本論文主旨在於探討混沌系統中，從一個已設計的連續時間狀態迴授控制器，利用狀態吻合數位再設計的方法去設計一個提升型前置基底數位控制器。文中，我們將提升型數位再設計分成兩個部分來討論，一為資料取樣系統其觀測基底追蹤器之提升型數位再設計；一為混合混沌系統其前置基底數位控制器之提升型數位再設計。本研究方法可使得數位再設計後的系統狀態能更為逼近吻合原先連續時間的系統狀態。此外，一個全階／半階的觀測基底追蹤器也將應用於此系統中，並於文末的範例中比較其優缺點。

A lifted prediction-based digital controller using the state-matching digital redesign method from a predesigned, state-feedback, continuous-time controller for a hybrid chaotic system is presented in this thesis. We discuss the lifted digital redesign in two categories. One is the lifted digital redesign of observer-based tracker for sampled-data system, and another is the lifted digital redesign of prediction-based digital controller for hybrid chaotic system. The proposed method provides the digitally redesigned system to close matching the states of the continuous-time controlled system. In addition, a dual-rate full-order/partial-order observer-based tracker is applied in this system. An illustrative example is presented to compare the advantages and disadvantages between these.

[1] Bamieh B., B. J. Pearson, B. Francis and A. Tannenbaum, “A lifting technique for linear periodic systems with applications to sampled-data control,” Systems and Control Letters, vol. 17, no. 1, pp. 79-88, 1991.
[2] Bollt E. M. and J. D. Meiss, “Targeting chaotic orbits to the moon through recurrence,” Physics Letter A, vol. 204, pp. 373-378, 1995.
[3] Chen G. and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos, vol. 9, pp. 1465-1466, 1999.
[4] Chen G. and X. Dong, “Controlling Chua’s circuit,” Journal of Circuits, Systems and Computers, vol. 3, pp. 139-149, 1993.
[5] Chen T. and B. A. Francis, Optimal Sampled-Data Control Systems, New York: Springer-Verlag, 1995.
[6] Fujimoto H., A. Kawamura and M. Tomizuka, “Generalized digital redesign method for linear feedback system based on n-delay control,” IEEE/ASME Transaction Mechaton, vol. 4, pp. 101-109, 1999.
[7] Fujimoto H., J. Hori and A. Kawamura, “Perfect tracking control based on multi-rate feedback control with generalized sampling periods,” IEEE Transaction on Industrial Electronics, vol. 48, no. 3, pp. 636-644, 2001.
[8] Franklin G. F., J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 3rd Edition, New York: Addison-Wesley, 1994.
[9] Guo S. M., L. S. Shieh, C. F. Lin and J. Chandra, “State-space self-tuning control for nonlinear stochastic and chaotic hybrid systems,” International Journal of Bifurcation and Chaos, vol. 11, no. 4, pp. 1079-1113, 2001.
[10] Guo S. M., L. S. Shieh, G. Chen and C. F. Lin, “Effective chaotic orbit tracker: a prediction-based digital redesign approach,” IEEE Transaction on Circuits and Systems–I, Fundamental Theory and Applications, vol. 47, no. 11, pp. 1557-1570 , November 2000.
[11] Guo S. M., L. S. Shieh and C. F. Lin, “Evolutionary-programming-based Kalman filter for discrete-time nonlinear uncertain systems,” Asian Journal of Control, vol. 3, no. 4, December, 2001.
[12] Ieko T., Y. Ochi and K. Kanai, “Digital redesign of linear state-feedback law via principle of equivalent areas,” Journal of Guidance, Control, and Dynamics, vol. 24, pp. 857-859, 2001.
[13] Kostelich E. J., C. Grebogi, E. Ott and J. A. Yorke, “Higher-dimensional targeting,” Physical Review E, vol. 47, pp. 305-310, 1993.
[14] Lewis F. L. and V.L. Syrmos, Optimal Control, 2nd Edition, New York: Wiley, 1986.
[15] Rafee N., T. Chen and O. P. Malik, “A technique for optimal digital redesign of analog controllers,” IEEE Transactions on Control Systems Technology, vol. 5, no. 1, pp. 89-99, 1997.
[16] Shieh L. S., C. K. Yeung and B. C. McInnis, “Solution of state-space equations via block-pulse functions,” International Journal of Control, vol. 28, no. 3, pp. 383-392, 1978.
[17] Shieh L. S., W. M. Wang, John Bain and John W. Sunkle, “Design of lifted dual-rate digital controllers for X-38 vehicle,” Journal of Guidance, Control and Dynamics, vol. 23, no. 4, July-August 2000.
[18] Shieh L. S., W. M. Wang and M. K. Appu Panicker, “Design of PAM and PWM digital controllers for cascaded systems,” ISA Transactions, vol. 37, pp. 201-213, 1998.
[19] Shinbrot T., E. Ott, C. Grebogi and J. A. Yorke, “Using chaos to direct orbits to targets,” Physical Review Letters, vol. 65, pp. 3215-3218, 1990.
[20] Teixeira Marcelo C. M. and Stanislaw H. Żak, “Stabilizing controller design for uncertain nonlinear systems using fuzzy models,” IEEE Transaction on Fuzzy Systems, vol. 7, no. 2, April 1999.
[21] Tsai J. S. H., L. S. Shieh, J. L. Zhang and N. P. Coleman, “Digital redesign of pseudo-continuous-time suboptimal regulators for large-scale discrete system,” Control Theory and Advanced Techniques, vol. 5, pp. 37-65, 1989.
[22] Yu X. and Y. Xia, “Detecting unstable periodic orbits in Chen’s chaotic attractor,” International Journal of Bifurcation and Chaos, vol. 10, pp. 1987-1991, 2000.