非线性

Given a finite training sample set, according to the proposal of establishing a Local Most Entropy probability density function to estimate the number of cluster a method for estimating 〓 is proposed, where a complicated method based on Maximum Likelihood Cross-Validation is replaced by Chebyshev inequality.

为改善BP算法的收敛速度慢、易陷入局部最小的问题，提出了带一类非线性特性动量项的变步长BP算法，构造了一个能自适应升降温的动量项非线性强度函数，在编程中又采用了有条件引入非线性特性动量项的措施，大大提高了搜索过程跳出局部极小、快速稳定收敛的能力。

In addition, the voltage-current characteristic of linear resistive components is the general solution of Clairaut equation, and the voltage-current characteristic of non- linear components is the singular solution of Clairaut equation.

论文摘要：本文讨论了任意伏安特性电阻元件满足的基本微分方程以及非线性电路的功率匹配问题的几个定理，指出任意伏安特性电阻元件均满足非线性一阶的clairaut方程，并且，线性电阻元件的伏安特性是clairaut 方程通解，而非线性电阻元件的伏安特性是clairaut 方程的奇解。

In allusion to dynamic nonlinear large-scale industrial processes, to bring up gained the method of decentralized identification for the strong consistency estimates of the divisible steady-state models, it is used that property of polynomial can infinitely approach to the nonlinear function and in optimization processes use step signals as input signals, the divisible steady-state models of dynamic nonlinear large-scale industrial processes, and the cognizable conditions are obtained.

针对动态非线性大工业过程，提出了得到其可分稳态模型强一致性估计的分散辨识方法；利用多项式对非线性函数的无限逼近的性质和优化过程中设定点的阶跃信号作输入激励信号，获得了动态非线性大工业过程的可分稳态模型和可辨识的条件。

The parameters of GHM model are determined by nonlinear curve fitting in complex frequency domain. This is converted into nonlinear optimization problem with constrained condition. The corresponding program is completed.

GHM模型的参数通过复频域内的非线性曲线拟合确定，最终转化为具有约束条件的非线性优化问题，并编制了相应的非线性优化程序。

A new computational formula to nonlinear adjustment by parameters, in consideration of the second-order terms, is derived in this paper from the precise orthogonality condition equations to nonlinear least squares by analyzing the direct solving process and iterative computing method of the linearized model.

在分析线性化的非线性参数平差的近似直接解法与迭代解法基础上，利用非线性最小二乘的精确正交性条件方程，推导出顾及到二次项的非线性参数平差的一种新的计算公式。

In the algorithm, the conditional linear state equation is first inserted into the measurement equation, which fuses the linear state process noise and the original measurement noise, whereafter the GHF is used to estimate the nonlinear states. Then the estimated means of the nonlinear states are inserted into the linear state equation and the original measurement equation to estimate the linear states by the KF. Moreover, in order to improve the accuracy of the estimates, the estimated variances of the nonlinear states are fed back to modify the estimations of the linear states using the KF.

算法将模型中的条件线性状态方程代入观测方程，并融合线性状态的过程噪声和观测噪声，由GHF获得非线性状态的估计；再将非线性状态的估计均值代入线性状态方程与观测方程，由KF获得线性状态的估计；获得的非线性状态估计方差还用于修正由KF估计的线性状态，以提高精度。

In this paper,from the global viewpoint we first define the nonlinear control system on a two dimensional surface in the three dimensional Euclidean space, give the represwentation of the state equation under a loca coordinate sysgtem of the surface, and study the connectin between the equilibrium state of the nonlinear system and the egodesics on the surface.

我们首先从整体化的观点定义了一种建立在三维欧氏空间的二维曲面上的非线性控制系统，并给出了在曲面的局部坐标系下非线性系统状态方程的表达式，研究了非线性系统的平衡态与曲面的测地线之间的关系。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables,and the state and costate variables inside the time interval were approximated by Lagrange interpolation.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

School of Electronic and Information Engineering,Dalian University of Technology,Dalian,Liaoning 116024,ChinaStable processes can better model the impulsive random signals and noises in physical observation.This paper briefly describes its spectral representation,proposes a new different spectral density from power spectrum density of second order processes,thus can get a new concept of stable white noise based on covariation spectrum,and a method of identification of nonlinear PAR system based on least p-norm.

描述了稳定分布的谱表示，提出了共变谱密度的概念，得到一种基于自共变序列与共变谱的稳定分布白噪声与有色噪声的概念及其判断标准，对传统意义上的白噪声进行了广义化，依据多项式自回归系统模型，对基于稳定白噪声输入的系统输出非线性稳定有色噪声建立其非线性PAR模型，提出基于最小P范数的EIRLP算法对非线性PAR系统进行辨识。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。