基於李亞普諾夫穩定度理論，在本論文中利用兩種適應性步階迴歸技術針對含有非匹配雜訊之多輸入系統設計適應性區塊步階迴歸控制器。此兩種方法的差別在於第二種方法使用了擾動估測機制於每一個虛擬控制中，而第一種方法只用
於最後一個區塊。在設計的過程中，根據受控體的區塊個數(m 個)，在前m-1 個區塊中，每個區塊分別設計虛擬輸入控制器，最後，在第m 個區塊設計強健控制器。在虛擬輸入和強健控制器中，加入適應增益來估測一些未知干擾的上界常
數，如此一來，系統之擾動或估測誤差的上界即可不必事先知道。另外系統亦不須滿足區塊嚴格回授形式，而且能獲得漸進穩定或有界的特性。最後，本論文提供一個數值範例及一個實際應用的例子，以驗證本控制器的可行性。

Based on the Lyapunov stability theorem, two design methodologies of adaptive block backstepping controller is proposed in this thesis for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The main difference between these two method is that perturbation estimations are only employed in each virtual control input in the second method, whereas in the first method, the perturbation estimation is only employed in the last block. According to
the number of block (m) in the dynamic equations of plant to be controlled, m-1 virtual input controllers are designed from the first block to the (m-1)th block, and the proposed robust controller is designed from the last block. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, so that the least upper bounds of perturbations and perturbation estimation errors are not required. Furthermore, the dynamic equations of the plant do not need to satisfy the block strict feedback form, and the resultant control system can achieve asymptotic stability or uniformly ultimately boundedness. Finally, a numerical example and a
practical example are given for demonstrating the feasibility of the proposed control schemes.

Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Design of Adaptive Backstepping Controllers 5
2.1 System Descriptions and Problem Formulations . . . . . . . . . 5
2.2 Design of Adaptive Backstepping Controllers . . . . . . . . . . 7
2.3 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Design of Adaptive Backstepping Controllers with Matched and
Mismatched Perturbation Estimator . . . . . . . . . . . . . . . 21
2.5 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter 3 Numerical example and Application 31
3.1 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Practical Application . . . . . . . . . . . . . . . . . . . . . . . 57
Chapter 4 Conclusions 71
Appendix A 72
Appendix B 74
Appendix C 76
Appendix D 79
Appendix E 81
Bibliography 83

