Sliding mode control with adaptive fuzzy dead-zone compensation for uncertain chaotic systems

Nonlinear Dynamics

Volumn 70, Issue 3, 2012, Pages 1989-2001

  Bessa, Wallace M ^a   De Paula, Aline S ^b   Savi, Marcelo A ^c  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

^b UNIVERSITY OF BRASILIA   (Brazil)

^c FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Chaos control; Dead zone; Fuzzy logic; Nonlinear pendulum; Sliding modes; Unstable periodic orbits

Indexed keywords

CHAOS CONTROL; DEAD-ZONE; NON-LINEAR PENDULUM; SLIDING MODES; UNSTABLE PERIODIC ORBITS;

ALGORITHMS; CONTROLLERS; FUZZY LOGIC; FUZZY SETS; PENDULUMS; SLIDING MODE CONTROL;

CHAOTIC SYSTEMS;

EID: 84870898670     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0591-z     Document Type: Article

References (74)

1. Alasty, A., Salarieh, H.: Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers. Chaos Solitons Fractals 26(2), 379-392 (2005)
2. Auerbach, D., Cvitanovíc, P., Eckmann, J.P., Gunaratne, G., Procaccia, I.: Exploring chaotic motion through periodic orbits. Phys. Rev. Lett. 58(23), 2387-2389 (1987)
3. Bessa, W.M.: Some remarks on the boundedness and convergence properties of smooth sliding mode controllers. Int. J. Autom. Comput. 6(2), 154-158 (2009)
4. Bessa,W.M., Barrêto, R.S.S.: Adaptive fuzzy sliding mode control of uncertain nonlinear systems. Control. Autom. 21(2), 117-126 (2010)
5. Bessa, W.M., Dutra, M.S., Kreuzer, E.: Depth control of remotely operated underwater vehicles using an adaptive fuzzy sliding mode controller. Robot. Auton. Syst. 56(8), 670-677 (2008)
6. Bessa, W.M., De Paula, A.S., Savi, M.A.: Chaos control using an adaptive fuzzy sliding mode controller with application to a nonlinear pendulum. Chaos Solitons Fractals 42(2), 784-791 (2009)
7. Bessa, W.M., Dutra, M.S., Kreuzer, E.: An adaptive fuzzy dead-zone compensation scheme and its application to electro-hydraulic systems. J. Braz. Soc. Mech. Sci. Eng. 32(1), 1-7 (2010)
8. Bessa, W.M., Dutra, M.S., Kreuzer, E.: An adaptive fuzzy sliding mode controller for remotely operated underwater vehicles. Robot. Auton. Syst. 58(1), 16-26 (2010)
9. Bessa, W.M., Dutra, M.S., Kreuzer, E.: Sliding mode control with adaptive fuzzy dead-zone compensation of an electro-hydraulic servo-system. J. Intell. Robot. Syst. 58(1), 3-16 (2010)
10. Boulkroune, A., M'Saad, M.: A fuzzy adaptive variablestructure control scheme for uncertain chaotic MIMO systems with sector nonlinearities and dead-zones. Expert Syst. Appl. 38(12), 14744-14750 (2011)
11. Chang, W., Park, J.B., Joo, Y.H., Chen, G.: Design of robust fuzzy-model-based controller with sliding mode control for SISO nonlinear systems. Fuzzy Sets Syst. 125(1), 1-22 (2002)
12. Corradini, M.L., Orlando, G.: Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator. IEEE Trans. Control Syst. Technol. 10(1), 158-166 (2002)
13. Cybenko, G.: Approximations by superpositions of sigmoidal functions. Math. Control Signals Syst. 2(4), 303-314 (1989)
14. De Paula, A.S., Savi, M.A., Pereira-Pinto, F.H.I.: Chaos and transient chaos in an experimental nonlinear pendulum. J. Sound Vib. 294(3), 585-595 (2006)
15. Filippov, A.F.: Differential Equations with Discontinuous Right-hand Sides. Kluwer, Dordrecht (1988)
16. Franca, L.F.P., Savi, M.A.: Distinguishing periodic and chaotic time series obtained from an experimental nonlinear pendulum. Nonlinear Dyn. 26(3), 253-271 (2001)
17. Fuh, C.C., Tung, P.C.: Robust control for a class of nonlinear oscillators with chaotic attractors. Phys. Lett. A 218(3-6), 240-248 (1996)
18. Hojati, M., Gazor, S.: Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Trans. Fuzzy Syst. 10(2), 198-210 (2002)
19. Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Netw. 4(2), 251-257 (1991)
