臺灣博碩士論文加值系統

本論文的研究目的有二，其一是：基於Lyapunov (-Krasovskii)穩定理論，應用線性矩陣不等式(LMI, Linear Matrix Inequality)和狀態回授控制方法，分別針對(1)隨機大型標稱系統(SLSNS, Stochastic Large-Scale Nominal System)、(2)隨機大型不確定系統(SLSUS, Stochastic Large-Scale Uncertain System)以及(3)隨機大型時延系統(SLSTDS, Stochastic Large-Scale Time-Delay System)等，三種不同類型的系統，進行符合控制目標：(1)雜訊衰減符合給定的 範數值( Norm)、(2)狀態方差(State Variance)符合給定的上界條件、(3)極點配置(Pole Placement)符合給定的圓盤區域條件等，三種不同性能控制器所需之LMI形式的充分條件推導。然後，利用LMI具有凸集最佳化演算法(COA, Convex Optimization Algorithm)的特性，得出符合由上述三種控制性能所組成之具多目標性能控制器。
為完成上述的目的，吾人首先針對SLSNS，依據大型系統匹配條件存在與否，分別採用(1)解耦式(Decoupled)、(2)集中式(Centralized)、(3)分散式(Decentralized)等，三種不同形式之狀態回授控制器的設計方法，進行符合多目標性能之次佳化狀態回授控制器(Suboptimal State Feedback Controller)所需之LMI形式的充分條件推導。
再者，分別針對具有範數有界(Norm-Bounded)和參數時變型(Time-Varying Parameter)之SLSUS及內連子系統具有時延性之SLSTDS等，二個具有不同特性的系統，採用分散式狀態回授控制器設計的方法，進行符合多目標性能之最佳化分散式狀態回授強健控制器(Robustly Decentralized Optimal State Feedback Controller)所需之LMI形式的充分條件的推導。
第二個目的則是：基於Lyapunov-Krasovskii穩定理論和利用分散式輸出回授控制器設計的方法，針對隨機大型不確定時延系統(SLSUTDS, Stochastic Large-Scale Uncertain Time-Delay System)，進行具 範數限制性能之最佳化分散式輸出回授強健控制器所需之LMI形式的充分條件的推導。最後，對本文中所提出的方法，可以藉由不同隨機大型系統(SLSSs, Stochastic Large-Scale Systems)模式的數值範例模擬，驗證出其有效性。

There are two purposes in this dissertation. The first one is to develop a multi-objectives performance state feedback controller for the stochastic large-scale systems (SLSSs). The addressed multi-objectives consist of (1) external disturbance attenuation constraints on the norm level, (2) individual state variance constraints on the upper bound limitation, and (3) pole-placement constraints on the disk region condition. The sufficient condition for satisfying each control objective, basing on the Lyapunov (-Krasovskii) stability theory, can be derived in terms of linear matrix inequalities (LMIs). Then, the multi-objectives performance controller can be constructed by using the convex optimization algorithm (COA) of a set of feasible LMIs. In addition, the discussed various SLSSs include (1) stochastic large-scale nominal systems (SLSNSs), (2) stochastic large-scale uncertain systems (SLSUSs), and (3) stochastic large-scale time-delay systems (SLSTDSs).
For achieving the above-mentioned goal, we first investigate the problem of developing the multi-objectives performance suboptimal state feedback controllers for the SLSNS. Three different design methods are used, which are (1) decoupled, (2) centralized, and (3) decentralized approaches, respectively. According to whether the matching condition in the large-scale system exists or not, the above-mentioned three controller design approaches are addressed accordingly. A set of corresponding sufficient conditions of suboptimal state feedback controllers to satisfy the multi-objectives performance can be derived in terms of feasible LMIs for solving each proposed problem.
