法向最小二乘法

<正> 通常的最小二乘法是以||·||_2z为准则,本文提出一种以数据点到拟合曲线的法向距离之平方和为准则的法向最小二乘法。设有m个数据点(x_i,y_i)(i=1,2,…m),n个基函数_f(x)(j=1,2,…,n),线性最小二乘拟合曲线函数为     

Gauss-Newton法的收敛球与解的唯一性球

0　引　言本文研究非线性最小二乘问题min F( x)∶ =12 f( x) Tf ( x) ( EP)的 Gauss-Newton法的局部收敛性 ,其中 f:Rn→ Rm是 Frechet可微的 ,m≥ n.非线性最小二乘问题在数据拟合 ,参数估计和函数逼近等方面有广泛的应用 .在工程应用中也起到很大作用 ,例如在神经网络中 ,对小波问题 ,FP网络等方面的数据 (图形 )传输 ,数据 (图形 )压缩等方面有极其重要的理论和实际意义 .目前 ,求解最小二乘问题的最基本的方法之一是 Gauss-Newton法 [1 ]xn+1 =xn -[f′( xn) Tf′( x) ] - 1 f′( xn) Tf( xn) . ( GN)就我们所知 ,目前关于 Gau…     

自动选取多非线性参数初始值的循环搜索法

1几何中心化加权最小二乘法给定观测数据集(x_i,y_i),i=1,2,…,n．(1．1)欲拟合加权非线性模型y_i=f(x_i,θ) ε_i,(1．2)其中模型函数f的参数为θ=(θ_1,…,θ_p)~T,随机观测误差项满足ε_i～N[0,(?)~2m(z_i,λ)],(1．3) m(z_i,λ)为已知正值函数,z_i可以是x_i,也可以是μ_i=f(x_i,θ)或二者的组合,λ为权参数,而(?)~2为未知的方差参数,λ和θ可统称为模型参数．模型的似然函数为     

浅谈数据资料的处理和函数拟合

为了研究解决一个实际问题,我们往往要从一组观察得到的数据(xi,yi),i=1,2,…,n中寻找自变量x与因变量y之间的函数关系.最小二乘法是寻找适当函数关系即数据拟合的一个常用的方法.……     

纵向数据半参数回归模型估计的r阶平均相合性

本文考虑纵向数据下半参数回归模型:yij=xij′β g(tij) eij,i=1,…,m,j=1,…,ni.基于最小二乘法和一般的非参数权函数方法给出了模型中参数β,回归函数g(·)和误差方差σ2的估计,并在适当条件下证明了估计量的r(r≥2)阶平均相合性.     

非线性回归模型参数估计量的随机展开及偏和方差的讨论

§1.引言 对于非线性回归模型y_t=f(x_t,θ)+ε_t, t=1,2,… (1.1) 若记 S(θ)=sum from t=1 to n([y_t-f(x_t,θ)]~2) (1.2) 则维数假定为p的参数向量θ的一个最小二乘估计量(简记为LSE)定义为满足下式的统计量(y):     

分段线性规划算法的一个注记

求解分段线性规划问题inf S(x) s.t.Ax≤b 0≤x≤(?) (1)其中(?)=((?)_1,(?)_2,…,(?)_n)及 b=(b_1,b_2,…,b_m)~T 是已知向量,A 是已知的(m,n)矩阵,元素为 α_(ij)。目标函数 s(x)是分段线性函数。即对[0,(?)_j)(j=1,2,…,n)存在分划0=x_j~(0)相似文献   

Asymptotic Behavior of Oscillatory Solutions of Forced Nonlinear Neutral Delay Differential Equations

§1.　IntroductionThispaperisconcernedwiththeasymptoticbehavioroftheoscillatorysolutionsofnonlin-earforcedneutraldelaydifferentialequationsoftheform[x(t)-∑mi=1pi(t)x(t-τi)]′ ∑nj=1qj(t)f(x(t-σj))=r(t),　t≥t0,(1)wherepi,qj,r∈C([t0,∞),R),τi,σj≥0,i=1,2,…,m;j=1,2,…,n,f∈C(R,R),xf(x)>0forx≠0.Whenpi(t)≡0,i=1,2,…,m,Eq.(1)reducestox(t) ∑nj=1qj(t)f(x(t-σj))=r(t),　t≥t0,(2)whoseasymptoticbehaviorofallsolutionshasbeenstudiedinJ.R.Yan[5].Whenr(t)≡0,f(x)≡xandm=n=1,Eq.(1)reducesto[…     

纵向数据变系数回归模型小波估计的渐近性质

考虑纵向数据下的变系数回归模型y_(ij)=x_(ij)~Tθ(t_(ij))+e_(ij)i=1,2,…,n j=1,2,…,m.利用小波光滑和加权最小二乘方法,分别研究了模型中未知参数θ(·)的小波估计θ(·)和误差方差σ~2的小波估计σ~2,在适当的条件下,证明了θ的强相合性,强相合速度,并得到θ和σ~2的渐近正态性.     

