博碩士論文 81323004 詳細資訊




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姓名 蕭永嘉( Yung-Chia Hsiao)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 非自治系統之複雜動態行為及混沌控制
(Complex Dynamics and Chaos Control of Nonautonomous systems)
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摘要(中) 在本論文中首先研究一個不對稱非自治系統的動態行為。此系統的動態行為顯示雙共同維度分歧為雙不穩定週期解合併所組成之鞍點?節點分歧的發生機制。此雙共同維度分歧由鞍點?節點分歧與週期加倍分歧交會所組成。另外由此系統的動態行為發現非自治系統的主要響應與第二響應會互相融合。此外,這個不對稱非自治系統有混沌現象存在。
許多非線性系統並不希望有混沌現象產生。一般利用混沌控制來消除系統中的混沌現象。設計混沌控制器前必須先標定某個存於混沌軌跡中的不穩定週期解。本論文以尤拉法來推導非自治系統之全域龐加萊映射的近似方程式,並利用此映射方程式來標定存在於混沌軌跡中的不穩定週期解。
傳統的混沌控制為區域式控制器。在啟動混沌控制器前必須有一段極冗長的等待時間。本論文以推導出之全域龐加萊映射來估算被混沌控制器穩定化之週期解的收斂區。利用此收斂區可有效減少混沌控制的等待時間。此外,為完全消除此等待時間,本論文利用全域龐加萊映射設計一個全域式混沌控制器。此控制器移除除選定的不穩定週期解外其他的不穩定週期解,並將此唯一的週期解漸進穩定化。如此全域式混沌控制器可在混沌現象出現時便將之消除,完全不需要等待時間。
摘要(英) A saddle-node bifurcation with the coalescence of a stable periodic orbit and an unstable periodic orbit is a common phenomenon in nonlinear systems. This study investigates the mechanism of producing another saddle-node bifurcation with the coalescence of two unstable periodic orbits. The saddle-node bifurcation results from a codimension-two bifurcation that a period doubling bifurcation line tangentially intersects a saddle-node bifurcation line in a parameter plane. Furthermore, this thesis investigates a coalescence of the primary responses and the secondary responses in the asymmetric nonautonomous system. A subharmonic orbit that bifurcates from the primary responses coalesces with a subharmonic orbit of the secondary responses via a saddle-node bifurcation. In addition, the output of the nonautonomous system is chaotic in a specific parameter range.
The chaotic motion is generally undesirable to a nonautonomous system. To control a chaotic motion to an unstable periodic orbit embedded in a chaotic trajectory, detection of the unstable periodic orbits from a chaotic time series is necessary to implement the control. This thesis presents a simple approach that detects unstable periodic orbits embedded in a chaotic motion of an unknown nonautonomous system with noisy perturbation. An identification technique is developed to obtain the model of the unknown system. The nonautonomous system is approximated by a difference system and then a global Poincare map function is derived from the difference system. The unstable periodic orbits can be detected via the map function. The proposed method is both accurate and feasible as demonstrated by two chaotic nonautonomous systems.
Many local controls of chaos were studied to suppress chaotic motions. However, there is tedious waiting time before activating the controllers. This thesis develops a strategy of controlling chaos with a region of attraction of a stabilized UPO. The strategy is activated when chaotic trajectories get into the region of attraction. The region of attraction is estimated via the approximate global Poincare map function. The proposed strategy considerably reduces a lot of the waiting time of controlling chaos.
To suppress the waiting time completely, this thesis develops a global control of chaos. The proposed global controller, who does not require waiting time in activating the controller, can be rapidly started to stabilize the targeted UPO. The global controller makes the all unstable periodic orbits vanish except a targeted unstable periodic orbit. Furthermore, a Lyapunov’s direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit. Simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit.
關鍵字(中) ★ 非自治系統
★ 雙共同維度
★ 分歧
★ 穩定週期解
★ 沌控制
關鍵字(英) ★ nonautonomous system
★ codimension-two
論文目次 封面
目次
論文摘要
第一章 緒論
第二章 非自治系統之分析方法
2.1 求取非自治系統之週期解
2.2 週期解之穩定性分析
第三章 不對稱非自治系統之複雜動態行為
3.1 雙不穩定週期解合併所組成之鞍點-節點分歧的發生機制
3.2 非自制系統中主要響應與第二響應之融合
3.3 不對稱非自治系統之混沌現象
第四章 存在於混沌中不穩定週期解之標定
4.1 混沌系統之系統判別
4.2 存在於混沌中不穩定週期解之標定方法
4.3 範例
第五章 非自治系統之混沌控制
5.1 非自治系統之全域龐加萊映射之近似方程式
5.2 收斂區於混沌控制之應用
5.3 非自治系統之全域渾沌控制
5.4. 範例
第六章 總結
參考文獻
參考文獻 [1] Abarbanel, H. D. I., Analysis of Observed Chaotic Data, Springer-Verlag, New York, 1996, Chapter 2.