We then focus on the problem of developing a multi-objectives performance robustly decentralized optimal state feedback controller for the SLSUS. The uncertainties are allowed to be unstructured but time-varying and norm-bounded. It is shown that the addressed problem can be solved by a set of sufficient conditions of multi-objectives robustness, which can be derived in terms of feasible LMIs for all admissible uncertainties.
Finally, we consider the problem of developing a multi-objectives performance robustly decentralized optimal state feedback controller for the SLSTDS. The considered time-delay parameters appear in the interconnections between individual subsystems. Similarly, a set of sufficient conditions of robustly decentralized optimal state feedback controller for satisfying the multi-objective performance can be derived in terms of feasible LMIs to solve the addressed problem for all time delays.
The second goal is to design a robust output feedback controller (RHOFC) for the stochastic large-scale uncertain time-delay system (SLSUTDS). The considered time-delay parameters and uncertainties are described as previously. The sufficient conditions of the desired RHOFC can be derived in terms of feasible LMIs for all admissible uncertainties and time delays. The effectiveness of all of the proposed methods is illustrated by different numerical examples.

目錄

誌謝 ii
摘要 iii
ABSTRACT v
目錄 vii
表錄 x
圖錄 xi
符號說明和縮寫 xiii
1. 緒論 1
1.1 研究動機 1
1.2 研究目的 4
1.3 文獻回顧 5
1.3.1 隨機系統穩定性分析 5
1.3.2 隨機系統可穩定性分析 9
1.3.3 控制目標問題的回顧 12
1.3.3.1 範數控制理論的回顧 12
1.3.3.2 上界協方差控制理論的回顧 12
1.3.3.3 極點配置控制理論的回顧 13
1.3.4 控制目標問題的公式化陳述 13
1.3.5 LMI理論回顧 16
1.3.6 LMI的COA應用於具多目標性能控制器之設計 19
1.3.6.1 RHC設計 19
1.3.6.2 SVUBC設計 22
1.3.6.3 DSC設計 24
2. 隨機大型標稱系統之狀態回授控制器設計 29
2.1 系統介紹 29
2.2 控制器設計方法介紹 30
2.2.1 解耦式控制設計法 30
2.2.2 集中式控制設計法 31
2.2.3 分散式控制設計法 33
2.3 在機率上的穩定性與可穩定性的定義 34
2.4 多目標控制問題的公式化陳述 36
2.5 多目標控制器設計 38
2.5.1 解耦式多目標控制器設計 39
2.5.1.1 解耦式RHC設計 42
2.5.1.2 解耦式SVUBC設計 44
2.5.1.3 解耦式DSC設計 45
2.5.2 集中式多目標控制器設計 46
2.5.3 分散式多目標控制器設計 49
2.5.3.1 分散式RHC設計 51
2.5.3.2 具多目標性能之分散式控制器設計 53
2.6 模擬與討論 54
2.6.1 解耦式控制器之模擬與討論 56
2.6.2 分散式控制器之模擬與討論 60
2.6.3 集中式控制器之模擬與討論 64
3. 隨機大型不確定系統之狀態回授控制器設計 69
3.1 系統介紹 69
3.2 在機率上的強漸穩定性與可穩定性的定義 71
3.3 多目標控制問題的公式化陳述 72
3.4 多目標分散式強建控制器設計 73
3.4.1 RDHC設計 73
3.4.2 SVUBC設計 77
3.4.3 DSC設計 78
3.5 模擬與討論 81
4. 隨機大型時延系統之狀態回授控制器設計 90
4.1系統介紹 90
4.2 在機率上的穩定性與可穩定性的定義 91
4.3 多目標控制問題的公式化陳述 92
4.4 多目標分散式強建控制器設計 93
4.5 模擬與討論 99
5. 隨機大型不確定時延系統之強健 輸出回授控制器設計 105
5.1 系統介紹 105
5.2 在機率上的穩定性與可穩定性的定義 107
5.3 控制器設計 108
5.4 模擬與討論 118
6. 結論 125
參考文獻 127
論文發表 133
自傳 135

參考文獻

[1]Chang, W. J. and Chang, K. Y., “ -norm and variance constrained controller design for stochastic model reference system via sliding mode control concept,” Proceeding of the American Control Conference, pp.2803-2807, 1999.
