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Volumn 222, Issue 3, 2008, Pages 175-184

Fractional controller to stabilize fixed points of uncertain chaotic systems: Theoretical and experimental study

Author keywords

Chaos; Fractional order controller; Stabilization; Uncertainty

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION;

EID: 45949102670     PISSN: 09596518     EISSN: None     Source Type: Journal    
DOI: 10.1243/09596518JSCE481     Document Type: Article
Times cited : (26)

References (52)
  • 1
    • 0038818452 scopus 로고    scopus 로고
    • Control of chaos: Methods and applications. Part I: methods
    • Andrievsky, B. R. and Fradkov, A. L. Control of chaos: methods and applications. Part I: methods. Automn and Remote Control, 2003, 64(5), 673-713.
    • (2003) Automn and Remote Control , vol.64 , Issue.5 , pp. 673-713
    • Andrievsky, B.R.1    Fradkov, A.L.2
  • 2
    • 0036969680 scopus 로고    scopus 로고
    • Stabilizing unstable equilibrium points of a class of chaotic systems using a state PI regulator
    • Jiang, G. P., Chen, G., and Tang, K. S. Stabilizing unstable equilibrium points of a class of chaotic systems using a state PI regulator. IEEE Trans., on Circuits and Systems I, 2002, 49, 1820-1826.
    • (2002) IEEE Trans., on Circuits and Systems , vol.1 , Issue.49 , pp. 1820-1826
    • Jiang, G.P.1    Chen, G.2    Tang, K.S.3
  • 3
    • 29144511513 scopus 로고    scopus 로고
    • A stabilization method of chaotic systems based on full delayed feedback controller design
    • Guan, X., Feng, G., and Chen, C. A stabilization method of chaotic systems based on full delayed feedback controller design. Phys. Lett., A, 2006, 348, 210-221.
    • (2006) Phys. Lett., A , vol.348 , pp. 210-221
    • Guan, X.1    Feng, G.2    Chen, C.3
  • 5
    • 30344435883 scopus 로고    scopus 로고
    • Stabilizing periodic solutions of nonlinear systems and applications in chaos control
    • Zhu, J. and Tian, Y. Stabilizing periodic solutions of nonlinear systems and applications in chaos control. IEEE Trans. on Circuits and Systems II: Express Briefs, 2005, 52(12), 870-874.
    • (2005) IEEE Trans. on Circuits and Systems II: Express Briefs , vol.52 , Issue.12 , pp. 870-874
    • Zhu, J.1    Tian, Y.2
  • 6
    • 33847307141 scopus 로고    scopus 로고
    • A full delayed feedback controller design method for time-delay chaotic systems
    • Guan, X., Feng, G., Chen, C., and Chen, G. A full delayed feedback controller design method for time-delay chaotic systems. Physica D: Nonlinear Phenomena, 2007, 227(1), 36-42.
    • (2007) Physica D: Nonlinear Phenomena , vol.227 , Issue.1 , pp. 36-42
    • Guan, X.1    Feng, G.2    Chen, C.3    Chen, G.4
  • 7
    • 33750409231 scopus 로고    scopus 로고
    • Linear controllers for the stabilization of unknown steady states of chaotic systems
    • Huijberts, H. Linear controllers for the stabilization of unknown steady states of chaotic systems. IEEE Trans., on Circuits and Systems I, 2006, 53(10), 2246-2254.
    • (2006) IEEE Trans., on Circuits and Systems I , vol.53 , Issue.10 , pp. 2246-2254
    • Huijberts, H.1
  • 11
    • 45949087060 scopus 로고    scopus 로고
    • Lune, B. J. Three-parameter tunable tilt-integral derivative (TID) controller. US Patent US5 371 670, 1994
    • Lune, B. J. Three-parameter tunable tilt-integral derivative (TID) controller. US Patent US5 371 670, 1994.
  • 12
    • 27744589296 scopus 로고    scopus 로고
    • α fractional control of robotic time - delay systems
    • α fractional control of robotic time - delay systems. Mechanics Res. Commun., 2006, 33, 269-279.
