本論文針對強韌追蹤之問題， 提出一個具有擾動估測器的最佳參考模式調適控制器。 且這些多輸入多輸出擾動的動態系統含有非線性輸入和時間延遲的性質。 運用李亞普諾夫理論 (Lyapunov Theorem) 設計一個具有擾動估測的強韌追蹤控制器。 本控制包含三種型式。 第一種型式是在假設無擾動的情況下之最佳回授控制器。 第二種型式為適應控制器， 具有自動調適擾動估測誤差之上界功能。 第三種型式為擾動估測器。 本控制器將保證 uniformly ultimately boundness 的特性， 並分析其中參數的特性。 最後， 本論文提供一範例以驗證控制器的可行性。

A simple design methodology of optimal model reference adaptive control (OMRAC) scheme with perturbation estimation for solving robust tracking problems is proposed in this thesis. The plant to be controlled belongs to a class of MIMO perturbed dynamic systems with input nonlinearity and time varying delay. The proposed robust tracking controller with a perturbation estimation scheme embedded is designed by using Lyapunov stability theorem. The control scheme contains three types of controllers. The first one is a linear feedback optimal controller, which is designed under the condition that no perturbation exists. The second one is an adaptive controller, it is used for adapting the unknown upper bound of perturbation estimation error. The third one is the perturbation estimation mechanism. The property of uniformly ultimately boundness is proved under the proposed control scheme, and the effects of each design parameter on the dynamic performance is also analyzed. An example is demonstrated for showing the feasibility of the proposed control scheme.

Abstract
List of Figures
Chapter 1 Introduction
1.1 Motivation
1.2 Brief Sketch of the Contents
Chapter 2 Optimal Model Reference Adaptive control
2.1 SystemDescriptions and ProblemFromulations
2.2 Design of Optimal Control for a Nominal System
2.3 Design of Robust Tracking Controller with Perturbation Estimation
2.4 Analysis of Stability
2.5 Summary of Design Procedure
Chapter 3 Simulations
Chapter 4 Conclusions
References

Bibliography
[1] J.-J. E.Slotine Weiping Li, Applied Nonlinear Control, New Jersey: Prentice-Hall, Inc., 1991.
[2] K. J. Astrom and B. Wittenmark, Adaptive Control, Second edition, Canada: Addison-Wesley Publishing Company, Inc., 1995.
[3] B. D. O. Anderson and J. B. Moore, Optimal Control - Linear Quadratic Methods, New Jersey: Prentice-Hall International, Inc.,1990.
[4] H. K. Khalil, Nonlinear Systems, Second edition, New Jersey: Prentice-Hall, Inc., 1996.
[5] S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, New Jersey: Prentice-Hall, Inc., 1989.
[6] P. A. Ioannou and J. Sun, Robust Adaptive Control, New Jersey: Prentice-Hall, Inc., 1996.
[7] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, New Jersey: Prentice-Hall, Inc., 1989. 47
[8] A. Datta and P. A. Ioannou, “Performance analysis and improvement in model reference adaptive control,”IEEE Trans. Automat. Contr.,Vol. 39, No. 12, pp. 2370 − 2387, 1994.
[9] Y.-J. Sun, G.-J. Yu, Y.-H. Chao, and J.-G. Hsieh,“Exponential stability and guaranteed tracking time for a class of model reference control systems via composite feedback control,” Int. J. Adaptive Contr. and Signal Processing, Vol. 11, pp. 155 − 165, 1997.
[10] K.-C. Hsu,“Decentralized variable structure model-following adaptive control for interconnected systems with series nonlinearities,” Int. J.Syst. Science, Vol. 29, No. 4, pp. 365 − 372, 1998.
[11] C.-H. Huang, “An optimal control problem for a generalized vibration system in estimating instantaneously the optimal control forces,” J. Franklin Institute, Vol. 340, No. 5, pp. 327 − 347, 2003.
[12] T.-Y. Kuc, W.-G. Han,“An adaptive PID learning control of robot manipulators ,” Automatica, Vol. 36, No. 5, pp. 717 − 725, 2000.
[13] S. Skogestad,“Control structure design for complete chemical plants,” Computers and Chemical Engineering., Vol. 28, No.2,pp. 219 − 234, 2004.
[14] Y.-J. Sun and J.-G. Hsieh, “Global exponential stabilization for a class of uncertain nonlinear systems with time-varying delay arguments and input deadzone nonlinearities,” J. Franklin Institute, Vol. 332B, No. 5,
pp. 619 − 631, 1995.
48
[15] K.-C. Hsu,“Sliding mode controllers design for uncertain systems with input nonlinearities,” J. Guidance, Contr., and Dynamics, Vol. 21, No. 4, pp. 666 − 669, 1998.
[16] K.-C. Hsu,“Adaptive variable structure control design for uncertain time-delayed systems with nonlinear input,” Dynamics and Contr., Vol. 8, pp. 341 − 354, 1998.
[17] C.-H. Chou, C.C. Cheng,“Design of adaptive variable structure controllers for perturbed time-varying state delay systems,” J. Franklin Institute, Vol. 338, No. 1, pp. 35 − 46, 2001.
[18] K.-C. Hsu,“Decentralized variable-structure control design for uncertain large-scale systems with series nonlinearities,” Int. J. Contr., Vol. 68, No. 6, pp. 1231 − 1240, 1997.
[19] K.-C. Hsu,“Variable structure control design for uncertain dynamic systems with sector nonlinearities,” Automatica, Vol. 34, No. 4, pp. 505 − 508, 1998.
[20] H. H. Choi,“On the uncertain variable structure systems with bounded controllers,” J. Feanklin Institute, Vol. 340, No. 2, pp. 135 − 146, 2003.
[21] X.-S. Wang, C.-Y. Su, H. Hong,“Robust adaptive control of a class of nonlinear systems with unknown dead-zone,” Automatica, Vol. 40, No. 3, pp. 407 − 413, 2004.
[22] K. S. Narendra and L. Valavani,“Stable adaptive controller design direct control,”IEEE Trans. Automat. Contr., Vol. AC-23,pp. 570 − 583, 1978.49
[23] K. S. Narendra, Y. H. Lin, and L. Valavani, “Stable adaptive controller design. Part II:proof of stability,” IEEE Trans. Automat. Contr., Vol. AC-25, pp. 440 − 448, 1980.
[24] G. Wheeler, C.-Y. Su, and Y. Stepanenko, “A sliding mode controller with improved adaptation laws for the upper bounds on the norm of uncertainties,” Automatica, Vol. 34, No. 12, pp. 1657 − 1661, 1998.
[25] M. Corless,“Control of uncertain nonlinear Systems,” ASME J. Dyn.Syst. Meas., Control., Vol. 115, pp. 362 − 372, 1993.
[26] H. C. Lee and Y. Choi,“A Least-Squares Method for Optimal Control Problems for a Second-Order Elliptic System in two Dimensions,”Jornal of Mathematical Analysis and Applications., Vol. 242, No.1,pp. 105 − 128, 2000.
[27] K.S. Yeung, C.C. Cheng and C.M. Kwan, “A unifying design of sliding mode and classical controllers,” IEEE Transactions on Automatic Control, Vol. 38, No.9, pp. 1422 − 1427, 1993.
[28] S.H. Zak, S.Hui,“On variable structure output feedback controllers for uncertain dynamic systems,” IEEE Transactions on Automatic Control, Vol. 38, No.10, pp. 1509 − 1512, 1993.
[29] S.H. Zak, S.Hui,“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.
50