在此論文中針對不同類型之具有非匹配干擾的非線性多輸入多輸出動態系統，介紹三個強韌追蹤控制設計策略。第一個控制器設計方法乃是針對某一類具有標準典型描述式的非線性多輸入多輸出動態系統。第二個控制器設計程序則是針對不具有標準典型描述式的非線性多輸入多輸出動態系統。最後對於受到干擾之具有子系統時變時間延遲相互鏈結項的大型系統，提出一個不需事先知道時間延遲之正確函數型式的分散式控制器。這些具有干擾估測與適應控制機制之強韌追蹤控制器，乃是利用可變結構控制技術與李亞普諾夫穩定理論所設計而成。適應控制機制乃是用來調適干擾估測誤差的未知上界，使得干擾與干擾估測誤差之上界的資訊可不需知曉。由於所提出之控制器的控制增益只需克服干擾估測誤差，一般而言比傳統順滑模態控制器的控制增益還小，所以震顫現象可以被有效地緩減。此外，在論文中也證明了整個控制系統的穩定度，而且所要求之追蹤精準度也可經由調整控制器的設計參數來達成。而針對論文中所提出之每一個控制器設計法則，分別以一個數值實例來展示其可行性。

Three robust tracking control design strategies are proposed in this dissertation for different classes of nonlinear MIMO dynamic systems with mismatched perturbations. The first controller design method is proposed for a class of nonlinear MIMO dynamic systems in canonical form. The second design procedure of controller is for the nonlinear MIMO dynamic systems without canonical form. A decentralized controller is presented in the last for perturbed large-scale systems with time-varying delay interconnections, where the knowledge of the exact function of time-delay is not required. These robust tracking controllers with a perturbation estimating scheme and an adaptive control mechanism embedded are designed by means of the variable structure control technique and Lyapunov stability theorem. The adaptive control mechanism is used to adapt the unknown upper-bound of perturbation estimation error, so that the knowledge of upper-bounds of perturbation as well as perturbation estimation error is not required. The chattering phenomenon is effectively alleviated, for the gain of the proposed controllers, which needs only to overcome the perturbation estimation error, is in general smaller than those of the traditional sliding mode controllers. Furthermore, the stability of the overall controlled systems is proved, and the desired tracking accuracy can be achieved by adjusting the design parameters of the proposed controller schemes. A numerical example for each controller's design is provided for demonstrating the feasibility of the proposed control schemes.

Abstract II
List of Figures VII
List of Notations IX
1 Introduction 1
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . 5
2 Design of Robust Tracking Controllers for Nonlinear MIMO
Systems with Canonical Form 6
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Systemdescriptions and general assumptions . . . . . . . . . . 7
2.3 Design of robust tracking controllers . . . . . . . . . . . . . . 8
2.3.1 Sliding surface design . . . . . . . . . . . . . . . . . . . 8
2.3.2 Controller design . . . . . . . . . . . . . . . . . . . . . 9
2.3.3 Estimation of perturbation . . . . . . . . . . . . . . . . 11
2.3.4 Determination of λi,j and "i . . . . . . . . . . . . . . . 12
2.4 Robustness of systemstability . . . . . . . . . . . . . . . . . . 14
2.5 Adjustment of tracking accuracy . . . . . . . . . . . . . . . . . 17
2.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Design of Robust Tracking Controllers for Nonlinear Mis-
matched Systems 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Systemdescriptions and assumptions . . . . . . . . . . . . . . 29
3.3 Design of Robust Tracking Controllers . . . . . . . . . . . . . 31
3.3.1 Estimation of Output Tracking Error Dynamics . . . . 32
3.3.2 Sliding Surface Design . . . . . . . . . . . . . . . . . . 36
3.3.3 Controller Design . . . . . . . . . . . . . . . . . . . . . 36
3.3.4 Estimation of ∆pi . . . . . . . . . . . . . . . . . . . . . 38
3.4 Robustness of System’s Stability and Adjustment Of Tracking
Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Design of Robust Tracking Controllers for Perturbed Large-
Scale Systems 53
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Systemdescriptions and assumptions . . . . . . . . . . . . . . 55
4.3 Design of decentralized robust tracking controllers . . . . . . . 56
4.3.1 Design of switching surface . . . . . . . . . . . . . . . . 56
4.3.2 Controller design . . . . . . . . . . . . . . . . . . . . . 57
4.3.3 Estimation of ∆Pi . . . . . . . . . . . . . . . . . . . . 58
4.4 Robustness of system’s stability . . . . . . . . . . . . . . . . . 59
4.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 Conclusions and Future Works 69
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References 71

[1] Barmish, B. R. and Leitmann, G., “On Ultimate Boundedness Control
of Uncertain Systems in the Absence of Matching Assumptions,” IEEE
Transactions on Automatic Control, Vol. AC-27, NO. 1, pp. 153—158,
1982.
