本論文提出一個適用於未知非線性隨機混合系統，以非線性自回歸移動平均模型為基底的主動容錯型狀態自調式控制方法。利用可調整的NARMAX模型來建構出非線性隨機系統模型。並對連續時間非線性隨機系統提出一個相符合的適應性數位控制方法，而且此非線性隨機系統的系統參數未知、狀態不可得知、有可量測的雜訊等。然後，一個適用於未知多變數隨機系統的有效率容錯方法被提出，它是修改傳統的狀態空間自調式控制法則；藉著比較在卡曼濾波器估測演算法中的誤差值，一種量化的準則被發展出來：權重矩陣重新設定技術，它是藉著調整和重新設定在卡曼濾波器估測演算法中用以估測參數的協方差矩陣。因此，這方法可以改善用於系統回復的參數估測，並且有效地處理局部突發式或逐步式錯誤的系統錯誤、以及突發式或逐步式的輸入錯誤。

An active fault tolerance using the novel nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuning is proposed in this thesis for unknown nonlinear stochastic hybrid systems. With the adjustable NARMAX-based noise model, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems which have unknown system parameters, measurement noises, and inaccessible system states. Then an effective fault tolerance scheme is proposed for unknown multivariable stochastic systems by modifying the conventional state-space self-tuning control approach for the detection of fault occurrence. A quantitative criterion is suggested by comparing the innovation process errors estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique is developed by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm to improve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the proposed fault detection.

[1] I. J. Leontaritis and S. A. Billings, “Input-output parametric models for nonlinear systems, Parts I and II,” International Journal of Control, vol. 41, pp. 303-328, pp. 329-344, 1985.
[2] S. Chen and S. A. Billings, “Representations of nonlinear system: the NARMAX model,” International Journal of Control, vol. 48, pp. 1013-1032, 1989.
[3] E. D. Sontag, Polynomial Response Maps – Lecture Notes in Control and Identification Science vol. 13. Berlin: Springer-Verlag, 1979.
[4] K. Warwick, “Self-tuning regulators – a state-space approach,” International Journal of
Control, vol. 33, pp. 839-858, 1981.
[5] Y. T. Tsay and L. S. Shieh, “State-space approach for self-tuning feedback control with pole assignment,” IEE Proc. D., Control Theory and Appl., vol. 123, pp. 93-101, 1981.
[6] L. S. Shieh, Y. L. Bao and F. R. Chang, “State-space self-tuning regulators for general multivariable stochastic systems,” IEE Proc. D., Control Theory and Appl., vol. 136, pp. 17-27, 1989.
[7] K. J. Äström and B. Wittenmark, Adaptive Control. NY: Addison-Wesley, 1989.
[8] S. M. Guo, L. S. Shieh, G.. Chen, C. F. Lin, and J. Chandra, “State-space self-tuning
cntrol for nonlinear stochastic and chaotic hybrid system, “ International Journal of
Bifurcation and Chaos, vol.11, no. 4, 1079－1113, 2001.
[9] J. S. H. Tsai, Y. Y. Lee, P. Cofie, L. S. Shieh, X. M. Chen, 2006, “Active fault tolerant
control using state-space self-tuning control approach,” International Journal of
Systems Science, vol. 37, no. 11, pp. 785-797, Sep. 2006.
[10] L. Ljung, System Identification Theory for the User, Englewood Cliffs: Prentice-Hall, 1987.
[11] T. Kailath, “An innovation approach to least-squares estimation. Part I: Linear filtering in additive white noise,” IEEE Trans. on Automatic Control, vol. AC-13, pp. 646-655, 1968.
[12] M. E. Polites, “Ideal state reconstructor for deterministic digital control
systems,” International Journal of Control, vol. 49, pp. 2001-2011, 1989.
[13] J. B. Dabney and T. L. Harman, Mastering Simulink 2. Englewood Cliffs, NJ: Prentice-Hall, 1998.
[14] M. C. M. Teixeira and S. H. Zak, “Stabilizing controller design for uncertain nonlinear systems using fuzzy models,” IEEE Trans. on Fuzzy Systems, vol. 7, no. 2, pp. 133-142, 1999.
[15] Y. T. Tsay, L. S. Shieh and S. Barnett, “Structural Analysis and Design of Multivariable Control Systems: an Algebraic Approach.” Berlin, Heidelberg: Springer-Verlag, 1988.
[16] L. S. Shieh and Y. T. Tsay, “ Transformations of a class of multivariable control systems to block companion forms,” IEEE Trans. on Automatic Control, vol. AC-27, pp. 199-203, 1982.
[17] L. S. Shieh, C. T. Wang and Y. T. Tsay, “Multivariable state feedback self-tuning controllers, ” Stochastic Analysis and Applications, vol. 3, no. 2, pp. 189-212, 1985.
[18] G.. G.. Yen, and L. W. Ho, “Online multiple-model-based fault diagnosis and accommodation”, IEEE Transactions on Industrial Electronics, 50, 296－312, 2003.
[19] T. Soderstrom, and P. Stoica, System Identification, Englewood Cliffs: Prentice-Hall, 1989.
[20] L. S. Shieh, H. M. Dib and S. Ganesan, “Linear quadratic regulators with eigenvalue placement in a specified region,” Automatica, vol. 24, pp. 819-823, 1988.
[21] F. L. Lewis, and V. L. Syrmos, “Optimal Control,” New York: John Wiley & Sons, 1995.
[22] K. J. Astrom, and B. Wittenmark, “Adaptive Control,” Boston: Addison Wesley, 1995.