[2] Alvarez-Ramirez, J., Nonlinear feedback for controlling the Lorenz equation, Physical Review E 50 (1994) 2339-2342.
[3] Barreto, E., Kostelich, E. J., Grebogi, C., Ott, E., and Yorke, J. A., Efficient switching between controlled unstable periodic orbits in higher dimensional chaotic systems, Physical Review E 51 (1995) 4169-4172.
[4] Blair, K. B., Krousgrill, C. M., and Farris, T. N., Nonlinear dynamic response of shallow arches to harmonic forcing, Journal of Sound Vibration 194 (1996) 353-367.
[5] Blair, K. B., Krousgrill, C. M., and Farris, T. N., Harmonic balance and continuation techniques in the dynamic analysis of Duffing's equation, Journal of Sound Vibration 202 (1997) 717-731.
[6] Buzug, Th. and Pfister, G., Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors, Physical Review A 45 (1992) 7073-7084.
[7] Chen, C.-L. and Yau, H.-T., Chaos in the imbalance response response of a flexible rotor supported by oil film bearings with non-linear suspension, Nonlinear Dynamics 16 (1998) 71-90.
[8] Chen, G. and Dong, X., From chaos to order—perspectives and methodologies in controlling chaotic nonlinear dynamical systems, International Journal of Bifurcation and Chaos 3 (1993) 1363-1409.
[9] Chen, G. and Dong, X., From Chaos to Order, World Scientific, Singapore, 1998.
[10] Chen, Y. H. and Chou, M. Y., Continuous feedback approach for controlling chaos, Physical Review E 50 (1994) 2331-2334.
[11] Chialvo, D. R., Gilmour, Jr R. F., and Jalife, J., Low dimensional chaos in cardiac tissue, Nature 343 (1990) 653-657.
[12] Davidchack, R. L. and Lai, Y.-C., Efficient algorithm for detecting unstable periodic orbits in chaotic systems, Physical Review E 60 (1999) 6172-6175.
[13] Diakonos, F. K., Schmelcher, P., and Biham, O., Systematic computation of the least unstable periodic orbits in chaotic attractors, Physical Review Letters 81 (1998) 4349-4352.
[14] Ding, M., Grebogi, C., Ott, E., Sauer, T., and Yorke, J. A., Plateau onset for correlation dimension: when does it occur?, Physical Review Letters 70 (1993) 3872-3875.
[15] Ditto, W. L., Rauseo, S. N., and Spano, M. L., Experimental control of chaos, Physical Review Letters 65 (1990) 3211-3214.
[16] Dolan, K., Witt, A., Spano, M. L., Neiman, A., and Moss, F., Surrogates for finding unstable periodic orbits in noisy data sets, Physical Review E 59 (1999) 5235-5241.
[17] Epureanu, B. I. and Dowell, E. H., System identification for the Ott-Grebogi-Yorke controller design, Physical Review E 56 (1997) 5327-5331.
[18] Friedmann, P. and Hammond, C. E., Efficient numerical treatment of periodic systems with application to stability problems, International Journal for Numerical Methods in Engineering 11 (1977) 1117-1136.
[19] Fuh, C.-C. and Tung, P.-C., Controlling chaos using differential geometric method, Physical Review Letters 75 (1995) 2952-2955.
[20] Garfinkel, A., Spano, M. L., Ditto, W. L., and Weiss, J. N., Controlling cardiac chaos, Science 257 (1992) 1230-1235.
[21] Ge, Z.-M. and Chen, H.-H., Double degeneracy and chaos in a rate gyro with feedback control, Journal of Sound Vibration 209 (1998) 753-769.
[22] Ge, Z.-M., Lee, C.-I., Chen, H.-H., and Lee, S.-C., Non-linear dynamics and chaos control of a damped satellite with partially-filled liquid, Journal of Sound Vibration 217 (1998) 807-825.
[23] Ge, Z.-M., Yang, H.-S., Chen, H.-H., and Chen, H.-K., Regular and chaotic dynamics of a rotational machine with a centrifugal governor, International Journal of Engineering Science 37 (1999) 921-943.
[24] Ge, Z.-M. and Lin, T.-N., Regular and chaotic dynamic analysis and control of chaos of an elliptical pendulum on a vibrating basement, Journal of Sound Vibration 230 (2000) 1045-1068.
