本論文主要提出一種線上觀測器/控制器鑑別方法能夠即時控制未知微非線性的系統，裡面的設計使用了輸入飽和限制和主動容錯追蹤器。此方法能夠克服因為奇異值分解所造成的系統參數不連續性，因此即時的控制可以被實現。此外，經由可量測閉迴路系統，系統辨識可以得到未知開迴路系統、既存控制器和既存觀測器的可觀測/可控制典型式，再利用新提出的補償機制來補償不足的控制器，根據希爾德雷思(Hildreth)二次規劃，提出了一個修改過基於觀測器的模式預測控制解決了輸入飽和限制的最佳化問題，因此不只是減少輸入控制，以達輸入飽和限制，當多種系統錯誤發生時也擁有好的追蹤效能。

In this thesis, we mainly propose a novel on-line observer/control identification (OCID) method for real-time control of unknown slightly nonlinear systems, and the on-line OCID method-based identified model is utilized for the design of a new input-constrained active fault-tolerant tracker. The proposed on-line OCID method overcomes the discontinuity of the parameters identified in real-time, induced by the singular value decomposition (SVD) which is supposed to be carried out at each sampling instant if it is performed by the direct extension of the off-line OCID method to the on-line manner; as a consequence, real-time control can be implemented. Besides, it identifies the minimally realized equivalent (reduced-order) mathematical models in the block observer/controller canonical forms of the unknown (i) open-loop system, (ii) existing feedback/feedforward controllers, and/or (iii) observer, based on available measurements of the operating closed-loop system. The proposed method enables us to enhance the computational aspects of designing self-tuning controllers for on-line adaptive control of slightly nonlinear systems. Besides, the newly proposed compensation improvement approach is able to compensate the undesirable operating controller. The Hildreth’s quadratic programming solves the constrained optimization problem. Based on Hildreth’s quadratic programming, a modified observer-based model predictive control (MPC) with input constraints is presented in this thesis. As a result, based on the proposed online OCID method, the presented input-constraint controller not only reduces the control input to fit the requirement of the input constraint, but also possesses the high tracking performance under various system faults.

[1] Chadli, M., Aouaouda, S., Karimi, H. R., and Shi, P., “Robust fault tolerant tracking controller design for a VTOL aircraft,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 350, no. 9, pp. 2627-2645, 2013.
[2] Chen, G. and Ueta, T., “Yet another chaotic attractor,” International Journal of Bifurcation Chaos, vol. 9. pp. 1465-1466, 1999.
[3] Fujita, M. and Shimemura, E., “Integrity against arbitrary feedback-loop failure in linear multivariable control system,” Automatica, vol. 24, no. 6, pp. 765-772, 1988.
[4] Gao, Z. and Antsaklis, P. J., “Stability of the pseudo-inverse method for reconfigurable control systems,” International Journal of Control, vol. 53, no. 3, pp. 717-729, 1991.
[5] Gao, Z. and Antsaklis, P. J., “Reconfigurable control system and design via perfect model following,” International Journal of Control, vol. 56, no. 4, pp. 783-798, 1992.
[6] Gao, Z. F., Jiang, B., Shi, P., Qian, M. S. and Lin, J. X., “Active fault tolerant control design for reusable launch vehicle using adaptive sliding mode technique,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 349, no. 4, pp. 1543-1560, 2012.
[7] Graham, C. G., Stefan, F. G., and Mario, E. S., Control System Design. Prentice Hall, New Jersey, 2000.
[8] Guo, S. M., Shieh, L. S., Chen, G. R., and Lin, C. F., “Effective chaotic orbit tracker: A prediction-based digital redesign approach,” IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications, vol. 47, no. 11, pp.1557-1570, 2000.
[9] Hildreth, C., “A quadratic programming procedure,” Naval Research Logistics Quarterly, vol. 4, pp. 79-85, 1957.
[10] Ho, B. L. and Kalman, R. E., “Effective construction of linear state-variable models from input-output data,” Proceedings of the 3rd Annual Allerton Conference on Circuit and System Theory, Monticello, IL: University of Illinois, pp. 449-459, 1965.
[11] Hu, N. T., Tsai, J. S. H., Guo, S. M., Shieh, L. S., and Chen, Y., “Low-order multi-rate linear time-invariant decentralized trackers using the new observer-based sub-optimal method for unknown sampled-data nonlinear time-delay system with closed-loop decoupling,” Optimal Control Applications and Methods, vol. 132, no. 4, pp. 433-475, 2010.
[12] Hu, T., Teel, A. R. and Zaccarian, L., “Anti-windup synpaper for linear control systems with input saturation: Achieving regional, nonlinear performance,” Automatica, vol. 44, no. 2, pp. 512-519, 2008.
[13] Jiang J., “Design of reconfigurable control-systems using eigenstructure assignments,” International Journal of Control, vol. 59, no. 2, pp. 395-410, 1994.
[14] Juang, J. N., Applied System Identification, Prentice Hall, New Jersey, 1994.
[15] Khosrowjerdi, M. J., Nikoukhah, R., and Safari-Shad, N., “A mixed approach to simultaneous fault detection and control,” Automatica, vol. 40, no. 2, pp. 261-267, 2004.
[16] Lee, Y.Y., Tsai, J.S.H., Shieh, L.S., and Chen, G., “Equivalent linear observer-based tracker for stochastic chaotic system with delays and disturbances,” IMA Journal of Mathematical Control and Information, vol. 22, no. 3, pp. 266-284, 2005.