20. Hu, C., Yao, B., Wang, Q.: Adaptive robust precision motion control of systems with unknown input dead-zones: a case study with comparative experiments. IEEE Trans. Ind. Electron. 58(6), 2454-2464 (2011)
21. Hua, C.C., Ding, S.X.: Model following controller design for large-scale systems with time-delay interconnections and multiple dead-zone inputs. IEEE Trans. Autom. Control 56(4), 962-968 (2011)
22. Hua, C.C.,Wang, Q.G., Guan, X.P.: Adaptive tracking controller design of nonlinear systems with time delays and unknown dead-zone input. IEEE Trans. Autom. Control 53(7), 1753-1759 (2008)
23. Ibrir, S., Su, C.Y.: Simultaneous state and dead-zone parameter estimation for a class of bounded-state nonlinear systems. IEEE Trans. Control Syst. Technol. 19(4), 911-919 (2011)
24. Ibrir, S., Xie,W.F., Su, C.Y.: Adaptive tracking of nonlinear systems with non-symmetric dead-zone input. Automatica 43(4), 522-530 (2007)
25. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New Jersey (2001)
26. Kim, J.H., Park, J.H., Lee, S.W., Chong, E.K.P.: A twolayered fuzzy logic controller for systems with deadzones. IEEE Trans. Ind. Electron. 41(2), 155-162 (1994)
27. Konishi, K., Hirai, M., Kokame, H.: Sliding mode control for a class of chaotic systems. Phys. Lett. A 245(6), 511-517 (1998)
28. Kosko, B.: Fuzzy systems as universal approximators. IEEE Trans. Comput. 43(11), 1329-1333 (1994)
29. Kung, C.C., Chen, T.H.: Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems. Fuzzy Sets Syst. 155(2), 292-308 (2005)
30. Lewis, F.L., Tim, W.K., Wang, L.Z., Li, Z.X.: Deadzone compensation in motion control systems using adaptive fuzzy logic control. IEEE Trans. Control Syst. Technol. 7(6), 731-742 (1999)
31. Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf. Sci. 177(18), 3901-3917 (2007)
32. Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dyn. 57(3), 431-439 (2009)
33. Liu, Y.J., Zhou, N.: Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input. ISA Trans. 49(4), 462-469 (2010)
34. Liu, Y.J., Tong, S.C., Wang, W.: Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst. 160(19), 2727-2754 (2009)
35. Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 40(1), 170-184 (2010)
36. Liu, Y.J., Chen, C.L.P.,Wen, G.X., Tong, S.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162-1167 (2011)
37. Liu, Y.J., Wang, W., Li, T.S.: Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems. Fuzzy Sets Syst. 164(1), 25-44 (2011)
38. Liu, Y.J.,Wang,W.,Wang, D., Li, T.S., Chen, C.L.P.: Adaptive neural output feedback controller design with reducedorder observer for a class of uncertain nonlinear SISO systems. IEEE Trans. Neural Netw. 22(8), 1328-1334 (2011)
39. Ma, H.J., Yang, G.H.: Adaptive output control of uncertain nonlinear systems with non-symmetric dead-zone input. Automatica 46(2), 413-420 (2010)
40. Mekircha, N., Mansouri, A.B.N.: Fuzzy control of original UPOs of unknown discrete chaotic systems. Appl. Math. Model. 36(10), 5135-5142 (2012)
41. Na, J., Ren, X., Herrmann, G., Qiao, Z.: Adaptive neural dynamic surface control for servo systems with unknown dead-zone. Control Eng. Pract. 19(11), 1328-1343 (2011)
42. Noroozi, N., Roopaei, M., Karimaghaee, P., Safavi, A.A.: Simple adaptive variable structure control for unknown chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 15(3), 707-727 (2010)
43. Oh, S.Y., Park, D.J.: Design of new adaptive fuzzy logic controller for nonlinear plants with unknown or timevarying dead zones. IEEE Trans. Fuzzy Syst. 6(4), 482-491 (1998)
44. Park, J., Sandberg, I.W.: Universal approximation using radial-basis-function networks. Neural Comput. 3(2), 246-257 (1991)
45. Pereira-Pinto, F.H.I., Ferreira, A.M., Savi, M.A.: Chaos control in a nonlinear pendulum using a semi-continuous method. Chaos Solitons Fractals 22(3), 653-668 (2004)
46. Poursamad, A., Davaie-Markazi, A.H.: Robust adaptive fuzzy control of unknown chaotic systems. Appl. Soft Comput. 9(3), 970-976 (2009)
