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**A neuro-augmented observer for robust fault detection in nonlinear systems.**
*(English)*
Zbl 1264.93234

Summary: A new fault detection method using neural-networks-augmented state observer for nonlinear systems is presented in this paper. The novelty of the approach is that instead of approximating the entire nonlinear system with neural network, we only approximate the unmodeled part that is left over after linearization, in which a radial basis function (RBF) neural network is adopted. Compared with conventional linear observer, the proposed observer structure provides more accurate estimation of the system state. The state estimation error is proved to asymptotically approach zero by the Lyapunov method. An aircraft system demonstrates the efficiency of the proposed fault detection scheme, simulation results of which show that the proposed RBF neural network-based observer scheme is effective and has a potential application in fault detection and identification (FDI) for nonlinear systems.

### MSC:

93E10 | Estimation and detection in stochastic control theory |

93C83 | Control/observation systems involving computers (process control, etc.) |

93B07 | Observability |

94C12 | Fault detection; testing in circuits and networks |

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\textit{H. Gong} and \textit{Z. Zhen}, Math. Probl. Eng. 2012, Article ID 789230, 8 p. (2012; Zbl 1264.93234)

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### References:

[1] | B. Jiang and F. N. Chowdhury, “Fault estimation and accommodation for linear MIMO discrete-time systems,” IEEE Transactions on Control Systems Technology, vol. 13, no. 3, pp. 493-499, 2005. · doi:10.1109/TCST.2004.839569 |

[2] | B. Jiang, Z. Gao, P. Shi, and Y. F. Xu, “Adaptive fault-tolerant tracking control of near-space vehicle using Takagi-Sugeno fuzzy models,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 1000-1007, 2010. · doi:10.1109/TFUZZ.2010.2058808 |

[3] | B. Jiang and F. Chowdhury, “Observer-based fault diagnosis for a class of nonlinear systems,” in Proceedings of the American Control Conference (AAC’04), pp. 5671-5675, July 2004. |

[4] | H. Hammouri, M. Kinnaert, and E. H. El Yaagoubi, “Observer-based approach to fault detection and isolation for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 10, pp. 1879-1884, 1999. · Zbl 0956.93005 · doi:10.1109/9.793728 |

[5] | H. Yang and M. Saif, “Fault detection in a class of nonlinear systems via adaptive sliding observer,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pp. 2199-2204, October 1995. |

[6] | W. Chen and M. Saif, “Robust fault detection in uncertain nonlinear systems via a second order sliding mode observer,” in Proceedings of the 40th IEEE Conference on Decision and Control (CDC’01), vol. 1, pp. 573-578, Orlando, Fla, USA, December 2001. |

[7] | D. N. Shields, S. A. Ashton, and S. Daley, “Robust fault detection observers for nonlinear polynomial systems,” International Journal of Systems Science, vol. 32, no. 6, pp. 723-737, 2001. · Zbl 1038.93510 · doi:10.1080/002077201750281936 |

[8] | C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, no. 4, pp. 541-553, 2000. · Zbl 0968.93502 · doi:10.1016/S0005-1098(99)00177-6 |

[9] | K. Adjallah, D. Maquin, and J. Ragot, “Non-linear observer-based fault detection,” in Proceedings of the 3rd IEEE Conference on Control Applications, vol. 2, pp. 1115-1120, Glasgow, UK, August 1994. · doi:10.1109/CCA.1994.381359 |

[10] | J. Wang, J. Zhao, and L. Ma, “A robust fault detection and isolation method via sliding mode observer,” in Proceedings of the 5th World Congress on Intelligent Control and Automation Conference (WCICA 2004), vol. 2, pp. 1727-1730, June 2004. |

[11] | C. W. Chan, K. C. Cheung, Y. Wang, and W. C. Chan, “On-line fault detection and isolation of nonlinear systems,” in Proceedings of the American Control Conference (ACC’99), pp. 3980-3984, June 1999. |

[12] | R. J. Schilling, J. J. Carroll, and A. F. Al-Ajlouni, “Approximation of nonlinear systems with radial basis function neural networks,” IEEE Transactions on Neural Networks, vol. 12, no. 1, pp. 1-15, 2001. · doi:10.1109/72.896792 |

[13] | H. Zhang, Y. Luo, and D. Liu, “Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints,” IEEE Transactions on Neural Networks, vol. 20, no. 9, pp. 1490-1503, 2009. · doi:10.1109/TNN.2009.2027233 |

[14] | H. Zhang, Z. Liu, G. B. Huang, and Z. Wang, “Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 91-106, 2010. · doi:10.1109/TNN.2009.2034742 |

[15] | H. Shousong and Z. Chuan, “An approach to robust fault detection for nonlinear system based on RBF neural network observer,” Control Theory & Applications, vol. 16, no. 6, pp. 853-857, 1999. · Zbl 1007.93032 |

[16] | Y. M. Cho and R. Rajamani, “A systematic approach to adaptive observer synthesis for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 42, no. 4, pp. 534-537, 1997. · Zbl 0873.93049 · doi:10.1109/9.566664 |

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