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2006 | 16 | 1 | 129-140

Tytuł artykułu

Fractional kalman filter algorithm for the states parameters and order of fractional system estimation

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation, the paper discusses the possibility of using these algorithms for parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in a general nonlinear case are presented.

Rocznik

Tom

16

Numer

1

Strony

129-140

Opis fizyczny

Daty

wydano
2006
otrzymano
2005-04-10
poprawiono
2005-12-08

Twórcy

  • Institute of Control and Industrial Electronics, Faculty of Electrical Engineering, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
  • Institute of Control and Industrial Electronics, Faculty of Electrical Engineering, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

Bibliografia

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  • Brown R.G. and Hwang P.Y.C. (1997): Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises and Solutions. -New York: Wiley.
  • Cois O., Oustaloup A., Battaglia E. and Battaglia J.-L. (2000): Non-integer model from modal decomposition for time domain system identification. - Proc. Symp. System Identification, SYSID 2000, Santa Barbara, CA, Vol. 3, p. 989-994.
  • Cois O., Oustaloup A., Poinot T. and Battaglia J.-L. (2001): Fractional state variable filter for system identification by fractional model. -Proc. European Contr. Conf., ECC'2001, Porto, Portugal, pp. 2481-2486.
  • Engheta N. (1997): On the role of fractional calculus in electromagnetic theory. - IEEE Trans. Antenn. Prop., Vol. 39, No. 4, pp. 35-46.
  • Ferreira N.M.F. and Machado J.A.T. (2003): Fractional-order hybrid control of robotic manipulators. - Proc. 11-th Int. Conf. Advanced Robotics, ICAR'2003, Coimbra, Portugal, pp. 393-398.
  • Gałkowski K. (2005): Fractional polynomials and nD systems. - Proc. IEEE Int. Symp. Circuits and Systems, ISCAS'2005, Kobe, Japan, CD-ROM.
  • Haykin S. (2001): Kalman Filtering and Neural Networks. - New York: Wiley.
  • Hilfer R., Ed. (2000): Application of Fractional Calculus in Physics. - Singapore: World Scientific.
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  • Kalman R.E. (1960): A new approach to linear filtering and prediction problems. -Trans. ASME J. Basic Eng., Vol. 82, Series D, pp. 35-45.
  • Miller K.S. and Ross B. (1993): An Introduction to the Fractional Calculus and Fractional Differenctial Equations. - New York: Wiley.
  • Moshrefi-Torbati M. and Hammond K. (1998): Physical and geometrical interpretation of fractional operators. - J. Franklin Inst., Vol. 335B, No. 6, pp. 1077-1086.
  • Nishimoto K. (1984): Fractional Calculus. - Koriyama: Decartes Press.
  • Oldham K.B. and Spanier J. (1974): The Fractional Calculus. - New York: Academic Press.
  • Ostalczyk P. (2000): The non-integer difference of the discrete-time function and its application to the control system synthesis. - Int. J. Syst. Sci., Vol. 31, No. 12, pp. 1551-1561.
  • Ostalczyk P. (2004a): Fractional-Order Backward Difference Equivalent Forms Part I - Horners Form. - Proc. 1-st IFAC Workshop Fractional Differentation and its Applications, FDA'04, Enseirb, Bordeaux, France, pp. 342-347.
  • Ostalczyk P. (2004b): Fractional-Order Backward Difference Equivalent Forms Part II - Polynomial Form. - Proc. 1-st IFAC Workshop Fractional Differentation and its Applications, FDA'04, Enseirb, Bordeaux, France, pp. 348-353.
  • Oustaloup A. (1993): Commande CRONE. -Paris: Hermes.
  • Oustaloup A. (1995): La derivation non entiere. - Paris: Hermes.
  • Podlubny I. (1999): Fractional Differential Equations. - San Diego: Academic Press.
  • Podlubny I. (2002): Geometric and physical interpretation of fractional integration and fractional differentiation. - Fract. Calc. Appl. Anal., Vol. 5, No. 4, pp. 367-386.
  • Podlubny I., Dorcak L. and Kostial I. (1997): On fractional derivatives, fractional-order systems and PI^λ D^μ-controllers. - Proc. 36-th IEEE Conf. Decision and Control, San Diego, CA, pp. 4985-4990.
  • Poinot T. and Trigeassou J.C. (2003): Modelling and simulation of fractional systems using a non integer integrator. - Proc. Design Engineering Technical Conferences, DETC'03, and Computers and Information in Engineering Conference, ASME 2003, Chicago, IL, pp. VIB-48390.
  • Reyes-Melo M.E., Martinez-Vega J.J., Guerrero-Salazar C.A. and Ortiz-Mendez U. (2004a): Application of fractional calculus to modelling of relaxation phenomena of organic dielectric materials. - Proc. Int. Conf. Solid Dielectrics, Toulouse, France, Vol. 2, pp. 530-533.
  • Reyes-Melo M.E., Martinez-Vega J.J., Guerrero-Salazar C.A. and Ortiz-Mendez U. (2004b): Modelling of relaxation phenomena in organic dielectric materials. Application of differential and integral operators of fractional order. -J. Optoel. Adv. Mat., Vol. 6, No. 3, pp. 1037-1043.
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  • Samko S.G., Kilbas A.A. and Maritchev O.I. (1993): Fractional Integrals and Derivative. Theory and Applications. - London: Gordon and Breach.
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  • Sierociuk D. (2005b): Application of a fractional Kalman filter toparameter estimation of a fractional-order system. -Proc. 15-th Nat. Conf. Automatic Control, Warsaw, Poland,Vol. 1, pp. 89-94, (in Polish).
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  • Vinagre B.M. and Feliu V. (2002): Modeling and control of dynamic system using fractional calculus: Application to electrochemical processes and flexible structures. -Proc. 41-st IEEE Conf. Decision and Control, Las Vegas, NV,pp. 214-239.
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Bibliografia

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