本研究針對具有系統不確定性與外在干擾的統一混沌系統和Sprott混沌系統做為受控系統，為了讓主、僕系統達到同步控制目標，提出改良型積分終端順滑模態控制與分數階積分終端順滑模態控制兩種控制方法，並使用干擾觀測器估測其系統物誤差和外在干擾以提高控制精度。研究上利用Lyapunov穩定性定理證明控制系統的穩定性外，並使用MATLAB進行控制系統性能模擬。模擬上在相同條件下的初始狀態和干擾項與現有文章進行控制性能比較，從模擬結果顯示所提出的積分終端順滑模態控制與分數階終端積分順滑模態控制有較優的控制誤差，且分數階終端順滑模態控制有較快的收斂效果和控制精度，以此來證明兩種控制方法的有效性。

This research aims at the unified chaotic system and Sprott chaotic system with system uncertainty and external disturbance as the controlled system. In order to achieve the synchronization control goal of the master and slave systems and the control precision, two control methods such as the improved integral terminal sliding mode control and the fractional integral terminal sliding mode control, and a disturbance observer used to estimate the system modelling error and the external disturbance are proposed in this dissertation. In this research, the Lyapunov stability theorem is used to prove the stability of the control system, and MATLAB Simulink is used to simulate the performance of the control system. Under the same conditions of the initial states and the disturbance, the control performances of the proposed control schemes are compared with those of the existing articles. From the simulation results, it is shown that the proposed control schemes have better control performance and the fractional order terminal sliding mode control has faster convergence effect and control accuracy.

目錄
摘要 i
ABSTRACT ii
目錄 iv
圖目錄 vi
表目錄 viii
符號說明 ix
第一章 緒論 1
1.1 研究背景與目的 1
1.2 文獻回顧 2
1.3 論文架構 4
第二章 混沌系統 6
2.1 前言 6
2.2 混沌系統與統一混沌系統 7
2.2.1 Lorenz混沌系統方程式 7
2.2.2 Chen混沌系統方程式 8
2.2.3 Lu ̈混沌系統方程式 10
2.2.4 統一混沌系統方程式 11
2.2.5 Sprott混沌系統方程式 14
2.3 混沌系統應用 16
第三章 控制理論 18
3.1 同步控制 18
3.2 順滑模態控制 19
3.3 終端順滑模態控制 20
3.4 非奇異終端順滑模態控制 23
3.5 積分順滑模態控制 26
第四章 控制器設計與模擬 29
4.1 前言 29
4.2 混沌系統同步控制 29
4.2.1 統一混沌系統同步控制 29
4.2.2 Sprott混沌系統同步控制 31
4.3 積分終端順滑模態控制 33
4.3.1 控制設計 33
4.3.2 統一混沌系統之積分終端順滑模態控制 34
4.3.3 穩定性證明 36
4.3.4 Sprott混沌系統之積分終端順滑模態控制 38
4.3.5 穩定性證明 41
4.4 分數階積分終端順滑模態控制 42
4.4.1 控制設計 42
4.4.2 統一混沌系統之分數階積分終端順滑模態控制 43
4.4.3 穩定性證明 46
4.4.4 Sprott混沌系統之分數階積分終端順滑模態控制 48
4.4.5 穩定性證明 51
4.5 模擬結果 53
4.5.1 統一混沌系統同步控制模擬結果 53
4.5.2 Sprott混沌系統同步控制模擬結果 71
4.5.3 訊號加密模擬結果 78
第五章 結論與未來展望 81
5.1 結論 81
5.2 未來展望 81
參考文獻 83