[2] Byrnes, C. I., Isidori, A. and Willems, J. C., “Passivity, feedback equiva-
lence, and the global stabilization of minimum phase nonlinear systems,”
IEEE Transactions on Automatic Control, Vol. 36, No. 11, pp. 1228—
1240, 1991.
[3] Chen, Y. H., “On the robustness of mismatched uncertain dynamical sys-
tems,” ASME Journal of Dynamic Systems, Measurement, and Control,
Vol. 109, pp. 29—35, March 1987.
[4] Chen, Y. H. and Leitmann, G., “Robustness of uncertain systems in
the absence of matching assumptions,” International Journal of Control,
Vol. 45, No. 5, pp. 1527—1542, 1987.
[5] Chen, Y. C., Lin, P. L. and Chang, S., “Design of output tracking
via variable structure system: for plants with redundant inputs,” IEE Proceedings-D Control Theory and Applications, Vol. 139, No. 4, pp. 421—
428, 1992.
[6] Chen, C. T., Analog and Digital Control System Design: Transfer-
Function, State-Space, and Algebraic Methods, Saunders College Pub-
lishing, 1993.
[7] Cheng, C. C. and Liu, I. M., “Design of MIMO output feedback integral
variable structure controllers,” Journal of the Franklin Institute, Vol. 336,
No. 7, pp. 1119-1134, 1999.
[8] Cheng, C. C., Lin, M. H. and Hsiao, J. M., “Sliding mode controllers
design for linear discrete-time systems with matching perturbations,”
Automatica, Vol. 36, No. 8, pp. 1205—1211, 2000.
[9] Cheres, E., Gutman, S. and Palmor, Z.J., “Stabilization of uncertain dy-
namic systems including state delay,” IEEE Transactions on Automatic
Control, Vol. AC-34, No. 11, pp. 1199-1203, 1989.
[10] Chiang, C.C., “Decentralized variable structure model-reference adap-
tive control of linear time-varying large-scale systems with bounded dis-
turbances,” International Journal of System Sciences. Vol. 26, No. 10,
pp. 1993—2003, 1995.
[11] Choi, H. H. and Chung, M. J., “Memoryless stabilization of uncertain
dynamic systems with time-varying delayed states and controls,” Auto-
matica, Vol. 31, No. 9, pp. 1349—1351, 1995.
[12] Chou, C.H. and Cheng, C.C., “Decentralized model following variable
structure control for perturbed large-scale systems with time-delay inter-
connections,” Proceedings of the American Control Conference, pp. 641—
645, 2000.
[13] DeCarlo, R. A., ú Zak, S. H. and Matthews, G. P., “Variable structure
control of nonlinear multivariable systems: A Tutorial,” Proceedings of
the IEEE, Vol. 76, No. 3, pp. 212—232, 1988.
[14] Drazenovic, B., “The invariance conditions in variable structure sys-
tems,” Automatica, Vol. 5, No. 3, pp. 287—295, 1969.
[15] Elmali, H. and Olgac, N., “Sliding mode control with perturbation es-
timation (SMCPE): a new approach,” International Journal of Control,
Vol. 56, No. 4, pp. 923-941, 1992.
[16] Elmali, H. and Olgac, N., “Satellite attitude control via sliding mode
with perturbation estimation,” IEE Proceedings-D Control Theory and
Applications, Vol. 143, No. 3, pp. 276—282, 1996.
[17] Elmali, H. and Olgac, N., “Implementation of sliding mode control with
perturbation estimation (SMCPE),” IEEE Transactions on Control Sys-
tems Technology, Vol. 4, No. 1, pp. 79—85, 1996.
[18] Emelyanov, S. V., “A technique to develop complex control equations
by using only the error signal of control variable and its Þrst derivative,”
Automatica Telemekhanika, Vol. 18, No. 10, pp. 873—885, 1957.
[19] Esfandiari, F. and Khalil, H. K., “Stability analysis of a continuous im-
plementation of variable structure control,” IEEE Transactions on Au-
tomatic Control, Vol. 36, No. 5, pp. 616—620, 1991.
