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**Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping.**
*(English)*
Zbl 1142.93378

Summary: A robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances. The controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique. For each auxiliary system, an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics, and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well. It is shown that the resulting closed-loop systems guarantee a satisfactory transient and asymptotic performance. A simulation example is also presented to illustrate the design procedure and controller performance.

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\textit{S. Zhou} et al., Fuzzy Sets Syst. 151, No. 1, 1--20 (2005; Zbl 1142.93378)

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### References:

[1] | Chang, Y.-C.; Chen, B.-S., Robust tracking designs for both holonomic and nonholonomic constrained mechanical systemsadaptive fuzzy approach, IEEE trans. fuzzy systems, 8, 1, 46-65, (2000) |

[2] | Chen, B.-S.; Lee, C.-H.; Chang, Y.-C., \(H_\infty\) tracking design of uncertain SISO systemsadaptive fuzzy approach, IEEE trans. fuzzy systems, 4, 1, 32-43, (1996) |

[3] | Hsu, F.-Y.; Fu, L.-C., A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping, Fuzzy sets and systems, 122, 1, 83-106, (2001) · Zbl 0991.93064 |

[4] | Ioannou, P.A.; Kokotovic, P.V., Adaptive systems with reduced models, (1983), Lecture Notes in Control and Information Sciences vol. 47, Springer, New York · Zbl 0516.93017 |

[5] | Ioannou, P.A.; Kokotovic, P.V., Instability analysis and improvement of robustness of adaptive control, Automatica, 20, 5, 583-594, (1984) · Zbl 0548.93050 |

[6] | Ioannou, P.A.; Sun, Jing, Robust adaptive control, (1996), Prentice-Hall Englewood Cliffs, NJ · Zbl 0839.93002 |

[7] | Jiang, Z.; Hill, D.J., A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics, IEEE trans. automat. control, 44, 9, 1705-1711, (1999) · Zbl 0958.93053 |

[8] | Khalil, H.K., Nonlinear systems, (1992), Macmillan Publishing Company New York · Zbl 0626.34052 |

[9] | Krstic, M.; Kanellakopoulos, I.; Kokotovic, P., Adaptive nonlinear control without overparameterization, Systems control lett., 43, 336-351, (1992) · Zbl 0763.93043 |

[10] | Lee, H.; Tomizuka, M., Robust adaptive control using a universal approximator for SISO nonlinear systems, IEEE trans. fuzzy systems, 8, 1, 95-106, (2000) |

[11] | Pan, Z.; Basar, T., Adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems, IEEE trans. automat. control, 43, 8, 1066-1083, (1998) · Zbl 0957.93046 |

[12] | S˘elmic, R.R.; Lewis, F.L., Deadzone compensation in motion control systems using neural networks, IEEE trans. automat. control, 45, 4, 602-613, (2000) · Zbl 0989.93068 |

[13] | Shi, L.; Singh, S.K., Decentralized adaptive controller design for large-scale systems with higher order interconnections, IEEE trans. automat. control, 37, 8, 1106-1118, (1992) · Zbl 0764.93051 |

[14] | Vedagarbha, P.; Dawson, D.M.; Feemster, M., Tracking control of mechanical systems in the presence of nonlinear dynamic friction effects, IEEE trans. control systems technol., 7, 446-465, (2000) |

[15] | Wang, L.X., Adaptive fuzzy systems and controldesign and stability and analysis, (1994), Prentice-Hall Englewood Cliffs, NJ |

[16] | Wang, L.X., Design and analysis of fuzzy identifiers of nonlinear dynamic systems, IEEE trans. automat. control, 40, 11-23, (1995) · Zbl 0823.93037 |

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