47. Roopaei, M., Sahraei, B.R., Lin, T.C.: Adaptive sliding mode control in a novel class of chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 15(12), 4158-4170 (2010)
48. Šelmíc, R.R., Lewis, F.L.: Deadzone compensation in motion control systems using neural networks. IEEE Trans. Autom. Control 45(4), 602-613 (2000)
49. Shen, D., Mu, Y., Xiong, G.: Iterative learning control for non-linear systems with deadzone input and time delay in presence of measurement noise. IET Control Theory Appl. 5(12), 1418-1425 (2011)
50. Shyu, K.K., Liu, W.J., Hsu, K.C.: Design of large-scale time-delayed systems with dead-zone input via variable structure control. Automatica 41(7), 1239-1246 (2005)
51. Slotine, J.J.E.: Sliding controller design for nonlinear systems. Int. J. Control 40(2), 421-434 (1984)
52. Su, J.P., Chen, T.M., Wang, C.C.: Adaptive fuzzy sliding mode control with GA-based reaching laws. Fuzzy Sets Syst. 120(1), 145-158 (2001)
53. Tao, G., Kokotovíc, P.V.: Adaptive control of plants with unknown dead-zones. IEEE Trans. Autom. Control 39(1), 59-68 (1994)
54. Tong, S., Li, Y.: Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 20(1), 168-180 (2012)
55. Tsai, C.H., Chuang, H.T.: Deadzone compensation based on constrained RBF neural network. J. Franklin Inst. 341(4), 361-374 (2004)
56. Tsai, H.H., Fuh, C.C., Chang, C.N.: A robust controller for chaotic systems under external excitation. Chaos Solitons Fractals 14(4), 627-632 (2002)
57. Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146-155 (1993)
58. Wang, J., Hu, J.: Robust adaptive neural control for a class of uncertain non-linear time-delay systems with unknown dead-zone non-linearity. IET Control Theory Appl. 5(15), 1782-1795 (2011)
59. Wang, X.S., Su, C.Y., Hong, H.: Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica 40(3), 407-413 (2004)
60. Yan, J.J., Shyu, K.K., Lin, J.S.: Adaptive variable structure control for uncertain chaotic systems containing deadzone nonlinearity. Chaos Solitons Fractals 25(2), 347-355 (2005)
61. Yȩsildirek, A., Lewis, F.L.: Feedback linearization using neural networks. Automatica 31(11), 1659-1664 (1995)
62. Yildiz, Y., Sabanovic, A., Abidi, K.: Sliding-mode neurocontroller for uncertain systems. IEEE Trans. Ind. Electron. 54(3), 1676-1685 (2007)
63. Yoo, B., Ham, W.: Adaptive fuzzy sliding mode control of nonlinear system. IEEE Trans. Fuzzy Syst. 6(2), 315-321 (1998)
64. Yoo, S.J., Park, J.B., Choi, Y.H.: Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. Automatica 45(2), 436-443 (2009)
65. Yu, X.: Variable structure control approach for controlling chaos. Chaos Solitons Fractals 8(9), 1577-1586 (1997)
66. Yu, X., Kaynak, O.: Sliding-mode control with soft computing: a survey. IEEE Trans. Ind. Electron. 56(9), 3275-3285 (2009)
67. Yu, J., Chen, B., Yu, H.: Fuzzy-approximation-based adaptive control of the chaotic permanent magnet synchronous motor. Nonlinear Dyn. 69(3), 1479-1488 (2012)
68. Zhang, T.P., Ge, S.S.: Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs. Automatica 43(6), 1021-1033 (2007)
69. Zhang, T.P., Ge, S.S.: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7), 1895-1903 (2008)
70. Zhang, T.P., Ge, S.S.: Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions. IEEE Trans. Neural Netw. 20(3), 483-497 (2009)
71. Zhou, J.: Decentralized adaptive control for large-scale time-delay systems with dead-zone input. Automatica 44(7), 1790-1799 (2008)
72. Zhou, J., Shen, X.Z.: Robust adaptive control of nonlinear uncertain plants with unknown dead-zone. IET Control Theory Appl. 1(1), 25-32 (2007)
73. Zhou, J., Wen, C., Zhang, Y.: Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Trans. Autom. Control 51(3), 504-511 (2006)
74. Zhou, N., Liu, Y.J., Tong, S.C.: Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input. Nonlinear Dyn. 63(4), 771-778 (2011)