[20] Fu, L. C. and Liao, T. L., “Globally stable robust tracking of nonlinear
systems using variable structure control and with an application to a
robotic manipulator,” IEEE Transactions on Automatic Control, Vol. 35,
No. 12, pp. 1345—1350, 1990.
[21] Garret, S. J., “Linear switching conditions for a third order positive-
negative feedback,” Appl. Ind., No. 54, 1961.
[22] Hsu, K.C., ”Decentralized variable-structure control design for uncertain
large-scale systems with series nonlinearities,” International Journal of
Control, Vol. 68, No. 6, pp. 1231—1240, 1997.
[23] Hsu, K.C., “Decentralized variable structure model-following adaptive
control for interconnected systems with series nonlinearities,” Interna-
tional Journal of Systems Science, Vol. 29, No. 4, pp. 365—372, 1998.
[24] Hu, J., Chu, J. and Su, H., “SMVSC for a class of time-delay uncertian
systems with mismatching uncertainties,” IEE Proceedings-D Control
Theory and Applications, Vol. 147, No. 6, pp. 687—693, 2000.
[25] Hui, S. and ú Zak, S. H., “Robust control synthesis for uncertain/nonlinear dynamical systems,” Automatica, Vol. 28, No. 2, pp. 289—298, 1992.
[26] Hung, J. Y., Gao, W. and Hung, J. C., “Variable Structure Control: A
Survey,” IEEE Transactions on Industrial Electronics, Vol. 40, No. 1,
pp. 2—22, 1993.
[27] Ioannou, P. A. and Sun, J., Robust adaptive control, New Jersey,
Prentice-Hall International, Inc., 1996.
[28] Khalil, H. K. and Esfandiari, F., “Semiglobal stabilization of a class of
nonlinear systems using output feedback,” IEEE Transactions on Auto-
matic Control, Vol. 38, No. 9, pp. 1412—1415, 1993.
[29] Khalil, H. K., Nonlinear systems, 2nd edition, New Jersey, Prentice-Hall
International, Inc, 1996.
[30] Letov, A. M., “Conditionally stable control systems(on a class of optimal
control systems),” Automat. Remote Contr., No. 7, pp. 649—664, 1957.
[31] Liao, T. L., Fu, L. C., and Hsu, C. F., “Output tracking control of
nonlinear systems with mismatched uncertainties,” Systems and Control
Letters, Vol. 18, pp. 38—47, 1992.
[32] Luo, N. and M. de la Sen, “State feedback sliding mode control of a class
of uncertain time delay systems,” IEE Proceedings-D Control Theory and
Applications, Vol. 140, No. 4, pp. 261—274, 1993.
[33] Martin, J. M. and Hewer, G. A., “Smallest destabilzing perturbations
for linear systems,” International Journal of Control, Vol. 45, No. 5,
pp. 1495—1504, 1987.
[34] Matthews, G.P. and DeCarlo, R. A., “Decentralized tracking for a class
of interconnected nonlinear systems using variable structure control,”
Automatica, Vol. 24, pp. 187-193, 1988.
[35] Nguang, S. K., “Robust stabilisation for a class of time-delay nonlinear
systems,” IEE Proceedings-D Control Theory and Applications, Vol. 141,
No. 5, pp. 285—288, 1994.
[36] Oucheriah, S., “Robust sliding mode control of uncertain dynamic de-
lay systems in the presence of matched and unmatched uncertain-
ties,” ASME Journal of Dynamic Systems, Measurement, and Control,
Vol. 119, pp. 69-72, 1997.
[37] Phoojaruenchanachai, S. and Furuta, K., “Memoryless stabilization of
uncertain linear systems including time-varying state delays,” IEEE
Transactions on Automatic Control, AC-37, No. 7, pp. 1022—1026, 1992.
[38] Qu, Z., “Global stabilization of nonlinear systems with a class of un-
matched uncertainties,” Systems and Control Letters, Vol. 18, pp. 301—
307, 1992.
[39] Richter, R., Lefebvres, S. and DeCarlo, R., “ Control of a class of nonlin-
ear systems by decentralized control,” IEEE Transactions on Automatic
Control, Vol. AC-27, pp. 492—494, 1982.
[40] Sandeep, “Deterministic controllers for a class of mismatched systems,”
Journal of Dynamic Systems, Measurement, and Control, Vol. 116,
pp. 17—23, March, 1994.
[41] Shen, J. C., Chen, B. S. and Kung, F. C., “Memoryless stabilization
of uncertain dynamic delay systems: Riccati equation approach,” IEEE
Transactions on Automatic Control, AC-36, No. 5, pp. 638—640, 1991.