[25] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, 1971, Chapter 1.
[26] Guckenheimer, J. and Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer-Verlag, New York, 1983, pp. 376-396.
[27] Hartley, T. T. and Mossayebi, F., A classical approach to controlling the Lorenz equations, International Journal of Bifurcation and Chaos 2 (1992) 881-887.
[28] Hayashi, C., Nonlinear oscillations in physical systems, Princeton Uninersity Press, Princeton, 1964, pp. 28-30.
[29] Holmes, C. and Holmes, P. J., Second order averaging and bifurcations to subharmonics in Duffing’s equation, Journal Sound Vibration 78 (1981) 161-174.
[30] Hsu, C. S., Impulsive parametric excitation: theory. Journal of Applied Mechanics, Transactions of the ASME 39 (1972) 551-558.
[31] Hunt, E. R., Stabilizing high-period orbits in a chaotic system: the diode resonator, Physical Review Letters 67 (1991) 1953-1955.
[32] Kantz, H. and Schreiber, T., Nonlinear Time Series Analysis, Cambridge University Press, New York, 1997, Chapter 3.
[33] Kapitaniak, T., Chaotic Oscillators — theory and applications, World Scientific, Singapore, 1992.
[34] Kawakami, H., Bifurcation of periodic responses in forced dynamic nonlinear circuits: computation of bifurcation values of the system parameters. IEEE Transactions on Circuits and Systems CAS-31 (1984) 248-260.
[35] Kawakami, H. and Yoshinaga, T., Codimension two bifurcation and its computational algorithm, in Bifurcation and Chaos - Theory and Applications, edited by Awrejcewicz, J., Springer-Verlag, Berlin, 1995, pp. 97-132.
[36] Kennel, M. B., Brown, R., and Abarbanel, H. D. I., Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A 45 (1992) 3403-3411.
[37] Khalil, H. K., Nonlinear Systems, 2nd edition, Prentice-Hall, Upper Saddle River, 1996, Section 5.2.
[38] Kloster, N. and Knudsen, C., Bifurcations near 1:2 subharmonic resonance in a structural dynamics model, Chaos, Solitons and Fractals 5 (1995) 55-66.
[39] Kuznetsov, Y. A., Elements of applied bifurcation theory, Springer-Verlag, New York, 1995.
[40] Liao, T.-L. and Chen, C.-K., Design and circuit simulation of observer based chaotic synchronization and communication system, International Journal of Electronics 86 (1999) 1423-1440.
[41] Miller, J. R. and Yorke, J. A., Finding all periodic orbits of maps using Newton methods: sizes of basins, Physica D 135 (2000) 195-211.
[42] Nayfeh, A. H. and Mook, D. T., Nonlinear oscillations, John Wiley & Sons, New York, 1979, pp. 273-283.
[43] Nijmeijer, H. and Berghuis, H., On Lyapunov control of the Duffing equation, IEEE Transactions on Circuits and Systems—I: Fundamental Theory and Applications 42 (1995) 473-477.
[44] Ott, E., Grebogi, C., and Yorke, J. A., Controlling chaos, Physical Review Letters 64 (1990) 1196-1199.
[45] Ott, E., Sauer, T., and Yorke, J. A., Coping with Chaos — analysis of chaotic data and the exploitation of chaotic systems, John Wiley & Sons, New York, 1994.
[46] Packard, N. H., Crutchfield, J. P., Farmer, J. D., and Shaw, R. S., Geometry from a time series, Physical Review Letters 45 (1980) 712-715.
[47] Padmanabhan, C. and Singh, R., Analysis of periodically excited non-linear systems by a parametric continuation technique, Journal of Sound Vibration 184 (1995) 35-58.
[48] Pei, X., Dolan, K., Moss, F., and Lai, Y.-C., Counting unstable periodic orbits in noisy chaotic systems: a scaling relation connecting experiment with theory, Chaos 8 (1998) 853-860.
[49] Petrick, M. H. and Wigdorowitz, B., A priori nonlinear model structure selection for system identification, Control Engineering Practice 5 (1997) 1053-1062.
[50] Pierson, D. and Moss, F., Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology, Physical Review Letters 75 (1995) 2124-2127.
[51] Pingel, D., Schmelcher, P., Diakonos, F. K., and Biham, O., Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems, Physical Review E 62 (2000) 2119-2134.
[52] Pyragas, K., Continuous control of chaos by self-controlling feedback, Physics Letters A 170 (1992) 421-428.
