO," Memorias de la Sexta Conferencia de Ingeniería Eléctrica, México, D.F., September, pp. 334-341.
41. Morris, C, and Lecar, H. (1981), "Voltage Oscillations in the Barnacle Giant Muscle Fiber," Biophysical Journal, 35, 193-213.
42. Neher, E., and Sakmann, B. (1976), "Single-channel Currents Recorded from Membrane Denervated Frog Muscle Fibers," Nature, 260, 799-802.
43. Nijmeijer, H., and Fossen, T.I. (1999), "New Directions in Nonlinear Observer Design," Lecture Notes in Control and Information Science (Vol. 244), London: Springer.
44. Rinzel, J., and Ermentrout, G.B. (1989), "Analysis of Neural Excitability and Oscillations," in Methods in Neuronal Modeling: From Synapses to Networks, (eds.) C. Koch, & I. Segev, Cambridge, MA, USA: MIT Press.
45. Rocha-Cózatl, E., and Moreno, J. (2002), "Passivity and Unknown Input Observers for Nonlinear Systems," 15th Triennial World Congress of the International Federation of Automatic Control Barcelona, 21-26 July 2002, Barcelona, Spain.
46. Sastry, P.S., Santharam, G., and Unnikrishnan, K.P. (1994), "Memory Neuron Networks for Identification and Control of Dynamical Systems," IEEE Transactions on Neural Networks, 5(2), 306-319.
47. Sastry, S., and Bodson, M. (1989), Adaptive Control - Stability, Convergence and Robustness, Englewood Cliffs, NJ: Prentice-Hall.
48. Seung, H.S., Lee, D.D., Reis, B.Y., and Tank, D.W. (2000), "The Autapse: A Simple Illustration of Short-term Analog Memory Storage by Tuned Synaptic Feedback," Journal Computational Neuroscience, 9(2), 171-185.
49. Sheikholeslam, S. (1995), "Observer-based Parameter Identifiers for Non-linear Systems with Parameter Dependencies," IEEE Transactions on Automatic Control, 40(2), 382-387.
50. Shumsky, A.Y. (1996), "Observer Based Online Parameter Estimation in Non-linear Systems," IF AC World Congress, Francisco, CA, USA, July, pp. 429-434.
51. Sima, V., Simal, D., and Van Huffel, S. (2002), "S1ICOT System Identification Software and Applications," in Proceedings 2002 IEEE International Symposium on Computer Aided Control System Design, Glasgow, Scotland, UK, September, pp. 45-50.
52. Smith, T.G., Lecar, H., Redman, S.J., and Gage, P.W. (1985), Voltage and patch Clamping with Microelectrodes, Baltimore, USA: William & Wilkins.
53. Thomas, R.E., and Rosa, A.J. (2004), The Analysis and Design of Linear Circuits (4th ed.), New York: Wiley.
54. Willms, A.R., Baro, D.J., Harris-Warrick, R.M., and Guckenheimer, J. (1999), "An Improved Parameter Estimation Method for Hodgkin-Huxley Models," Journal Computational Neuroscience, 6(2), 145-168.