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By using the interpolation mechanism of fuzzy system, an approach of building the series of fuzzy systems, which can uniformly approximate any continuous function on a compact domain to any accuracy, is given, and then the universal approximation theorem is generally proved.

利用模糊系统的插值模型来代替被控对象的真实模型,设计了一个自适应模糊控制策略;为保证系统的全局稳定性,增加了一个补偿控制律,它是根据模糊系统的逼近误差估计量来设计的,因此这里系统跟踪误差的收敛性不依赖于模型最小误差的平方可积性[70,71]。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道,当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时,初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上,其中必定存在一个投影点离问题解点的距离最短,即把该点作为下一次迭代的初始点,从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

From our results we know that the average error of the Lagrange interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes in the 1-fold integrated Wiener space equal weakly to the average error of their corresponding optimal approximation polynomial in the 1-fold integrated Wiener space,and as a kind of information-based operation,they have simple form and their recover functions are polynomials,in the 1-fold integrated wiener space,their average error equal weakly to the corresponding minimal information radius whose permissible information operators class is function values.

通过我们的结果可以知道,基于第一类Chebyshev多项式零点的Lagrange插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差弱等价于相应的最佳逼近多项式在1-重积分Wiener空间下的平均误差,并且作为形式简单且恢复函数为多项式的一种信息基算法,其在1-重积分Wiener空间下的平均误差弱等价于相应的以函数值计算为可允许信息算子的最小平均信息半径。

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