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Moreover, the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately. Even with unmodeled dynamics and bounded disturbances presented the controller has good robust performance without need of correct dynamic model and parameter estimation.

并且这种控制器的设计不需要有精确的系统动态模型，不需要未知参数来满足线性依赖条件，不需要具体的系统参数估计，即使存在未建模动态和有界扰动，系统仍然具有很好的鲁棒性。

We have proposed the switching adaptive control law for the systems and designed the Lyapunov function in this thesis. It is proved that the proposed switching adaptive control law guarantees the solutions of the nonlinear systems boundedness and convergence of the tracking error to a residual set based on the Lyapunovs stability theory. The residual set can be made arbitrarily small by choosing a certain design parameters.

文中设计出了这类系统的切换自适应控制律，并构造出相应的Lyapunov函数，基于Lyapunov稳定性理论证明了系统在所设计的控制律作用下，闭环信号都有界并且跟踪误差收敛到一个集合，通过选择适当的参数可使这个集合任意小。

A theorem shows that if we apply the FNN with its algorithm in the control of the systems above mentioned, the static error will be small arbitrarily as long as the parameter δ in hypercylinder is small enough. The feasibility and the control effectiveness of the method are examined through simulation example of nonlinear dynamic system.

将基于超柱体聚类的模糊神经网络及其学习算法用于不可逆的非线性系统模型Ⅱ的控制中，定理表明，静态误差可以任意小，只要聚类的底面直径足够小。

It is shown that under the supervision of the monitoring functions, the switching of control signal will stop after a finite number of switching and the tracking error will converge to a residual set that can be made arbitrarily small by choosing some design parameters sufficiently small.

进而证明，当被控对象相对阶大于1、高频增益符号未知时，在监控函数的监测下，相关控制信号经至多有限次切换后将停止切换，跟踪误差将收敛到一个残集内，且该残集可通过减小某些设计参数而变得任意小。

This is true for an arbitrarily small electron-phonon coupling within the mean-field adiabatic approximation, which treats the phonon degree of freedom classically.

在电子半满情况下，晶格形成二聚化，基态具有二聚化长程序；在平均场近似下，声子自由度是经典的，对于任意小的电声耦合，都有Peierls相变，基态是二聚化的绝缘相。

I'm not an arbitrary person,i'm not a person when arbitrarily.

我不是随便的人，我随便起来不是人。

I can not give any conclusion arbitrarily .

我不能随意的给出任何结论。

On this basis, can be arbitrarily extended.

在此基础上可以进行任意扩展。

The relationship between the sound and meaning of a word is arbitrarily determined.

单词的发音和语义之间的关系是任意确定的。

Well,I don't want to arbitrarily calculate a figure

嗯，我不想武断地说出一个金额

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。