[2]Chang, W. J. and Chang, K. Y., “Variance and -norm constrained controller design for stochastic large-scale system,” Journal of Chinese Institute of Electrical Engineering, Vol. 7, No. 4, pp. 307-314, 2000.
[3]Florchinger, P., “Stabilization of partially linear composite stochastic systems in infinite dimension,” Proceeding of the 35th Conference on Decision and Control, Kobe, Japan, pp. 648-649, 1996.
[4]Gao, W. B. and Hung, J. C., “Variable structure control go nonlinear system: A new approach,” IEEE Trans. Ind. Electron, Vol. 40, No. 1, pp. 45-55, 1993.
[5]Sandell, N. R., Varaiya, P., Athans, M., and Safonov, M. G., “Survey of decentralized control method for large-scale system,” IEEE Trans. Automatic Control, Vol. 23, No. 2, pp. 108-128, 1978.
[6]Jamshidi, M., Large-scale system: modeling, control, and fuzzy logic. Prentice-Hall, New Jersey, pp. 229-280, 1997.
[7]Chang, W. J. and Chang, K. Y., “ -norm and variance constrained controller design for perturbed stochastic system via variance structure control,” Journal of Marine Science and Technology, Vol. 1, No. 1, pp. 26-34, 1999.
[8]Chang, K. Y. and Chen, P. C., “Multi-objective state feedback control for stochastic large-scale systems,” Journal of Chinese Institute of Electrical Engineering, Vol. 10, No. 3, pp. 305-314, 2003.
[9]Scherer, C., Gahinet, P., and Chilali, M., “Multiobjective output-feedback control via LMI optimization,” IEEE Trans. on Automatic Control, Vol. 42, No. 7, pp. 896-911, 1997.
[10]Chilali, M. and Gahient, P., “ design with pole placement constraints: an LMI approach,” IEEE Trans. on Automatic Control, Vol. 41, No. 3, pp. 358-367, 1996.
[11]Zhou, K. and Doyle, J., Essentials of robust control, Prentice-Hall, New Jersey, pp.45-89, 1998.
[12]褚健，俞立，蘇宏業，魯棒控制理論及應用，浙江大學出版社，浙江，第18至43頁，1998。
[13]Bernstein, D. S. and Harddad, W. M., “LQG control with an performance bound: a Riccati equation approach,” IEEE Trans. on Automatic Control, Vol. 34, No. 3, pp. 293-305, 1989.
[14]Siljak, D. D. and Stipanovic, D. M., “Robust decentralized turbine/governor control using linear matrix inequality,” IEEE Trans. on Power System, Vol. 17, No. 3, pp. 715-722, 2002.
[15]Boukas, E. K. and Liu, Z. K., Deterministic and stochastic time delay system. Birkh user, Boston, pp. 177-183, 2002.
[16]De Souza, C. E. and Xie, L., “Delay-dependent robust control of uncertain linear state-delay systems,” Automatica, Vol. 35, No. 7, pp. 1313-1321, 1999.
[17]Xu, S. and Chen, T., “Robust control for uncertain stochastic system with state delay,” IEEE Trans. on Automatic Control, Vol. 47, No. 12, pp. 2089-2094, 2002.
[18]Wu, H., “Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections,” IEEE Trans. on Automatic Control, Vol. 47, No. 10, pp.1745-1751, 2002.
[19]Xie, S. and Xie, L., “Stabilization of class of uncertain large-scale stochastic system with time delay,” Automatica, Vol. 36, No. 1, pp. 161-167, 2000.
