全向攻击空空导弹发射包线的快速精确拟合

基于对攻击区的定性和定量分析，提出了一种使用目标进入角与机动过载的复合三角函数作为自变量的空空格斗导弹攻击区拟合方法。使用同样的阶次，较之于传统的纯多项式拟合方法而言，本文的处理方法显著地降低了界外发射概率和失机概率。     

模糊推理神经网络的函数逼近能力

研究了模糊推理神经网络计算模型及其连续函数逼近能力。同时给出了模糊推理神经网络与传统BP神经网络的连续函数逼近等价定理 ,即任何一个传统的BP网络都存在某个模糊推理神经网络以给定的精度逼近它 ;任何一个模糊推理神经网络都有一个传统的BP网络以任意精度逼近 ,并且这两种网络都可以逼近定义在某一紧支集上的连续函数     

Efficiently counting affine roots of mixed trigonometric polynomial systems

Estimating the number of isolated roots of a polynomial system is not only a fundamental study theme in algebraic geometry but also an important subproblem of homotopy methods for solving polynomial systems. For the mixed trigonometric polynomial systems, which are more general than polynomial systems and rather frequently occur in many applications, the classical B′ezout number and the multihomogeneous B′ezout number are the best known upper bounds on the number of isolated roots. However, for the deficient mixed trigonometric polynomial systems, these two upper bounds are far greater than the actual number of isolated roots. The BKK bound is known as the most accurate upper bound on the number of isolated roots of a polynomial system. However, the extension of the definition of the BKK bound allowing it to treat mixed trigonometric polynomial systems is very difficult due to the existence of sine and cosine functions. In this paper, two new upper bounds on the number of isolated roots of a mixed trigonometric polynomial system are defined and the corresponding efficient algorithms for calculating them are presented. Numerical tests are also given to show the accuracy of these two definitions, and numerically prove they can provide tighter upper bounds on the number of isolated roots of a mixed trigonometric polynomial system than the existing upper bounds, and also the authors compare the computational time for calculating these two upper bounds.     

单调RBF神经网络的逼近性分析

针对工程中输入输出呈单调关系系统首先提出单调径向基神经网络，然后给出单调性条件定理，并证明用单调径向基神经网络插值可以逼近紧致集上任意单输入单输出的单调函数。     

Neural network-based H∞ filtering for nonlinear systems with time-delays

A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed. Firstly, neural networks are employed to approximate the nonlinearities. Next, the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion （LDI）. Finally, based on the LDI model, a neural network-based nonlinear filter （NNBNF） is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality （LMI） constraints. Compared with the existing nonlinear filters, NNBNF is time-invariant and numerically tractable. The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.     

基于多项式网络的空袭目标类型识别模型

给出了进行目标类型识别的指标集 ,建立了基于多项式前向神经网络识别模型。该模型具有三层结构 ,隐层、输出层分别采用多项式函数和线性函数作为激活函数 ;隐层 输出层的权值用最速下降法学习 ,输入层 隐层的权值用遗传算法进行学习。实例表明该模型是可行的。     

Complex Function Approximation Based on Multi-ANN Approach

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基于递阶粒子群方法的RBF网络自动设计

针对径向基函数网络（RBFN）的结构和参数难以同时优化及粒子群不同结构的粒子飞跃困难问题,提出一种维数自适应变化递阶粒子群方法,同时完成对网络的结构和参数自动优化设计。此方法中,粒子群编码采用二进制和十进制相结合的混合形式,二进制表示网络隐层神经元的数量,十进制编码表示网络参数,每个粒子在不同代的飞翔维数由当前代最好粒子的适应度和粒子到目前为止的最好适应度及粒子群处于两个最好位置时的有效维数确定。适应度函数引导粒子向小规模和小误差方向运动。通过对函数建模和混沌时间序列的预测实验,验证了方法的有效性。

Abstract：

In order to solve difficulties optimizing the structure and the parameters of RBFN simultaneously and flying among particles with different dimension,a hierarchical particle swarm optimization （PSO） with adaptive dimension was proposed to design structure and parameters of radical basis function neural networks （RBFN） automatically.In the method,the number of hidden layer for RBFN is coded by binary,and parameters are coded by decimal,the dimensions of the flying particle is determined by the best position of current generation and the best position that the particle derived so far and effective dimensions of the two best positions.Furthermore,the swarm will incline to small scales and small error by choosing a special fitness function which takes account factors of structure and parameters of RBFN.Simulation results with function approximation and prediction of chaotic time sequence demonstrate that the proposed method is efficient.     

基于样条逼近和小波分解的Hammerstein模型辨识

采用三次B-样条方法取代传统的多项式方法逼近Hammerstein模型中的非线性部分，在保持多项式的简单性和逼近的可行性的同时，大大提高了逼近精度。同时采用小波变换对辨识数据进行多尺度分解，通过在低频空间抑制高频噪声干扰从而实现精确建模。理论分析和仿真结果都表明估计结果具有渐近无偏性和一致收敛性，该方法辨识精度高，具有良好的实用性。     

Functional coefficient autoregressive conditional root model

This paper proposes an extended model based on ACR model:Functional coefficient autoregressive conditional root model（FCACR）.Under some assumptions,the authors show that the process is geometrically ergodic,stationary and all moments of the process exist.The authors use the polynomial spline function to approximate the functional coefficient,and show that the estimate is consistent with the rate of convergence O_p(h^v+1+n^-1/3).By simulation study,the authors discover the proposed method can approximate well the real model.Furthermore,the authors apply the model to real exchange rate data analysis.     