[17] Lewis, F. L. and Syrmos, V. L., Optimal Control, Wiley-Interscience, New York, 1995.
[18] Ljung, L., System Identification Theory for the User 2nd, Prentice-Hall, New Jersey, 1999.
[19] Soderstorm, T. and Stoica, P., System Identification, Prentice Hall, New Jersey, 1989.
[20] Solmaz, S. K. and Faryar, J., “Modified anti-windup compensators for stable plants,” IEEE Transactions on Automatic Control, vol. 54, pp. 1934-1939, 2009.
[21] Teixeira, M. C. M. and Zak, S. H., “Stabilizing controller design for uncertain nonlinear systems using fuzzy models,” IEEE Transactions on Fuzzy Systems, vol. 7, no. 2, pp.133-142, 1999.
[22] Tiwari, P. Y., Mulder, E. F., and Kothare, M. V., “Synpaper of stabilizing antiwindup controllers using piecewise quadratic Lyapunov functions,” IEEE Transactions on Automatic Control, vol. 52, no. 12, pp. 2341-2345, 2007.
[23] Tsai, J. S. H., Chen, F. M., Yu, T. Y., Guo, S. M., and Shieh, L. S., “Efficient decentralized iterative learning trackers for the unknown sampled-data interconnected large-scale state-delay system with closed-loop decoupling property,” ISA Transactions, vol. 41, pp. 81-94, 2012.
[24] Tsai, J. S. H., Huang, C. C., Guo, S. M., and Shieh, L. S., “Continuous to discrete model conversion for the system with a singular system matrix based on matrix sign function,” Applied Mathematical Modelling, vol. 35, no. 8, pp. 3893-3904, 2011.
[25] Tsai, J. S. H., Lee, Y. Y., Cofie, P., Shieh, L. S., and Chen, X. M., “Active fault tolerant control using state-space self-tuning control approach,” International Journal of Systems Science, vol. 37, no. 11, pp. 785-797, 2006.
[26] Tsai, J. S.H., Su, T. J., Cheng, J. C., Lin, Y. Y., Giap, V. N., Guo, S.M., and Shieh, L.S., 2018, “Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system,” International Journal of Systems Science, Published online https://doi.org/10.1080/00207721.2018.1443231, Feb. 2018.
[27] Wang, C. T., Tsai, J. S. H., Chen, C. W., Lin, Y., Guo, S. M., and Shieh, L. S., “An active fault-tolerant PWM tracker for unknown nonlinear stochastic hybrid systems: NARMAX model and OKID based state-space self-tuning control,” Journal of Control Science and Engineering 2010, pp. 1-27, 2010.
[28] Wang H. and Wang Y., “Neural-network-based fault-tolerant control of unknown nonlinear systems,” IEE Proceedings Control Theory and Applications, vol. 146, no. 5, pp. 389-398, 1999.
[29] Wang, J. H., Tsai, J. S. H., Huang, J. S., Guo, S. M., and Shieh, L. S., “A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 1242-1274, 2013.
[30] Wang, L. P., Model Predictive Control System Design and Implementation using MATLAB, Springer, London, 2009.
[31] Wu, C. Y., Tsai, J. S. H., Guo, S. M., Shieh, L. S., Canelon, J. I., Ebrahimzadeh, F., and Wang, L., “A novel on-line observer/Kalman filter identification method and its application to input-constrained active fault-tolerant tracker design for unknown stochastic systems,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 352, pp. 1119-1151, 2015.
[32] Wu, C. Y., Tsai, J. S.-H., Su, T. J., Guo, S.-M., Shieh, L.-S., and Yan, J. J., “Novel OCID method-based minimal realizations in block observable/controllable canonical forms and compensation improvement,” International Journal of Systems Science, vol. 48, no. 7, pp. 1522-1535, 2017.
[33] Wu, F. and Lu, B., “Anti-windup control design for exponentially unstable LTI systems with actuator saturation,” Systems & Control Letters, vol. 52, no. 4, pp. 305-322, 2004.
[34] Xu, Y. Y., Tong, S. C., and Li, Y. M., “Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults based on dynamic surface technique,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 350, no. 7, pp. 1768-1786, 2013.
[35] Xu, Y. Y., Tong, S. C., and Li, Y. M., “Adaptive fuzzy fault-tolerant decentralized control for uncertain nonlinear large-scale systems based on dynamic surface control technique,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 351, no.1, pp. 456-472, 2014.
[36] Yang Y., Yang G. H., and Soh Y. C., “Reliable control of discrete-time systems with actuator failure,” IEE Proceedings-Control Theory and Applications, vol. 147, no. 4, pp. 428-432, 2000.
[37] Yen, G. G. and Ho, L. W., “Online multiple-model-based fault diagnosis and accommodation,” IEEE Transactions on Industrial Electronics, vol. 50, no. 2, pp. 296-312, 2003.
[38] Zaccarian, L. and Teel, A. R., “Nonlinear scheduled anti-windup design for linear systems,” IEEE Transactions on Automatic Control, vol. 49, no. 11, pp. 2055-2061, 2004.
[39] Zhang, X. D., Parisini T., and Polycarpou, M. M., “Adaptive fault-tolerant control of nonlinear uncertain systems: An information-based diagnostic approach,” IEEE Transactions on Automatic Control, vol. 49, no. 8, pp. 1259-1274, 2004.