[20]Wang, Z. and Ho, W. C., “Output feedback robust control with D-stability and variance constraints: parameterization approach,” Journal of Dynamical and Control Systems, Vol. 11, No. 2, pp. 263-280, 2005.
[21]Choi, H. H. and Chung, M. J., “Robust observer-based controller design for linear uncertain time-delay systems,” Automatica, Vol. 33, No. 91, pp. 1749-1752, 1997.
[22]Xie, S., Xie, L., and Wen, C., “Decentralized output feedback control of interconnected time-delay systems,” Proceedings of the American Control Conference, Chicago, Illinois, pp. 824-828, 2000.
[23]蔡尚峰，隨機控制理論，上海交通大學出版社，上海，第72至75頁，1983。
[24]黃俊欽，隨機訊號處理，儒林圖書公司，台北，第53至57頁，1992。
[25]Verriest, E. I. and Florchinger, P., “Stability of stochastic systems with uncertain time delays,” Systems and Control Letters, vol. 24, pp. 41-47, 1995.
[26]Mao, X., Kololeva, N., and Rodkina, A., “Robust stability of uncertain stochastic differential delay equation,” Systems and Control Letters, Vol.35, No. 2, pp. 325-336, 1998.
[27]Saridis, G. N., Stochastic, process, estimation, and control: The entropy approach, Wiley, New York, pp. 33-40, 1994.
[28]Doyle, J., Glover, K., Khargonekar, P., and Francis, B., “State-space solutions to standard and control problems,” IEEE Trans. on Automatic Control, Vol. 34, No.8, pp.831-847, 1989.
[29]Doyle, J., Zhou, K., Glover, K., and Bodenheimer, B., “Mixed and performance objectives, II, optimal control,” IEEE Trans. on Automatic Control, Vol. 39, No.8, pp.1575-1587, 1994.
[30]Yu, J. and Sideris, A., “ control with parametric Lyapunov functions,” Systems and Control Letters, Vol. 30, No.1, pp. 57-69, 1997.
[31]Kim, J. H. and Park, H. B., “ state feedback control for generalized continuous/discrete time-delay system,” Automatica, Vol. 35, No.7, pp.1443-1451, 1999.
[32]Iwasaki, T., Skelton, R. E., and Corless, M., “A recursive algorithm for covariance control,” IEEE Trans. on Automatic Control, Vol. 43, No. 2, pp. 268-272, 1998.
[33]Collins, E. G. and Skelton, R. E., “A theory of state covariance assignment for discrete system,” IEEE Trans. on Automatic Control, Vol. 32, No. 1, pp. 35-41, 1987.
[34]Xu, J. H. and Skelton, R. E., “An improved covariance assignment theory for discrete systems,” IEEE Trans. on Automatic Control, vol. 37, No. 10, pp. 1588-1591, 1992.
[35]Xu, J. H., Skelton, R. E., and Zhu, G., “Upper and lower covariance bounds for perturbed linear systems,” IEEE Trans. on Automatic Control, vol. 35, No. 8, pp. 944-948, 1990.
[36]Chang, K. Y. and Wang, W. J., “ norm constraint and variance control for stochastic uncertain large-scale systems via sliding mode concept,” IEEE Trans. on Circuits and Systems-I Fundamental Theory and Applications, Vol. 46, No. 10, pp. 1275-1280, 1999.
[37]Chang, W. J. and Chung, H. Y., “Extention of the covariance control principle to nonlinear stochastic systems,” IEE Proc.-Control Theory Appl., Vol. 141, No. 2, pp.93-98, 1994.
[38]Harddad, W. M. and Bernstein, D. S., “Controller design with regional pole constraints,” IEEE Trans. on Automatic, Vol. 31, No. 1, pp.54-69, 1992.
[39]Labibi, B., Lohmann, B., Sedigh, A. K., and Maralani, P. J., “Robust decentralized stabilization of large-scale systems via eigenstructure assigment,” International Journal of Systems Science, Vol. 34, No. 6, pp. 389-393, 2003.