[53] Raghothama, A. and Narayanan, S., Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method, Ocean Engineering 27 (2000) 1087-1107.
[54] Rebelo, C. and Zanolin, F., Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities, Transactions of the American Mathematical Society 348 (1996) 2349-2389.
[55] Reinhall, P. G., Caughey, T. K., and Storti, D. W., Order and chaos in a discrete Duffing oscillator: implications on numerical integration, Journal of Applied Mechanics, Transactions of the ASME 56 (1989) 162-167.
[56] Romeiras, F. J., Grebogi, C., Ott, E., and Dayawansa, W. P., Controlling chaotic dynamical systems, Physica D 58 (1992) 165-192.
[57] Sauer, T., Yorke, J. A., and Casdagli, M., Embedology, Journal of Statistical Physics 65 (1991) 579-616.
[58] Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L., and Ditto, W. L., Controlling chaos in the brain, Nature 370 (1994) 615-620.
[59] Schmelcher, P. and Diakonos, F. K., Detecting unstable periodic orbits of chaotic dynamical systems, Physics Review Letters 78 (1997) 4733-4736.
[60] Schmelcher, P. and Diakonos, F. K., General approach to the localization of unstable periodic orbits in chaotic dynamical systems, Physical Review E 57 (1998) 2739-2746.
[61] Schuster, H. G., Deterministic chaos — an introduction, Physik-Verlag, Weinheim, 1984, pp. 126-130.
[62] Shaw, S. W., The dynamics of a harmonically excited system having rigid amplitude constraints, Journal Applied Mechanics, Transactions of the ASME 52 (1985) 453-458.
[63] Shieh, H.-J. and Shyu, K.-K., Nonlinear sliding-mode torque control with adaptive backstepping approach for induction motor drive, IEEE Transactions on Industrial Electronics 46 (1999) 380-389.
[64] Shinbrot, T., Grebogi, C., Ott, E., and Yorke, J. A., Using small perturbations to control chaos, Nature 363 (1993) 411-417.
[65] So, P., Ott, E., Schiff, S. J., Kaplan, D. T., Sauer, T., and Grebogi, C., Detecting unstable periodic orbits in chaotic experimental data, Physical Review Letters 76 (1996) 4705-4708.
[66] So, P., Ott, E., Sauer, T., Gluckman, B. J., Grebogi, C., and Schiff, S. J., Extracting unstable periodic orbits from chaotic time series data, Physical Review E 55 (1997) 5398-5417.
[67] Summers, J. L., Variable-coefficient harmonic balance for periodically forced nonlinear oscillators, Nonlinear Dynamics 7 (1995) 11-35.
[68] Szempli?ska-Stupnicka, W., The resonant vibration of homogeneous non-linear systems, International Journal of Nonlinear Mechanics 15 (1980) 407-415.
[69] Szempli?ska-Stupnicka, W. and Rudowski, J., Local methods in predicting occurrence of chaos in two-well potential systems: superharmonic frequency region, Journal of Sound Vibration 152 (1992) 57-72.
[70] Takahashi, Y., Rabins, M. J., and Auslander, D. M., Control, Addison-Wesley, Reading, 1970.
[71] Takens, F., Detecting strange attractors in turbulence, in Dynamical Systems and Turbulence, Lecture Notes in Mathematics No. 898, edited by Rand, D.A. and Young, L.-S., Springer-Verlag, Berlin, 1981, pp. 366-381.
[72] Van Dooren, R. and Janssen, H., A continuation algorithm for discovering new chaotic motions in forced Duffing systems, Journal of Computational and Applied Mathematics 66 (1996) 527-541.
[73] Yagasaki, K. and Uozumi, T., A new approach for controlling chaotic dynamical systems, Physics Letters A 238 (1998) 349-357.
[74] Yagasaki, K., Higher-order averaging and ultra-subharmonics in forced oscillators, Journal of Sound Vibration 210 (1998) 529-553.
[75] Yasuda, K., Kawamura, S., and Watanabe, K., Identification of nonlinear multi-degree-of-freedom systems (presentation of an identification technique). JSME International Journal, Series III 31 (1988) 8-14.
[76] Yau, H.-T., Chen, C.-K., and Chen, C.-L., Sliding mode control of chaotic systems with uncertainties, International Journal of Bifurcation and Chaos 10 (2000) 1139-1147.
[77] Yau, H.-T., Chen, C.-K., and Chen, C.-L., Chaos and bifurcation analysis of a flexible rotor supported by short journal bearings with nonlinear suspension, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science 214 (2000) 931-947.
指導教授 董必正(Pi-Cheng Tung) 審核日期 2001-7-19
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