[42] Shen, J. C., “Designing stabilising controllers and observers for uncer-
tain linear systems with time-varying delay,” IEE Proceedings-D Control
Theory and Applications, Vol. 144, No. 4, pp. 331—333, 1997.
[43] Singh, S. N. and Coelho, A. R., “Nonlinear control of mismatched uncer-
tain linear systems and application to control of aircraft,” ASME Journal
of Dynamic Systems, Measurement, and Control, Vol. 106, pp. 203—210,
September, 1984.
[44] Sira-Ramirez, H., “Non-linear discrete variable structure systems in
quasi-sliding mode,” International Journal of Control, Vol. 54, No. 54,
pp. 1171—1187, 1991.
[45] Sira-Ramirez, H. and Fliess, M., “A sliding mode control approach
to predictive regulation,” Control Theory and Advanced Technology,
Vol. 10, No. 4, Part 3, pp. 1297-1316, 1995.
[46] Slotine, J. J. and Sastry, S. S., “Tracking control of non-linear systems
using sliding surfaces with application to robot manipulators”, Interna-
tional Journal of Control, Vol. 38, No. 2, pp. 465-492, 1983.
[47] Slotine, J. J., “Sliding controller design for nonlinear systems,” Interna-
tional Journal of Control, Vol. 40, No. 2, pp. 421—434, 1984.
[48] Slotine, J. E. and Li, W., Applied nonlinear control, Prentice-Hall Inter-
national, Inc, 1991.
[49] Spurgeon, D. K. and Davies, R., “A nonlinear control strategy for robust
sliding mode performance in the presence of unmatched uncertainty,”
International Journal of Control, Vol. 57, No. 5, pp. 1107—1123, 1993.
[50] Utkin, V. I., “Variable structure systems with sliding mode,” IEEE
Transactions on Automatic Control, Vol. 4, pp. 212-221, 1977.
[51] Utkin, V. I., Sliding modes and their applications in variable structure
systems, MIR Publishers, Moscow, 1978.
[52] Verghese, G. C., B. Fernandez R. and Hedrick, J. K., “Stable, robust
tracking by sliding mode control,” Systems and Control Letters, Vol. 10,
pp. 27—34, 1988.
[53] Walcott, B. L. and ú Zak, S. H., “Combined observer-controller synthesis
for uncertain dynamical systems with applications,” IEEE Transactions
on Systems, Man and Cybernetics, Vol. 18, No. 1, pp. 88-104, 1988.
[54] Wang, W.J. and Lee, J.L., “Decentralized variable structure control de-
sign in perturbed nonlinear systems,” ASME Journal of Dynamics Sys-
tems, Measurement and Control, Vol. 115, pp. 551—554, 1993.
[55] Wang, J.-D, Lee, T.-L and Juang, Y.-T, “New method to design an
Integral variable structure controller, ” IEEE Transactions on Automatic
Control, Vol. 41, No. 1, pp. 140-143, 1996.
[56] Xu, J. X., Heng, L. T. and Mao, W., “On the design of adaptive deriv-
ative estimator using variable structure,” Proceedings of 1995 American
Control Conference, pp. 529—533, 1995.
[57] Yeung, K. S., Cheng, C. C. and Kwan, C. M., “A unifying design of
sliding mode and classical controllers,” IEEE Transactions on Automatic
Control, Vol. 38, No. 9, pp. 1422-1427, 1993.
[58] Young, K. D., Utkin, V. T. and ¨ Ozg¨uner, ¨ U., “A control engineer’s
guide to sliding mode control,” IEEE Transactions on Control Systems
Technology, Vol. 7, No. 3, pp. 328—342, 1999.
[59] Yu, Y., “On stabilizing uncertain linear systems,” Journal of Optimiza-
tion Theory and Applications, Vol. 41, No. 3, pp. 503—507, 1983.
[60] ú Zak, S. H., and Hui, S., “On variable structure output feedback con-
trollers for uncertain dynamic systems,” IEEE Transactions on Auto-
matic Control, Vol. 38, No. 10, pp. 1509—1512, 1993.
[61] ú Zak, S. H. and Hui, S., “Output feedback variable structure controllers
and state estimators for uncertain/nonlinear dynamic systems,” IEE
Proceedings-D Control Theory and Applications, Vol. 140, No. 1, pp. 41-
50, 1993.
[62] Zhou, F., Fisher, D. G., “Continuous sliding mode control,” Interna-
tional Journal of Control, Vol. 55, No. 2, pp. 313-327, 1992.