Lorenz, E. N., 1963, “Deterministic Non-Periods Flow”, Journal of the Atmospheric Sciences, Vol. 20, pp. 130-141.
He ́non, M., 1976, “A two-dimensional mapping with a strange attractor”, Communications in Mathematical Physics, Vol. 50, pp.69-77.
Sprott, J. C., 1997, “Simplest dissipative chaotic flow”, Physics Letters A, Vol. 228, pp.271-274.
Gen, G. and Ueta, T., 1999, “Yet another chaotic attractor”, Journal of Bifurcation and Chaos, Vol. 09, pp. 1465-1466.
Lu ̈, J., Chen, G. and Zhang, S., 2002, “The compound structure of a new chaotic attractor”, Chaos, Solitons & Fractals, Vol. 14, pp. 669-672.
Lu ̈, J., Chen, G., Cheng, D. and Celikovsky, S., 2002, “Bridge the gap between the Lorenz system and the Chen system”, International Journal of Bifurcation and Chaos, Vol. 12, pp. 2917-2926.
Wang, X. Y. and Zhao, G. B., 2010, “Hyperchaos generated from the unified chaotic system and its control”, International Journal of Bifurcation and Chaos, Vol. 24, pp. 4619-4637.
梁偉倫，2017，新統一超混沌系統之電路實現與同步控制。國立高雄應用科技大學機械與精密工程研究所碩士論文，高雄市。
Pecora, L. M. and Carroll, T. L., 1990, “Synchronization in chaotic system”, Physical Review Letters, Vol. 64, pp. 821-825.
Li, W. L. and Chang, K. M., 2009, “Robust synchronization of drive-response chaotic systems via adaptive sliding mode control”, Chaos, Solitons & Fractals, Vol. 39, pp. 2086-2092.
Nian, F., Liu, X. and Zhang, Y., 2018, “Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances”, Chaos, Solitons & Fractals, Vol. 116, pp. 22-28.
Deepika, D., Kaur, S. and Narayan S., 2018, “Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control”, Chaos, Solitons & Fractals, Vol. 115, pp. 196-203.
Li, W. L., Liang, W. L. and Chang, K. M., 2019, “Adaptive Sliding Mode Control for Synchronization of Unified Hyperchaotic Systems”, 2019 24th International Conference on Methods and Models in Automation and Robotics, Vol. 20, pp. 93-98.
Zhu, Z. Y., Zhao, Z. S., Zhang, J., Wang, R. K. and Li, Z., 2020, “Adaptive fuzzy control design for synchronization of chaotic time-delay system”, Information Sciences, Vol. 535, pp. 225-241.
Pal, P., Mukherjee, V., Alemayehu, H., Jin, G. G. and Feyisa, G., 2021, “Generalized adaptive backstepping sliding mode control for synchronizing chaotic systems with uncertainties and disturbances”, Mathematics and Computers in Simulation, Vol. 190, pp. 793-807.
Su, H., Luo, R., Fu, J. and Huang, M., 2022, “Fixed time control and synchronization of a class of uncertain chaotic systems with disturbances via passive control method”, Mathematics and Computers in Simulation, Vol. 198, pp. 474-493.
Qiao, L. and Zhang, W., 2017, “Adaptive non-singular integral terminal sliding mode tracking control for autonomous underwater vehicles”, Control Theory & Applications, Vol. 11, pp. 1293-1306.
Labbadi, M, and Cherkaoui, M., 2019, “Robust Integral Terminal Sliding Mode Control for Quadrotor UAV with External Disturbances”, International Journal of Aerospace Engineering, Vol. 2019.
Ahmed, S., Wang, H. and Tian, Y., 2021, “Adaptive High-Order Terminal Sliding Mode Control Based on Time Delay Estimation for the Robotic Manipulators with Backlash Hysteresis”, IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 51, pp. 1128-1137.
Yao, Q., 2021, “Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control”, Chaos, Solitons & Fractals, Vol. 142, pp. 130-141.
Chang, K. M., Cheng, J. L. and Liu, Y. T., 2022, “Machining control of non-axisymmetric aspheric surface based on piezoelectric fast tool servo system”, Precision Engineering, Vol. 76, pp. 160-172.
Baleanu, D., Sajjadi, S. S., Jajarmi, A. and Defterli, O., 2021, “On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control”, Advances in Difference Equations 2021, Vol. 234.
Venkataraman, S. T. and Gulati, S., 1992, “Control of Nonlinear Systems Using Terminal Sliding Modes”, 1992 American Control Conference, pp. 891-893.
Zhihong, M., Paplinski, A. P. and Wu, H. R., 1994, “A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators”, IEEE Transactions on Automatic Control, Vol. 39, pp. 2464-2469.
Feng, Y., Yu, X. and Man, Z., 2002, “Non-singular terminal sliding mode control of rigid manipulators”, Automatica, Vol. 38, pp. 2159-2167.
Utkin, V. amd Shi, J., 1996, “Integral sliding mode in systems operating under uncertainty conditions”, Proceedings of 35th IEEE Conference on Decision and Control, pp. 4591-4596.
Asi, R. M., Hagh, Y. S., Palm, R. and Handroos, H., 2019, “Integral Non-Singular Terminal Sliding Mode Control for nth-Order Nonlinear Systems”, IEEE Access, Vol. 7, pp. 102792-102802.
陳建銘，2022，終端順滑模態控制於具液壓式放大機構之壓電進給刀座研究。國立高雄科技大學機械工程系碩士論文，高雄市。
Mofid, O., Momeni, M., Mobayen, S. and Fekih, A., 2021, “A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security”, IEEE Access, Vol. 9, pp. 16546-16555.
Takhi, H., Kemih, K., Moysis, L. and Volos, C., 2021, “Passivity based sliding mode control and synchronization of a perturbed uncertain unified chaotic system”, Mathematics and Computers in Simulation, Vol. 181, pp. 150-169.