对压电陶瓷执行器迟滞特性的智能建模

由于压电陶瓷执行器固有的迟滞非线性会影响系统的控制精度,甚至能导致系统不稳定,基于神经网络建立一个迟滞非线性的智能模型。提出一个迟滞因子将多映射的迟滞非线性转换成能够被神经网络逼近的一一映射。该模型结构简单,简化了辨识过程。最后用该方法对实际的压电陶瓷执行器进行建模,结果表明,该模型能够准确的逼近迟滞非线性。     

Robust adaptive neural network control with supervisory controller

The problem of direct adaptive neural network control for a class of uncertain nonlinear systems with unknown constant control gain is studied in this paper. Based on the supervisory control strategy and the approximation capability of multilayer neural networks (MNNs), a novel design scheme of direct adaptive neural network controller is proposed.The adaptive law of the adjustable parameter vector and the matrix of weights in the neural networks and the gain of sliding mode control term to adaptively compensate for the residual and the approximation error of MNNs is determined by using a Lyapunov method. The approach does not require the optimal approximation error to be square-integrable or the supremum of the optimal approximation error to be known. By theoretical analysis, the closed-loop control system is proven to be globally stable in the sense that all signals involved are bounded, with tracking error converging to zero.Simulation results demonstrate the effectiveness of the approach.     

Learning algorithm and application of quantum BP neural networks based on universal quantum gates

A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which （1） is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects： convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.     

基于RBF-HMM模型的时间序列在线预测

针对非线性非高斯时间序列,提出观测噪声服从隐马尔可夫模型(HMM)的径向基函数(RBF)神经网络预测模型—RBF-HMM模型,该模型具有如下两个特点:(1)用隐节点数可变的RBF神经网络对时间序列进行非线性建模;(2)用HMM对非高斯噪声进行建模.并采用序列蒙特卡罗(SMC)方法实现RBF-HMM模型参数的动态调整和时间序列的在线预测.最后采用南京禄口国际机场日旅客吞吐量数据进行实证研究,结果表明该模型的有效性.     

基于分布式并行计算的神经网络算法

为了提高计算性能（速度与可扩展性），提出了一种新颖的神经网络的并行计算体系结构和计算网络权函数的训练算法。权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。各个权函数能够独立求解，可以通过并行系统采用并行算法计算。算法可以求得全局最优点，得到反映网络误差的一个有用的表达式。此外,算法在不超过权函数总数的范围内，还具有维持加速比与并行系统中提供的处理器的数量成线性增长的能力。仿真实验结果表明，本文算法的计算性能远远优于传统算法。     

RBF网络及其在数值计算中的应用

由经典的函数逼近理论衍生的很多数值算法有共同的缺点：计算量大、适应性差，对模型和数据要求高，在实际应用中受到限制。神经网络可以被用来计算复杂输入与输出结果之间的关系，具有很强的函数逼近功能。文章阐述如何利用RBFNN进行函数逼近、求解非线性方程组以及散乱数据插值，结合MATLAB神经网络工具箱给出了数值实例，并与BP网络等方法进行了比较。应用结果表明RBFNN是数值计算的一个有力工具，与传统方法比较具有编程简单、实用的特点。     

MPSO-RBF优化策略在锅炉过热系统辨识中的仿真研究

提出了基于改进PSO算法的RBF神经网络混合优化（MPSO-RBF）方法，并将其应用到非线性系统的辨识中。该方法将改进PSO算法的全局搜索能力和RBF神经网络局部优化的高效性相融合，克服了普通PSO算法收敛的不稳定性和RBF网络易陷入局部极小值的缺点。经典型非线性系统仿真试验，并与GA-RBF和RBF辨识效果进行了对比，结果表明基于MPSO-RBF的混合优化方法较GA-RBF和RBF优化速度快、逼近性能好，可以达到更优的辨识精度。最后，通过对火电厂的过热汽温动态特性的辨识实例，同样证明了MPSO-RBF方法具有更好的性能指标。     

具有混合执行器故障的多智能体分布式有限时间自适应协同容错控制

针对多智能体编队系统执行器发生故障时,所引起的参数不确定以及系统瞬态不稳定问题,本文采用径向基函数神经网络(radial basis function neural networks, RBFNNs)对不确定参数(未知函数)进行估计。同时,基于反推技术设计出合理的自适应容错控制器,并通过有限时间理论保证系统实现瞬态稳定。首先,本文采用10个智能体作为被控对象,基于有向通讯拓扑结构理论,构建了非线性多智能体系统模型。其次,基于RBFNNs逼近特性,采用反推技术与动态面技术相结合,设计出合理的容错控制器,补偿多智能体中出现的未知非线性执行器故障,并采用有限时间理论解决系统瞬态不稳定问题。接着,基于Lyapunov稳定性理论分析了控制器的稳定性和快速收敛性。最后,通过两种算例对比,验证了所设计的控制器性能优于传统的反推技术,为工程实践提供了一种有效的研究思路。     

回归神经网络辩识电液伺服系统模型与仿真

建立了一种回归神经网络辩识非线性电液伺服控制系统数学模型的辩识方法,研究了基于回归神经网络内部状态反馈的辩识算法,利用辩识实验获得的过程输入/输出数据动态调整神经网络权值。仿真结果辨明:神经网络描述的电液伺服控制系统数学模型具有较高精度,算法全局逼近能力良好。     

光滑支持向量机多项式函数的研究

为了找到多项式光滑支持向量机(polynomial smooth support vector machine,PSSVM)中性能更好的光滑函数,将正号函数变形并展开为多项式级数,得到一类光滑函数。证明了这类函数的性能,它既能满足任意阶光滑的要求,也能达到任意给定的逼近精度。用Newton-Armijo算法求解相应的PSSVM模型,实验结果表明,随着多项式光滑函数阶数的提高,逼近精度和相应PSSVM模型的分类性能也相应提高。