一类多变量非线性系统的自适应模糊控制_图文

1、 1168 自 动 化 学 报 33 卷 ij = 1, · · · , j , j = 1, · · · , m 也是有界的. 因此, 闭 环系统的所有信号是有界的. 4 仿真实验 为了证实提出的控制方法的有效性, 把设计的 自适应模糊控制方法应用到多输入多输出非仿射非 线性系统, 系统模型如下 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 是系统的状态, u = T u1 , u2 是 系 统 的 控 制 输 入, 系 统 (32 的 状 态 T 初始值为 x1, 1 (0 , x2, 1 (0 , x1, 2 (0 , x2, 2 (0 = T 0.4, 2, 1, 1 . 对变量 xj, ij , j = 1,

3、 2, ij = 1, 2 定义下面的隶 属度函数 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 图1 Fig. 1 z1, 1 (实线 和 z2

4、, 1 (虚线 的轨迹 line The trajectories of z1,1 (solid line and z2,1 (dash 图2 Fig. 2 z1, 2 (实线 和 z2, 2 (虚线 的轨迹 line The trajectories of z1, 2 (solid line and z2, 2 (dash 利用第 3 节中的设计方法并选择 H j, ij = cos j, ij , j = 1, 2, ij = 1, 2 作为 Nussbaum 类 型 函 数, 选 择 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 以及设计参数 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 过 利 用 Matlab 仿 真 工 具, 可 以 得 到 仿 真 图 1 4. 从 图 1 和 图

6、2 可 以 看 出, 闭 环 系 统 中 的 变 量 z1, 1 , z2, 1 , z1, 2 , z2, 2 是 有 界 的. 图 3 和 图 4 (见 下 页 指 出 了 自 适 应 调 节 参 数 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, 仿真实验证实了设计方法的可行性. 2 j, ij 图3 Fig. 3 p 1, 1 (实线, q 1, 1 (虚线, p 2, 1 (点线 和 q 2, 1 (点划 线 的轨迹 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 刘艳军等：一类多变量非线性系统的自适应模糊控制 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 图4 Fig. 4 p 1, 2 (实线, q 1, 2 (虚线, p 2,2 (点线 和 q 2, 2 (点划 线 的轨迹 The trajectories of p 1, 2 (solid line, q 1, 2 (da

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13、文针对一类具有干扰和不确定性的非线性多 变量非仿射互连系统, 提出了一种自适应模糊控制 方法. 通过利用均值定理、 模糊系统、 Backstepping 设计方法以及引入 Nussbaum 类型函数, 提出的方 法克服了由于非仿射函数的存在和子系统之间的耦 合所带来的设计上的困难. 通过只调节最优模糊逼 近参数向量范数的估计值和逼近误差未知界限的估 计值, 提出方法的另外一个显著特点是减少了在线 调节参数的数量. 利用李雅普诺夫稳定性分析方法 证明了系统的收敛性并获得控制器和自适应律. 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 刘艳军 博士生, 主要研究方向为自适 应控制、 模糊控制和神经网络控制. 本文 通信作者. E-mail: liuyjsir (LIU Yan-Jun Ph. D. His research interest covers adaptive control, fuzzy control, and neural