本論文提出一種適用於具有內部連結未知資料取樣大尺度線性延遲的奇異系統且具有閉迴路解耦特性的分散式線性觀測器與軌跡追蹤器設計方法。透過離線的觀測器/卡爾曼濾波器鑑別方法計算出包含有直接傳輸項的內部連結未知資料取樣大尺度線性延遲的奇異系統之適當階數(或低階)的分散式線性觀測器，然後基於一個含有直接傳輸項的對等分散式系統，以等效的系統來架構一個高增益的類比二次式觀察器和軌跡追蹤器。然後，利用數位再設計法則以得到一個實用的數位觀測器和軌跡追蹤器以控制資料取樣的系統。具有高增益的特性使分散式數位軌跡追蹤器在有內部連結的閉迴路系統具有解耦的特性。最後，藉由進化論演算法來獲得每一個適當的分散式觀測器的權重以增進追蹤性能。

Modeling of decentralized linear observers and trackers for the unknown sampled-data interconnected large-scale linear singular system with time delay and closed-loop decoupling property is proposed in this thesis. Through the off-line observer / Kalman filter identification (OKID), the appropriate (low-) order decentralized linear observers with direct transmission terms from input to output for the unknown sampled-data interconnected large-scale linear singular system with time delay are determined. Then, the high-gain linear quadratic suboptimal analogue observer and tracker are proposed based on the each decentralized equivalent regular system with a direct transmission term from input to output. Subsequently, the prediction-based digital redesign method is utilized to obtain practically implemental digital observer and tracker for the sample-data system. With the high-gain property, the decentralized digital-redesign trackers have the decoupling property for the closed-loop interconnected system. Finally, appropriate weighting of the each decentralized observer can be obtained to improve the performance of observer-based tracker by the evolutionary programming (EP).

[1] H. J. Wang, A. K. Xue, Y. F. Guo, and R. Q. Lu, “Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays,” Journal of Zhejiang University-Science A, vol. 9, no. 4, pp. 546-551, 2008.
[2] J. S. H. Tsai, C. T. Wang, and L. S. Shieh, “Model conversion and digital redesign of singular systems,” Journal of Franklin Institute, vol. 330, pp. 1063-1086, 1993.
[3] B. G. Mertzios, M. A. Christodoulou, B. L. Syrmos, and F. L. Lewis, “Direct controllability and Observability time domain conditions of singular systems,” IEEE Transactions Automatic Control, vol. 33, no. 8, pp. 788-7 91, August 1988.
[4] C. J. Wang and H. E. Liao, “Impulse observability and impulse controllability of linear time-varying singular systems,” Automatica, 37 pp. 1867-1872, 2001.
[5] P. A. Ioannou and J. Sun, Robust Adaptive Control, New Jersey: Prentice Hall, 1996.
[6] D. T. Gavel and D. D. Seljuk, “Decentralized adaptive control: structural conditions for stability,” IEEE Transactions on Automatic Control, vol. 34, pp. 413-426, 1989.
[7] L. Shi and S. K. Singh, “Decentralized adaptive controller design of large-scale systems with higher order interconnections,” IEEE Transactions on Automatic Control, vol. 37, pp. 1106-1118, 1992.
[8] R. Ortega and A. Herrera, “A solution to the decentralized adaptive stabilization problem,” Systems and Control Letters, vol. 20, pp. 299-306, 1993.
[9] A. Datta, “Performance improvement in decentralized adaptive control: A modified model reference scheme,” IEEE Transactions on Automatic Control, vol. 38, no. 11, pp. 1717-1722, 1993.
[10] Y. H. Chen, G. Leitmann, and Z. K. Xiong, “Robust control design for interconnected systems with time-varying uncertainties,” International Journal of Control, vol. 54, pp. 1119-1124, 1991.
[11] C. Wen, “Direct decentralized adaptive control of interconnected systems having arbitrary subsystem relative degrees,” in Proceedings of the 33rd conference on Decision and Control, Lake Buena Vista, FL, pp. 1187-1192, Dec 14 - Dec 16, 1994.
[12] C. Wen, “Indirect robust totally decentralized adaptive control of continuous-time interconnected systems,” IEEE Trans on Automatic Control, vol. 38, no. 6, pp. 1122-1126, June 1995.
[13] K. Ikeda and S. Shin, “Fault tolerant decentralized control systems using backstepping,” in Proceedings of the 33rd conference on Decision and Control, New Orleans, LA, pp. 2340-2345, Dec 14 - Dec 16, 1995.
[14] P. R. Pagilla, “Robust decentralized control of large-scale interconnected systems: General interconnections,” in Proceedings of American Control Conference, San Diego, CA, pp. 4527-4531, June 2 - June 4, 1999.
[15] O. Huseyin, M. E. Sezer, and D. D. Siljak, “Robust decentralized control using output feedback,” IEE Proceedings, vol. 129, pp. 310-314, 1982.
[16] A. Datta and P. A. Ioannou, “Decentralized indirect adaptive control of interconnected systems,” International Journal of Adaptive Control and Signal Processing, vol. 5, no. 4, pp. 259-281, 1991.
[17] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Upper Saddle River, New Jersey: Prentice-Hall, 1989.
[18] J. S. H. Tsai, N. T. Hu, P. C. Yang, S. M. Guo, and L. S. Shieh,“Modeling of decentralized linear observer and tracker for a class of unknown interconnected large-scale sampled-data nonlinear system with closed-loop decoupling property”, Computers and mathematics with applications”, (accepted for publication, in galley, to appear in June) 2010.
[19] M. J. Lin, “Novel Design Methodologies for Quadratic Observers and Trackers of Sampled- data Linear Singular System,” M.S. Thesis, University of Cheng-Kung, Tainan, Taiwan, 2009.
[20] J. N. Juang, Applied System Identification, Englewood Cliffs. NJ, Prentice-Hall, 1994.
[21] S. M. Guo, L. S. Shieh, G. Chen, and C. F. Lin, “ Effective chaotic orbit tracker a prediction based digital redesign approach,” IEEE Transaction on Circuits and System-I:, Fundamental Theory and Applications, vol. 47, no. 11, pp. 1557-1570, 2000.
[22] L. S. Shieh, Y. T. Tsay, and R. E. Yates, “Some properties of matrix-sign functions derived from continued fractions,” IEE Proceedings D - Control Theory and Applications, vol. 130, no. 3, pp.111-118, 1983.
[23] M. Phan, L. G. Horta, J. N. Juang, and R. W. Longman, “LinearSystem Identification Via an Asymptotically Stable Observer,” Journal of Optimization Theory and Applications, vol. 79, no. 1, pp. 59-86, October 1993.
[24] S. M. Guo, L. S. Shieh, G. Chen, and C.F. Lin, “Effective chaotic orbit tracker: A prediction-based digital redesign approach,” IEEE Transaction on Circuits and Systems-I: Fundamental Theory and Applications, vol. 47, no. 11, pp. 1557-1570, Nov. 2000.
[25] J. H. Halton, “On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals,” Numerische Mathematik, vol. 2, pp. 84-90, 1960.
[26] J. C. Van, “Verteilungsfunktionen,” Pro. Kon Akad. Wet., Amsterdam, vol. 38, pp. A13-A21, pp. 1058-1066, 1935.