    • (2006) Mechanics Res. Commun , vol.33 , pp. 269-279
    • Lazarevic, M.P.1
  • 14
    • 0001848898 scopus 로고    scopus 로고
    • From fractal robustness to CRONE control. Fractional Calculus and Appl
    • Oustaloup, A., Sabatier, J., and Lanusse, P. From fractal robustness to CRONE control. Fractional Calculus and Appl. Analysis, 1999, 2(1), 1-30.
    • (1999) Analysis , vol.2 , Issue.1 , pp. 1-30
    • Oustaloup, A.1    Sabatier, J.2    Lanusse, P.3
  • 17
    • 0343715573 scopus 로고    scopus 로고
    • State-space representation for fractional order controllers
    • Raynaud, H. F. and Inoh, A. Z. State-space representation for fractional order controllers. Automatica, 2000, 36, 1017-1021.
    • (2000) Automatica , vol.36 , pp. 1017-1021
    • Raynaud, H.F.1    Inoh, A.Z.2
  • 19
    • 33847623276 scopus 로고    scopus 로고
    • Fractional robust control of main irrigation canals with variable dynamic parameters
    • Feliu-Batlle, V., Rivas Perez, R., and Sanchez Rodriguez, L. Fractional robust control of main irrigation canals with variable dynamic parameters. Control Engng Practice, 2007, 15, 673-686.
    • (2007) Control Engng Practice , vol.15 , pp. 673-686
    • Feliu-Batlle, V.1    Rivas Perez, R.2    Sanchez Rodriguez, L.3
  • 20
    • 0242339711 scopus 로고    scopus 로고
    • Using fractional calculus for lateral and longitudinal control of autonomous vehicles
    • Springer, Berlin/Heidelberg
    • Suárez, J. I., Vinagre, B. M., Calderón, A. J., Monje, C. A., and Chen, Y. Q. Using fractional calculus for lateral and longitudinal control of autonomous vehicles. In Lecture notes in computer science (LNCS), vol. 2809, 2004 (Springer, Berlin/Heidelberg).
    • (2004) Lecture notes in computer science (LNCS , vol.2809
    • Suárez, J.I.1    Vinagre, B.M.2    Calderón, A.J.3    Monje, C.A.4    Chen, Y.Q.5
  • 21
    • 33745712064 scopus 로고    scopus 로고
    • Fractional order control strategies for power electronic buck converters
    • Calderon, A. J., Vinagre, B. M., and Feliu, V. Fractional order control strategies for power electronic buck converters. Signal Processing, 2006, 86, 2803-2819.
    • (2006) Signal Processing , vol.86 , pp. 2803-2819
    • Calderon, A.J.1    Vinagre, B.M.2    Feliu, V.3
  • 22
  • 23
    • 0036651020 scopus 로고    scopus 로고
    • Fractional differentiation in passive vibration control
    • Moreau, X., Ramus-Serment, C., and Oustaloup, A. Fractional differentiation in passive vibration control. Nonlinear Dynamics, 2002, 29, 343-362.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 343-362
    • Moreau, X.1    Ramus-Serment, C.2    Oustaloup, A.3
  • 24
    • 15544389469 scopus 로고    scopus 로고
    • Robust speed control of a low damped electromechanical system based on CRONE control: Application to a four mass experimental test bench
    • Sabatier, J., Poullain, S., Latteux, P., Thomas, J. L., and Oustaloup, A. Robust speed control of a low damped electromechanical system based on CRONE control: application to a four mass experimental test bench. Nonlinear Dynamics, 2004, 38, 383-400.
    • (2004) Nonlinear Dynamics , vol.38 , pp. 383-400
    • Sabatier, J.1    Poullain, S.2    Latteux, P.3    Thomas, J.L.4    Oustaloup, A.5
  • 25
    • 0036648507 scopus 로고    scopus 로고
    • A suggestion of fractional order controller for flexible spacecraft attitude control
    • Manabe, S. A suggestion of fractional order controller for flexible spacecraft attitude control. Nonlinear Dynamics, 2002, 29, 251-268.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 251-268
    • Manabe, S.1
  • 26
    • 45949103713 scopus 로고    scopus 로고
    • Matignon, D. Stability results for fractional differential equations with applications to control processing. In the Computational Engineering in Systems and Applications Multi-conference, 2, IMACS, IEEE-SMC Proceedings, Lille, France, July 1996, pp. 963-968.
