臺灣博碩士論文加值系統

在本論文中,具狀態相依雜訊的離散時間非線性隨機T-S模糊模型之H∞動態輸出回授控制被著手討論。我們所討論之模糊T-S模型具有隨機不確定項,即在系統矩陣,輸入矩陣,與輸出矩陣中的狀態相依雜訊。首先,當模糊模型中的假定變數可取得時, 我們使用與T-S模糊系統中相同假定變數之動態模糊H∞輸出回授控制,已達到規定控制系統能符合H∞所要求之具體提出的性能指標。其次, 當模糊模型中的假定變數無法取得時,基於估測器之模糊H∞狀態回授控制被提出。由上面兩種情況,我們推導出充分的條件去描述線性矩陣不等式(LMI)以保證閉迴路系統之穩定度。上述提出之模糊控制將由模擬證明之。

In this thesis, H∞ dynamic output feedback control for discrete-time nonlinear stochastic T-S fuzzy model with state-dependent noise is attacked. We consider the fuzzy T-S models has stochastic uncertainties, i.e., state-dependent noise, in the system matrix, input matrix, and output matrix. First, when the premise variables in the fuzzy plant model are available, an H∞ fuzzy dynamic output feedback controller, which uses the same premise variables as the T-S fuzzy model, is proposed for regulation of the controlled system to meet the H∞ control performance specification. Next, when the premise variables for building the fuzzy plant model are not available, a fuzzy H∞ observer-based state feedback controller, in which the premise variables are the estimated version of the premise variables in the T-S fuzzy model, is proposed. For the two cases, we conduct sufficient conditions described by linear matrix inequalities (LMI) to ensure stability of the closed-loop system. Performance of the proposed fuzzy controller is verified by simulation study.

1 Introduction 1
1.1 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Optimal H1 Output Feedback Control of Stochastic Fuzzy Systems 5
2.1 The Stochastic T-S Fuzzy Model . . . . . . . . . . . . . . . . . . . . 5
2.2 Optimal H1 Output Feedback Control with measurable premise variables 8
2.3 Optimal H1 Output Feedback Control without measurable premise
variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Simulation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Conclusion and Discussion 29
4 Appendix 31
4.1 Constructing a Fuzzy Design Model Using a Nonlinear Model . . . . 31

1 Sheng-Guo Wang, H. Y. Yeh, and Paul N. Roschke, “Robust control for struc-
tural systems with parametric and unstructured uncertainties,”Proceedings of
the American Control Conference, pp. 1109-1114, June 25-27, 2001.
2 Tielong Shen and Katsutoshi Tamura, “Robust H1 control of uncertain nonlin-
ear system via state feedback,”IEEE Transactions on Automatic Control, vol.
40, no. 4, pp. 766-769, April 1995.
3 Je¤ery R. Layne and Kevin M. Passino, “A fuzzy dynamic model based state
estimator”, Fuzzy Sets and Systems, vol. 122, pp.45–72, 2001.
4 C. S. Tseng and B. S. Chen, “H1 fuzzy estimation for a class of nonlinear
discrete-time dynamic systems,” IEEE Trans. Signal Processing, Vol. 49, pp.
2605-2619, 2001.
5 Nadav Berman, Uri Shaked, “ H1 for the nonlinear stochastic systems,”IEEE
Conference on Decision and Control, Msui, Hawaii USA, December 2003.
6 X. Feng, K. A. Loparo, and Y. Fang, “Optimal state estimation for stochastic
systems: an information theoretic approach,” IEEE Trans. on Auto. Contr.,
vol. 42, no. 6, pp. 771-785, 1997.
7 H. Cox, “On the estimation of state variables and parameters for noisy dynamic
systems”, IEEE Trans. on Auto. Contr., vol. 9, no. 1, pp. 12-19, 1964.
8 R. E. Kalman, “New Methods and Results in Linear Prediction and Filter-
ing Theory,”Research Institute for Advanced Studies, Baltimore, Md., Rept.
No. 61-1, 1961. Also in “Proc. On First Symp. Engrg. Applications of Random
Function Theory and Probability,“ John Wiley and Sons, Inc., New York, N. Y.,
1963.
9 A. S. Gilman and I. B. Rhodes, “Cone-bounded nonlinearities and mean-square
bounds - Estimation upper bound,”IEEE Trans. on Auto. Contr., vol. AC-18,
no. 3, pp. 260-265, 1973.
10 I. B. Rhodes and A. S. Gilman, “Cone-bounded nonlinearities and mean-square
bounds - Estimation lower bound,”IEEE Trans. on Auto. Contr., vol. AC-20,
no. 5, pp. 632-641, 1975.
11 T.-J. Tarn and Y. Rasis, “Observers for nonlinear stochastic systems,”IEEE
Trans. on Auto. Contr., vol. AC-21, no. 4, pp. 441-448, August 1976.
12 Li Xin Wang, “A Course in Fuzzy Syatems and Control,”Prentice-Hall Inc.,
America, 1997.
13 T. Takagi and M. Sugeno, “Fuzzy identi…cation of systems and its applications
to modeling and control,”IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no.
1, pp. 116-132, Jan. 1985.
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