Pseudo phase plane, delay and fractional dynamics

Journal Europeen des Systemes Automatises

Volumn 42, Issue 6-8, 2008, Pages 1037-1051

  Lima, Miguel Francisco Martins ^a   Machado, José Antonio Tenreiro ^b   Crisóstomo, Manuel Marques ^c  

^a POLYTECHNIC INSTITUTE OF VISEU   (Portugal)

^b INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

^c UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Fractal dimension; Fractional calculus; Mutual information; Pseudo phase plane; Robotics

Indexed keywords

CALCULATIONS; ROBOTICS;

FRACTIONAL CALCULUS; FRACTIONAL DYNAMICS; INTEGER ORDER; MUTUAL INFORMATIONS; PAPER ANALYSIS; PSEUDO-PHASE; SIGNAL DELAYS; SIGNALS SPECTRA;

FRACTAL DIMENSION;

EID: 77954260940     PISSN: 12696935     EISSN: None     Source Type: Journal    
DOI: 10.3166/JESA.42.1037-1051     Document Type: Article

References (24)

1. Abarbanel H. D. I., Brown R., Sidorowich J. J., Tsimring L. Sh., "The analysis of observed chaotic data in physical systems", Reviews of Modern Physics, vol. 65, no 4, 1993, p. 1331-1392.
2. Barbosa R. S., Tenreiro Machado J. A., Ferreira I. M., "Tuning of PID controllers based on Bode's ideal transfer function", Nonlinear Dynamics, vol. 38, Kluwer Academic Publishers, 2004, p. 305-321.
3. Bohannan G. W., "Analog realization of a fractional control element revisited", mechatronics.ece.usu.edu/foc/cdc02tw/cdrom/aditional/FOC- Proposal-Bohannanpdf, 2002.
4. Choi J.-G., Park J.-K., Kim K.-H., Kim J.-C., "A daily peak load forecasting system using a chaotic time series", Proc. Int. Conf. on Intelligent Systems Applications to Power Systems, IEEE, 28 January-2 February, 1996, p. 283-287.
5. Deng W. H., Li C. P., Lü J., "Stability analysis of linear fractional differential system with multiple time-delays", Nonlinear Dynamics, vol. 48, no 4, 2007, p. 409-416.
6. Driver R. D., "Ordinary and delay differential equations", Applied Mathematical Sciences, vol. 20, Springer-Verlag, New-York, 1977.
7. Faybishenko B., "Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives", Rev. Geophys., vol. 42, 2004, RG2003.
8. Feeny B. F., Lin G., "Fractional derivatives applied to phase-space reconstructions", Nonlinear Dynamics, vol. 38, no 1-4, special issue on fractional calculus, 2004, p. 85-99.
9. Koga H., Masahiro N., "Method of evaluation of fractal dimensions in terms of fractional integro-differential equations", Electronics and Communications in Japan (Part III: Fundamental Electronic Science), vol. 87, no 4, 2004, p. 30-39.
10. Le Méhauté A., Howlett J., Fractal Geometries: Theory and Applications, CRC Press, Inc., Boca Raton, FL, 1991.
11. Lima M. F. M., Tenreiro Machado J. A., Crisóstomo M., "Experimental set-up for vibration and impact analysis in robotics", WSEAS Trans. on Systems, Issue 5, vol. 4, May, 2005, p. 569-576.
12. Lima M. F. M., Tenreiro Machado J. A., Crisóstomo M., "Windowed Fourier transform of experimental robotic signals with fractional behavior", Proc. IEEE Int. Conf. on Computational Cybernetics, Tallin, Estonia, August, 2006, p. 21-26.
13. Lima M. F. M., Tenreiro Machado J. A., Crisóstomo M., "Fractional dynamics in mechanical manipulation", Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC), Las Vegas, Nevada, USA, September 4-7, 2007.
14. st IFAC Conference on Mechatronic Systems, Darmstadt, Germany, September 2000.
15. Nigmatullin R. R., "Fractional' kinetic equations and "universal" decoupling of a memory function in mesoscale region", Physica A: Statistical Mechanics and its Applications, vol. 363, Issue 2, 1 May 2006, p. 282-298.
16. Novikov V. V., Voitsekhovskii K. V., "Viscoelastic properties of fractal media", Journal of Applied Mechanics and Technical, vol. 41, no 1, 2000, p. 149-158.
17. th Conference on Decision & Control, San Diego, California, USA, December, 1997.
18. Podlubny I., "Geometrical and physical interpretation of fractional integration and fractional differentiation", Journal of Fractional Calculus and Applied Analysis, vol. 5, no 4, 2002, p. 357-366.
19. Sabatier J., Garcia Iturricha A., Oustaloup A., Levron F., "Third generation CRONE control of continuous linear time periodic systems", Proc. of the IFAC Conference on System Structure and Control, Nantes, France, July 1998.
20. Spataru Al., Théorie de la transmission de l'information - Signaux et Bruits, Editura technica, Bucarest, Roumanie, 1970.
21. Tenreiro Machado J. A., "Analysis and design of fractional-order digital control systems", Journal Systems Analysis-Modelling-Simulation, Gordon & Breach Science Publishers, vol. 27, 1997, p. 107-122.
22. Tenreiro Machado J. A., "A probabilistic interpretation of the fractional-order differentiation", Journal of Fractional Calculus and Applied Analysis, vol. 6, no 1, 2003, p. 73-80.
23. Trendafilova I., Van Brussel H., "Non-linear dynamics tools for the motion analysis and condition monitoring of robot joints", Mech. Sys. and Signal Proc., vol. 15, issue 6, November 2001, p. 1141-1164.
24. st IEEE Conference on Decision and Control, tutorial workshop #2, Las Vegas, USA, 2002.