    • Matignon, D. Stability results for fractional differential equations with applications to control processing. In the Computational Engineering in Systems and Applications Multi-conference, vol. 2, IMACS, IEEE-SMC Proceedings, Lille, France, July 1996, pp. 963-968.
  • 27
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • Deng, W., Li, C., and Lü, J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics, 2007, 48, 409-416.
    • (2007) Nonlinear Dynamics , vol.48 , pp. 409-416
    • Deng, W.1    Li, C.2    Lü, J.3
  • 28
    • 33750295344 scopus 로고    scopus 로고
    • Equilibrium points, stability and numerical solutions of fractional order predator-prey and rabies models
    • Ahmed, E., El-Sayed, A. M. A., and El-Saka, H. A. A. Equilibrium points, stability and numerical solutions of fractional order predator-prey and rabies models. J. Math. Analysis and Applics, 2007, 325, 542-553.
    • (2007) J. Math. Analysis and Applics , vol.325 , pp. 542-553
    • Ahmed, E.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 30
    • 0037227409 scopus 로고    scopus 로고
    • Pole placement by static output feedback for generic linear systems
    • Eremenko, A. and Gabrielov, A. Pole placement by static output feedback for generic linear systems. SIAM J. Control Optimization, 2002, 41(1), 303-312.
    • (2002) SIAM J. Control Optimization , vol.41 , Issue.1 , pp. 303-312
    • Eremenko, A.1    Gabrielov, A.2
  • 31
    • 0029370403 scopus 로고
    • Generalized Bass - Gura formula for the control of linear time - varying systems
    • Chen, M. S. Generalized Bass - Gura formula for the control of linear time - varying systems. J. Control Systems and Technol., 1995, 3(3), 163-169.
    • (1995) J. Control Systems and Technol , vol.3 , Issue.3 , pp. 163-169
    • Chen, M.S.1
  • 32
    • 70450048998 scopus 로고
    • Der entwulf linear regelungs systems in zustandsraum
    • Ackermann, J. E. Der entwulf linear regelungs systems in zustandsraum. Regelungstech und Pro-zessdatenv Erarb., 1972, 7, 297-300.
    • (1972) Regelungstech und Pro-zessdatenv Erarb , vol.7 , pp. 297-300
    • Ackermann, J.E.1
  • 33
    • 0035502865 scopus 로고    scopus 로고
    • New computational procedure to the pole placement problem by static output feedback
    • Carotenuto, L., Franze, C., and Muraca, P. New computational procedure to the pole placement problem by static output feedback. IEE Proc: Control Theory and Applics, 2001, 148(6), 466-471.
    • (2001) IEE Proc: Control Theory and Applics , vol.148 , Issue.6 , pp. 466-471
    • Carotenuto, L.1    Franze, C.2    Muraca, P.3
  • 34
    • 0028397052 scopus 로고
    • An iterative algorithm for pole placement by output feedback
    • Lee, T. H., Wang, Q. G., and Koh, E. K. An iterative algorithm for pole placement by output feedback. IEEE Trans. on Autom. Control, 1994, 39(3), 565-568.
    • (1994) IEEE Trans. on Autom. Control , vol.39 , Issue.3 , pp. 565-568
    • Lee, T.H.1    Wang, Q.G.2    Koh, E.K.3
  • 35
    • 38149125451 scopus 로고    scopus 로고
    • Chaos control via a simple fractional-order controller
    • In Press
    • Tavazoei, M. S. and Haeri, M. Chaos control via a simple fractional-order controller. Physics Letters A, In Press, 2007 (http://dx.doi.Org/10.1016/j. physleta.2007.08.040).
    • (2007) Physics Letters A
    • Tavazoei, M.S.1    Haeri, M.2
  • 36
    • 0346910376 scopus 로고    scopus 로고
    • New 3-D-scroll attrac-tors in hyperchaotic Chua's circuit forming a ring
    • Cafagna, D. and Grassi, G. New 3-D-scroll attrac-tors in hyperchaotic Chua's circuit forming a ring. Int. J. Bifurcation and Chaos, 2003, 13(10), 2889-2903.
