一類多變量非線性系統(tǒng)的自適應(yīng)模糊控制_圖文

1、 1168 自 動 化 學(xué) 報 33 卷 ij = 1, · · · , j , j = 1, · · · , m 也是有界的. 因此, 閉 環(huán)系統(tǒng)的所有信號是有界的. 4 仿真實驗 為了證實提出的控制方法的有效性, 把設(shè)計的 自適應(yīng)模糊控制方法應(yīng)用到多輸入多輸出非仿射非 線性系統(tǒng), 系統(tǒng)模型如下 2 2 x 1, 1 = 1 + 0.1x2 1, 1 x2, 1 x1, 2 0.4, x 1, 2 = x2, 1 x2, 2 + 2 + cos (x1, 1 x2, 1 u2 1+ x1, 1 x1, 2 x 2, 1 = 2 +

2、sin (x1, 1 x2, 1 x2 2, 2 + x1, 1 x2, 1 2 x 2, 2 = (x1, 1 x1, 2 + x2, 1 x2, 2 + u1 + u2 + ex1, 1 + ex2, 1 yj = xj, 1 , j = 1, 2 (32 T 其中 = x11 , x21 , x12 , x22 是系統(tǒng)的狀態(tài), u = T u1 , u2 是 系 統(tǒng) 的 控 制 輸 入, 系 統(tǒng) (32 的 狀 態(tài) T 初始值為 x1, 1 (0 , x2, 1 (0 , x1, 2 (0 , x2, 2 (0 = T 0.4, 2, 1, 1 . 對變量 xj, ij , j = 1,

3、 2, ij = 1, 2 定義下面的隸 屬度函數(shù) 2 µA1 xj, ij = exp 0.5 xj, ij + 2 j, ij 2 xj, ij = exp 0.5 xj, ij + 1 µA2 j, ij 2 µA3 xj, ij = exp 0.5 xj, ij j, ij (33 2 4 x = exp 0 . 5 x 1 µ j, ij j, ij Aj, i j 2 xj, ij = exp 0.5 xj, ij 2 µA5 j, ij j = 1 , 2, i = 1 , 2 j 圖1 Fig. 1 z1, 1 (實線 和 z2

4、, 1 (虛線 的軌跡 line The trajectories of z1,1 (solid line and z2,1 (dash 圖2 Fig. 2 z1, 2 (實線 和 z2, 2 (虛線 的軌跡 line The trajectories of z1, 2 (solid line and z2, 2 (dash 利用第 3 節(jié)中的設(shè)計方法并選擇 H j, ij = cos j, ij , j = 1, 2, ij = 1, 2 作為 Nussbaum 類 型 函 數(shù), 選 擇 p 1, 1 (0 = q 1, 1 (0 = p 2, 1 (0 = q 2, 1 (0 = p 1,

5、 2 (0 = q 1, 2 (0 = p 2, 2 (0 = q 2, 2 (0 = 0.5 以及設(shè)計參數(shù) 1, 1 = 2, 1 = 1, 2 = 2, 2 = 0.1, 1, 1 = 2, 1 = 1, 2 = 2, 2 = 0.1, 1, 1 = 2, 1 = 1, 2 = 2, 2 = 5, 1, 1 = 2, 1 = 1, 2 = 2, 2 = 10, 1, 1 = 2, 1 = 1, 2 = 2, 2 = 5, 1, 1 = 2, 1 = 1, 2 = 2, 2 = 10. 通 過 利 用 Matlab 仿 真 工 具, 可 以 得 到 仿 真 圖 1 4. 從 圖 1 和 圖

6、2 可 以 看 出, 閉 環(huán) 系 統(tǒng) 中 的 變 量 z1, 1 , z2, 1 , z1, 2 , z2, 2 是 有 界 的. 圖 3 和 圖 4 (見 下 頁 指 出 了 自 適 應(yīng) 調(diào) 節(jié) 參 數(shù) p 1, 1 , q 1, 1 , p 2, 1 , q 2, 1 , p 1,2 , q 1, 2 , p 2, 2 , q 2, 2 也 是 有 界 的. 因此, 仿真實驗證實了設(shè)計方法的可行性. 2 j, ij 圖3 Fig. 3 p 1, 1 (實線, q 1, 1 (虛線, p 2, 1 (點線 和 q 2, 1 (點劃 線 的軌跡 The trajectories of p 1,

7、 1 (solid line, q 1, 1 (dash line, p 2, 1 (dot line, and q 2, 1 (dash-dot line 11 期 劉艷軍等：一類多變量非線性系統(tǒng)的自適應(yīng)模糊控制 1169 6 Tong S C, Tang J T, Wang T. Fuzzy adaptive control of multivariable nonlinear systems. Fuzzy Sets and Systems, 2000, 111(2: 153167 7 Labiod S, Boucherit M S, Guerra T M. Adaptive fuzzy

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9、2000, 30(6: 878885 9 Ge S S, Wang J. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Transactions on Neural Networks, 2002, 13(6: 14091419 圖4 Fig. 4 p 1, 2 (實線, q 1, 2 (虛線, p 2,2 (點線 和 q 2, 2 (點劃 線 的軌跡 The trajectories of p 1, 2 (solid line, q 1, 2 (da

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13、文針對一類具有干擾和不確定性的非線性多 變量非仿射互連系統(tǒng), 提出了一種自適應(yīng)模糊控制 方法. 通過利用均值定理、 模糊系統(tǒng)、 Backstepping 設(shè)計方法以及引入 Nussbaum 類型函數(shù), 提出的方 法克服了由于非仿射函數(shù)的存在和子系統(tǒng)之間的耦 合所帶來的設(shè)計上的困難. 通過只調(diào)節(jié)最優(yōu)模糊逼 近參數(shù)向量范數(shù)的估計值和逼近誤差未知界限的估 計值, 提出方法的另外一個顯著特點是減少了在線 調(diào)節(jié)參數(shù)的數(shù)量. 利用李雅普諾夫穩(wěn)定性分析方法 證明了系統(tǒng)的收斂性并獲得控制器和自適應(yīng)律. References 1 Krstic M, Kanellakopoulos I, Kokotovic P.

14、 Nonlinear and Adaptive Control Design. New York: Weley Interscience, 1995 2 Wang L X. Fuzzy systems are universal approximators. In: Proceedings of IEEE International Conference on Fuzzy Systems. San Diego: 1992. 11631170 3 Park J, Sandberg I W. Universal approximation using radial-basis-function n

15、etwork. Neural Computation, 1991, 3(2: 246257 4 Tong S C, Wang T, Tang J T. Fuzzy adaptive output tracking control of nonlinear systems. Fuzzy Sets and Systems, 2000, 111(2: 169182 5 Tong S C, Li H X. Direct adaptive fuzzy output tracking control of nonlinear systems. Fuzzy Sets and Systems, 2002, 128(1: 107115 劉艷軍 博士生, 主要研究方向為自適 應(yīng)控制、 模糊控制和神經(jīng)網(wǎng)絡(luò)控制. 本文 通信作者. E-mail: liuyjsir (LIU Yan-Jun Ph. D. His research interest covers adaptive control, fuzzy control, and neural