[40]Labibi, B., “Decentralized control via disturbance attenuation and eigenstructure assignment,” IEEE Trans. on Circuit & System-II, Vol. 53, No. 6, pp. 468-472, 2006.
[41]Furuta, K. and Kim, S. B., “Pole assignment in a specified disk,” IEEE Trans. on Automatic Control, Vol. AC-32, No. 5, pp. 423-427, 1987.
[42]Garcia, G. and Bernussou, J., “Pole assignment for uncertain systems in a specified disk by state feedback,” IEEE Trans. on Automatic Control, Vol. 40, No. 1, pp. 184-190, 1995.
[43]Yu, L., “Robust control of linear uncertain systems with regional pole and variance constraints,” International Journal of Systems Science, Vol. 31, No. 3, pp. 367-371, 2000.
[44]Chilali, M. and Gahient, P., “Robust pole placement in LMI regions,” IEEE Trans. on Automatic Control, Vol. 44, No. 12, pp. 2257-2270, 1999.
[45]Fridman, E and Shaked, U., “ -control of linear state-delay descriptor systems: an LMI approach,” ELSEVIER LINEAR ALGEBRA AND ITS APPLICATIONS, 351-352, pp. 271-302, 2002.
[46]Wu, W. B., Chen, P. C., Chen, G., Chang, K. Y., and Chang, Y. H., “Multiobjective state-feedback control for stochastic large-scale system via LMI approach,” Journal of Chung Cheng Institute of Technology, Vol. 34, No. 2, pp. 1-20, 2006.
[47]Wu, W. B., Chen, G., Chen, P. C., Chang, K. Y., and Chang, Y. H., “Robust decentralized controller with multi-objective performance design for stochastic large-scale systems via linear matrix inequalities approach,” Proc. IMechE Part I: J. Systems and Control Engineering, Vol. 221, pp. 1047-1060, 2007.
[48]Vandenberghe, L. V. and Balakrishnan, V. K., “Algorithm and software for LMI problems in control,” IEEE Control Systems Lecture Notes, Vol. 17, No. 1, pp. 89-95, 1997.
[49]Gahinet, P., Nemirovski, A., Laub, A. J., and Chilali, M., LMI control toolbox for use with MATLAB, The Math Work Inc., Natick, Massachusetts, p.3-1 to p.4-14, 1995.
[50]Boyd, S., Ghaoui, L. E., Feron, E., and Balakrishnan, V., Linear matrix inequality in system and control Theory, SIAM, Philadelphia, pp. 1-56, 1994.
[51]Prajna, S, Schaft, A., and meinsma G., “An LMI approach to stabilization of linear port-controlled Hamiltonian systems”, Systems and Control Letters, Vol. 45, No.2, pp. 371-385, 2002.
[52]Boyd, S. and Vandenberghe, L., “Convex optimization”, http://www.stanford.edu /class/ee364.
[53]Sreeram, V. and Liu, W. Q., “Theory of state covariance assignment for linear single-input system,” IEE Proc. of Control Theory and Applications, Vol. 41, No. 3, pp. 289-295, 1996.
[54]Wang, S. and Davison, E., “On the statbilization of decentralized control systems,” IEEE Trans. on Automatic Control, Vol. AC-18, No. 5, pp.473-478, 1973.
[55]Khurana, H. and Ahson, S. I., “On stabilization of large-scale control system using variable structure system theory,” IEEE Trans. on Automatic Control, Vol. 31, No. 1, pp.176-178, 1986.
[56]Wang, Y., Xie L., and De Souza, C. E., “Robust control of a class of uncertain nonlinear system,” Systems and Control Letters, Vol. 19, No. 1, pp. 139-149, 1992.
[57]Kharitonov, V. L. and Zhabko, A. P., “Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems,” Automatica, Vol. 39, No. 1, pp. 15-20, 2003.