    • (2003) Int. J. Bifurcation and Chaos , vol.13 , Issue.10 , pp. 2889-2903
    • Cafagna, D.1    Grassi, G.2
  • 39
    • 10944251999 scopus 로고    scopus 로고
    • Design and analysis of multi scroll chaotic attractors from saturated function series
    • Lü, J., Chen, G., Yu, X., and Leung, H. Design and analysis of multi scroll chaotic attractors from saturated function series. IEEE Trans. on Circuits and Systems I, 2004, 51(12), 2476-2490.
    • (2004) IEEE Trans. on Circuits and Systems I , vol.51 , Issue.12 , pp. 2476-2490
    • Lü, J.1    Chen, G.2    Yu, X.3    Leung, H.4
  • 40
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional order systems
    • Tavazoei, M. S. and Haeri, M. A necessary condition for double scroll attractor existence in fractional order systems. Phys. Lett. A, 2007, 367(1-2), 102-113.
    • (2007) Phys. Lett. A , vol.367 , Issue.1-2 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 42
    • 2042430768 scopus 로고    scopus 로고
    • Viewing the efficiency of chaos control
    • Chanfreau, P. and Lyyjynen, H. Viewing the efficiency of chaos control. J. Nonlinear Math. Physics, 1999, 6(3), 314-331.
    • (1999) J. Nonlinear Math. Physics , vol.6 , Issue.3 , pp. 314-331
    • Chanfreau, P.1    Lyyjynen, H.2
  • 43
    • 0001454658 scopus 로고
    • Using chaos to direct trajectories to targets
    • Shinbrot, T., Ott, E., Grebogi, C., and Yorke, J. Using chaos to direct trajectories to targets. Phys. Rev. Lett., 1990, 65(26), 3215-3218.
    • (1990) Phys. Rev. Lett , vol.65 , Issue.26 , pp. 3215-3218
    • Shinbrot, T.1    Ott, E.2    Grebogi, C.3    Yorke, J.4
  • 44
    • 0000801336 scopus 로고
    • Techniques for the control of chaos
    • Ditto, W. L., Spano, M. L., and Lindner, J. F. Techniques for the control of chaos. Physica D, 1995, 86, 198-211.
    • (1995) Physica D , vol.86 , pp. 198-211
    • Ditto, W.L.1    Spano, M.L.2    Lindner, J.F.3
  • 45
    • 11944270703 scopus 로고
    • Experimental control of chaos
    • Ditto, W. L., Rauseo, S. N., and Spano, M. L. Experimental control of chaos, Phys. Rev. Lett., 1990, 65(26), 3211-3213.
    • (1990) Phys. Rev. Lett , vol.65 , Issue.26 , pp. 3211-3213
    • Ditto, W.L.1    Rauseo, S.N.2    Spano, M.L.3
  • 47
    • 0033888365 scopus 로고    scopus 로고
    • Frequency-band complex non integer differentiator: Characterization and synthesis
    • Oustaloup, A., Levron, F., Nanot, F., and Mathieu, B. Frequency-band complex non integer differentiator: characterization and synthesis. IEEE Trans. on Circuits and Systems I, 2000, 47(1), 25-39.
    • (2000) IEEE Trans. on Circuits and Systems I , vol.47 , Issue.1 , pp. 25-39
    • Oustaloup, A.1    Levron, F.2    Nanot, F.3    Mathieu, B.4
  • 48
    • 4644369885 scopus 로고
    • Norms and exclusion theorems
    • Bauer, F. and Fike, C. Norms and exclusion theorems. Numer. Math., 1960, 2, 137-141.
    • (1960) Numer. Math , vol.2 , pp. 137-141
    • Bauer, F.1    Fike, C.2
  • 50
    • 45949090190 scopus 로고    scopus 로고
    • http://www.analog.com/UploadedFiles/Data_Sheets/ AD633.pdf.
  • 51
    • 16244422016 scopus 로고    scopus 로고
    • Real-time control systems: A tutorial
    • In the, Melbourne, Australia, 20-23 July
    • Gambier, A. Real-time control systems: a tutorial. In the Fifth Asian Control Conference, Melbourne, Australia, vol. 2, 20-23 July 2004, pp. 1024-1031.
    • (2004) Fifth Asian Control Conference , vol.2 , pp. 1024-1031
    • Gambier, A.1
  • 52
    • 45949093927 scopus 로고    scopus 로고
    • http://www.advantech.com/products/model_detail. asp?model_id = 1-1TWPF6.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.