[1] V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Automatic Control, vol. 22, no. 1, pp. 212-222, 1977.
[2] W. J. Wang, G. H. Wu, and D. C. Yang, “Variable structure control design for uncertain discrete-time systems,” IEEE Trans. Automatic Control, vol. 39, no. 1, pp. 99-102, 1994.
[3] R. A. DeCarlo, S. H. Zak, and G. P. Mattews, “Variable structure control of nonlinear multivariable systems: a tutorial,” Proc. of IEEE, vol. 76, no. 3, pp. 212-232, 1988.
[4] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: a survey,” IEEE Trans. on Industrial Electronic, vol. 40, no. 1, pp. 2-22, 1993.
[5] C. C. Cheng, C. C. Wen, and W. T. Lee, “Design of decentralised sliding surfaces for a class of large-scale systems with mismatched perturbations,”
International Journal of Control, vol. 82, no. 11, pp. 2013-2025, 2009.
[6] Y. Chang and C. C. Cheng, “Adaptive sliding mode control for plant with mismatched perturbations to achieve asymptotical stability,” International
Journal of Robust and Nonlinear Control, vol. 17, no. 9, pp. 880-896, 2007.
[7] C. C. Cheng and Y. Chang, “Design of decentralised adaptive sliding mode controllers for large-scale systems with mismatched perturbations,” International
Journal of Control, vol. 81, no. 10, pp. 1507-1518, 2008.
[8] X.-G. Yan, S. K. Spurgeon, and C. Edwards, “Global stabilisation for a class of nonlinear time-delay systems based on dynamical output feedback sliding mode control,” International Journal of Control, vol. 82, no. 12, pp.
2293-2303, 2009.
[9] H. K. Khalil, Nonlinear Control, Prentice-Hall, New Jersey, 1996.
[10] M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and adaptive control design, John Wiley & Sons, Inc. New York, 1995.
[11] X. Tang, G. Tao, and S. M. Joshi, “Virtual grouping based adaptive actuator failure compensation for MIMO nonlinear systems,” IEEE Trans. on Automatic Control, vol. 50, no. 11, pp. 1775-1780, 2005.
[12] B. Chen and X. Liu, “Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes,” IEEE Trans.on Fuzzy Systems, vol. 13, no. 6, pp. 832-847, 2005.
[13] Y. Zhang, S. Li, and Q. Zhu, “Backstepping-enhanced decentralised PID control for MIMO processes with an experimental study,” IET Proceedings- Control Theory and Applications, vol. 1, no. 3, pp. 704-712, 2007.
[14] J. Zhang, S. S. Ge, and T. H. Lee, “Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs,” IEEE
Trans. on Neural Networks, vol. 16, no. 6 pp. 1491-1503, 2005.
[15] Y. Xia, M. Fu, P. Shi, Z. Wu, and J. Zhang, “Adaptive backstepping controller design for stochastic jump systems,” IEEE Trans. on Automatic Control,
vol. 54, no. 12, pp. 2853-2859, 2010.
[16] J. Fu, “Extended backstepping approach for a class of nonlinear systems in
generalised output feedback canonical form,” IET Control Theory Applications,
vol. 3, no. 8, pp. 1023-1032, 2008.
[17] S.-J. Liu, S. S. Ge, and J.-F. Zhang, “Adaptive output-feedback control for
a class of uncertain stochastic non-linear systems with time delays,” International
Journal of Control, vol. 81, no. 8, pp. 1210-1220, 2008.
[18] W. Lin and C. Qian, “Semi-global robust stabilization of multi-input nonlinear
systems by partial state and dynamic output feedback,” Automatica,
vol. 37, no. 7, pp. 1093-1101, 2001.
[19] X. Liu, A. Jutan, and S. Rohani, “Almost disturbance decoupling of multiinput
nonlinear systems and application to chemical processes,” Automatica,
vol. 40, no. 3, pp. 465-471, 2004.
[20] X. Liu, G. Gu, and K. Zhou, “Robust stabilization of multi-input nonlinear
systems by backstepping,” Automatica, Vol. 35, no. 5, pp. 987-992, 1999.
[21] B. Yao and M. Tomizuka, “Adaptive robust control of multi-input nonlinear
systems in semi-strict feedback forms,” Automatica, vol. 37, no. 7,
pp. 1305-1321, 2001.
[22] A. J. Koshkouei, A. S. I. Zinober, and K. J. Burnham, “Adaptive sliding
mode backstepping control of nonlinear systems with unmatched uncertanty,”
Asian Journal of Control, vol. 6, no. 4, pp. 447-453, 2004.
[23] B. Chen, X. Lin, K. Lin, and C. Lin, “Novel adaptive neural control design
for nonlinear systems,” Automatica, vol. 45, pp. 1554-1560, 2009.
[24] J. T. Huang, “Hybrid-based adaptive NN backstepping control of strictfeedback
systems,” Automatica, vol. 45 pp. no. 6, 1497-1503, 2009.
[25] Y. Wu and Y. Zhou, “Output feedback control for multi-input non-linear
systems with unknown sign of the high frequency gain matrix,” International
Journal of Control, vol. 77, no. 1, pp. 9-18, 2004.
[26] Y. Chang and C. C. Cheng, “Block Backstepping Control of Multi-Input
Nonlinear Systems with Mismatched Perturbations for Asymptotic Stability,”
International Journal of Control, vol. 83, no. 10, pp. 2028-2039, 2010.
[27] C. C. Cheng and M.W. Chang, “Design of derivative estimator using adaptive
sliding mode technique,” Proc. of 2006 American Control Conference ,
pp. 2611-2615, 2006.
[28] Tao, G., Adaptive control design and analysis , John Wiley & Sons, Inc.
New York, 2003.
[29] C. C. Cheng, J. M. Hsiao, and Y. P. Lee, “Design of robust tracking controllers
using sliding mode technique ,” JSME international journal, Mechanical
Systems, Machine Elements and Manufacturing, Series C , vol. 44,
pp.89-95, 2001.
[30] Terasoft, Terasoft Electro-Mechanical Engineering Control System , Terasoft,
2007.
[31] B. C. Kuo, Automatic Control Systems, Prentice-Hall, New Jersey, 1995.