本論文提出針對於含有直接傳輸項之資料取樣系統之進化規劃法線性二次式降階觀測器與追蹤器的設計法則。首先，在含有輸入至輸出之直接傳輸項的系統模型為基礎下，架構一個高增益的類比二次式軌跡追蹤器，是一種兼具高效能與品質之軌跡追蹤與狀態觀測的設計法則。以上述之高增益類比軌跡追蹤器為基底，利用數位再設計法則得到一個低增益且實用的數位軌跡追縱器使模型在離散系統下依舊有良好的軌跡追蹤能力。此時，以此數位軌跡追蹤器為基礎，設計一個資料取樣系統之進化規劃法線性二次式降階觀測型軌跡追蹤器，此進化規劃法線性二次式降階觀測型軌跡追蹤器能夠在減少感測器使用的環境下，利用已知的狀態預估未知的狀態，且能保持完美的輸出軌跡追蹤能力。最後，我們提出數個例子，來說明我們所提出方法的可行性。

A newly evolutionary programming-based linear quadratic reduced-order observer-based tracker for the linear sampled-data system with a direct transmission term from input to output is proposed in this thesis. First, a high-gain optimal linear quadratic analog tracker based on the reduced-order observer is proposed for the system model with a direct transmission term from input to output, so that it can effectively induce a high quality performance on trajectory tracking design and state estimation. Then, the prediction-based digital redesign method enables it to make the digitally controlled system to track the desired trajectory closely. In addition, an EP-based reduced-order observer-based tracker is proposed in this thesis to reduce the order of the observer by the number of sensed outputs and to estimate the unmeasured state variables correctly by measured state variables, in the meanwhile, it can keep the tracking performance well. Illustrative examples are presented to demonstrate the effectiveness of the proposed method.

[1] Chen, T. and Francis, B. A., Optimal Sampled-Data Control Systems, New York: Springer-Verlag, 1995.
[2] Corput, J. C. V. D., “Verteilungsfunktionen,” Proc. Kon Akad. Wet., Amsterdam, vol. 38 A13-A21, pp. 1058-1066,1935.
[3] Franklin, G. F., Powell, J. D. and Emami-Naeini, A., Feedback Control of Dynamic Systems, 3rd Edition, New York: Addison-Wesley, 1994
[4] Fujimoto, H., Kawamura, A. and Tomizuka, M., “Generalized digital redesign method for linear feedback system based on n-delay control,” IEEE/ASME Transaction Mechaton, vol. 4, pp. 101-109, 1999.
[5] 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, no. 11, pp. 1557-1570, 2000.
[6] Guo, S. M., Shieh, L. S. and Lin, C. F., “Evolutionary-programming-based Kalman filter for discrete-time nonlinear uncertain systems,” Asian Journal of Control, vol. 3, no. 4, pp. 319-333, December, 2001.
[7] Halton, J. H., “On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals,” Numerische Mathematic, vol. 2, no.1, pp. 84-90, 1960.
[8] Ieko, T., Ochi, Y. and Kanai, K., “Digital redesign of linear state-feedback law via principle of equivalent areas,” Journal of Guidance, Control, and Dynamics, vol. 24, pp. 857-859, 2001.
[9] 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, no. 12, pp.1595-1600, 2003.
[10] Lewis , F. L. and Syrmos, V. L., Optimal Control, 3nd Edition, New York: Wiley, 2012.
[11] Mertzios, B. G., Christodoulou, M. A., Syrmos, B. L. and Lewis, F. L., “ Direct controllability and observability time domain conditions of singular systems, ” IEEE Transactions Automatic Control, vol.33, no.8, pp.788-791, 1988.
[12] Shieh, L. S., Wang , W. M. and Appu Panicker, M. K., “Design of PAM and PWM digital controllers for cascaded systems,” ISA Transactions, vol. 37, no.3, pp. 201-213, 1998.
[13] Tsai, J. S. H., Chen, C. H. and Lin, M. J., “A novel linear quadratic observer and tracker for the linear sampled–data regular system with a direct feedthrough term: Digital redesign approach”, Applied Mathematical Sciences, vol. 6, no. 68, pp. 3381 - 3409, 2012
[14] Tsai, J. S. H., Du, Y. Y., Zhuang, W. Z., Guo, S. M., Chen C. W. and Shieh, L. S., “ Optimal anti-windup digital redesign of multi-input multi-output control systems under input constraints, ” IET Control Theory Applications, vol.5, no.3, pp. 447-464, 2011.
[15] Tsai, J. S. H., Wang, C. T. and Shieh, L. S., Model conversion and digital redesign of singular systems, Journal of Franklin Institute, 330(1993), 1063-1086.
[16] Wang , C. J. and Liao, H. E., “ Impulse observability and impulse controllability of linear time-varying singular systems, ” Automatica, vol.37, no.11, pp.1867-1872, 2001.
[17] Wang, H. J., Xue, A. K., Guo, Y. F. and Lu, R. Q., “ 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, pp. 546-551, 2008.