本論文提出一個新方法針對多輸入多輸出的未知奇異系統之觀測基底追蹤器，為了簡化奇異系統，在此提出一個法則使奇異系統轉換為等效的線性系統而仍保留相同輸入及輸出的關係，換句話說，奇異系統可以分解成一個降階的正規系統及一個非動態系統，然後變換二者得到一個正規模型，然而，一個正規的觀測/卡爾曼濾波器鑑別法可以有效的鑑別一個未知的奇異系統，此外，為了改善觀測器的表現，此觀測器被設計於一個等效的線性模型，並使用進化演算法調整該觀測增益，除此之外，數位再設計追蹤器被提出於觀測器調整及線性鑑別模型，最後，我們使用幾個範例來證明此新法則的有效性。

A new methodology of the observer-based trackers of unknown multi-input multi-output (MIMO) singular systems is proposed in this thesis. For simplifying the singular systems, a new method is proposed to transfer the singular systems into the equivalent linear models that contain the same input-output relationship. In the other words, the singular system can be decomposed into a reduced order regular system and a nondynamic equation, then convert them into a regular model. Therefore, the regular Observer/Kalman Filter Identification (OKID) can be applied to identify unknown singular systems effectively. Moreover, in order to improve the performance of the observer, an observer is designed based on the identified equivalent linear model, and the corresponding observer gain is weighted by a tuning matrix through the evolutionary programming (EP). Beside, the digital redesign tracker is proposed based on the tuned observer and the linear identified model. Some examples are presented to demonstrate the effectiveness of the proposed methodology.

[1].Roberts, J. D., “Linear model reduction and solution of the algebraic Riccati equation by use of the sign function,” International Journal Control, vol. 32, pp. 677-687, 1980.
[2].Tsai, J. S. H., Wang, C. T., and L. S. Shieh, “Model conversion and digital redesign of
singular systems, ” Journal of Franklin Institute, vol. 330, pp.1063-1086, 1993.
[3].Halton, J. H., “On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals,” Numerische Mathematic, vol. 2, pp84-90, 1960.
[4].Van Der Corput, J. C., “Verteilungsfunktionen,” Proc. Kon Akad. Wet., Amstrerdam, vol. 38, pp. 1058-1066, 1935.
[5].Juang, J. N., Applied System Identification, Englewood Cliffs. NJ, Prentice-Hall, 1994.
[6].Kuo, C., Digital Control System, New York: Holt, Rinehart, and Winston, 1980.
[7].Yokoyama, T., Kosuge, K. and Furuta, K., “Digital redesign of robot control” , Proc. IECON’ 89, 15th Ann. Conf. IEEE,vol.2, pp. 409-414, 1989.
[8].Xu, J., Chen, G. and Shieh, L.S., “Digital redesign for controlling chaotic Chua’s circuit”, IEEE Tran. Aerosp. Electron. Syst, vol.32, pp. 1488-1499, 1996.
[9].Joo, Y.H., Chen, G. and Shieh, L.S., “Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems”, IEEE Transaction Fuzzy System, vol.7, pp. 394-408, 1999.
[10].Shieh., L.S., Wang, W. and Tsai J.S.H., “Optimal digital redesign of hybrid uncertain systems using genetic algorithms”, Proc. Inst. Elect. Eng.-Control Theory Appl., vol.146, pp. 119-130, 1999.
[11].Shieh, L,S., Wang, W.M., Bain, J. and Chandra, J., “Design of lifted dual-rate digital controllers for X-38 vechicle”, AIAA, J. Guid Control Dyn., vol23, pp.629-639, 2000.
[12].Guo, S. M., Shieh, L. S., Chen, G. and Lin, C.F., “Effective chaotic orbit tracker : a prediction-based digital redesign approach”, IEEE Transaction on Circuits and System-I , Fundamental Theory and Applications, vol. 47(11), pp.1557-1570, 2000.
[13].Chang, W., Park, Y.H., Joo, Y.H. and Chen, G., “Design of sampled-data fuzzy-model-based control systems by using intelligent digital redesign”, IEEE Transaction Circuits System, vol. 49 , pp. 509-517, 2002.
[14].Lee, H. J., Park, J. B. and Joo, Y. H., “An efficient observer-based sampled-data control : digital redesign approach”, IEEE Transaction Circuits and Systems-I, Fundamental Theory and Applications, vol. 50(12) , 2003.
[15].Shieh, L. S., Tsay, Y. T., and Yates, R. E., “Some properties of matrix-sign functions derived from continued fractions,” IEE Proceedings Part D, vol. 130, no. 3, pp. 111-118, 1983.
[16].Tsai, J. S. H., Shieh, L. S., and Yates, R. E., “Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix-sector function,” International Journal of Computers and Mathematics with Applications, vol. 15, no. 11, pp. 903-913, 1988.
[17].L. S. Shieh, W. M. Wang, J. Bain, and J. W. Sunkel, “Design of lifted dual-rate digital controllers for X-38 vehicle”, AIAA, J. Guid. Control Dyn., vol. 23, pp. 629-639, 2000.
[18].S. M. Guo, L. S. Shieh, C. F. Lin, and J. Chandra, “State-space self-tuning control for nonlinear stochastic and chaotic hybrid systems”, Int, J. Birfurcation Chaos, vol. 11, (4), pp. 1079-1113, 2001.