非线性最小二乘问题的一类迭代解法

本给出了求解非线性最小二乘问题的一种迭代解法，即由已知节点数据（xi,yi）(i=1,2,…,m）求函数y=f(x,b1,b2,…，bn）中非线性参数b1,b2,…，bn的一种迭代解法。并用实际算例的结果说明了该迭代解法优于一般线性化方法，说明了该种方法在实际工程领域中的应用。     

Hybrid Methods for Nonlinear Least Squares

The conjecture is considered that the hybrid GN-BFGS methodof Al-Baali and Fletcher [1] is superlinearly convergent. Acounterexample is constructed for which the method is only linearlyconvergent whereas the BFGS method alone would be superlinearlyconvergent, thus disproving the conjecture. Two new hybrids methods are suggested, and it is shown thatthese are superlinearly convergent under mild conditions. Awide range of numerical experience is reported and is seen tofavour the new methods. Some interesting theoretical propertiesof a variational Hessian error measure are given.     

Robust state estimation and fault diagnosis for uncertain hybrid systems

Robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems. In this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults. Model uncertainties, disturbances and faults are represented as structured unknown inputs. The robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling. Furthermore, the detectability and mode identifiability conditions are rigorously analyzed. On the basis of the robust hybrid observer, a robust fault detection and isolation scheme is presented also in the paper. Simulations of a hybrid four-tank system show the proposed approach is effective.     

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed.

An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented.

The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor.

Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.     

基于混合时滞观测器的混合反馈控制

对于一类具有状态和有限自动机输出时滞的离散混合系统,研究基于混合时滞观测器的混合反馈控制问题.通过系统线性部分和离散事件部分的Lyapunov函数构造了整个时滞系统的混合Lyapunov函数,进一步,给出混合反馈控制的设计方法且证明了闭环系统的稳定性.仿真例子说明该方法的有效性.     

Energy dissipating hybrid control for impulsive dynamical systems

A novel class of fixed-order, energy-based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in nonsmooth Euler–Lagrange, hybrid port-controlled Hamiltonian, and lossless impulsive dynamical systems. These dynamic controllers combine a logical switching architecture with hybrid dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to hybrid closed-loop systems described by impulsive differential equations. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and an illustrative numerical example is given to demonstrate the efficacy of the proposed approach.     

蚁群遗传混合算法

将蚁群遗传混合算法分别求解离散空间的和连续空间优化问题.求解旅行商问题的混合算法是以遗传算法为整个算法的框架,利用了蚁群算法中的信息素特性的进行交叉操作;根据旅行商问题的特点,给出了4种变异策略;针对遗传算法存在的过早收敛问题,加入2-0pt方法对问题求解进行了局部优化.与模拟退火算法、标准遗传算法和标准蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.求解连续空间优化问题是以蚁群算法为整个算法的框架,加入遗传算法的交叉操作和变异操作,用测试函数验证了混合蚁群算法的正确性.     

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.     

Theory and application of conflict resolution with hybrid preference in colored graphs

An algebraic approach is proposed to calculate stabilities in a colored graph with hybrid preference. The algebraic approach establishes a hybrid framework for stability analysis by combining strength of preference and unknown preference. The hybrid system is more general than existing models, which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, matrix representations of four basic stabilities in a colored graph are extended to include mild, strong, and uncertain preference and algorithms are developed to calculate efficiently the inputs essential to the stability definitions. A specific case study, including multiple decision makers and hybrid preference, is used to illustrate how the proposed method can be applied in practice.     

Neural network hybrid adaptive control for nonlinear uncertain impulsive dynamical systems

A neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.     

Optimal disturbance rejection control for nonlinear impulsive dynamical systems

In this paper, we develop an optimality-based framework for addressing the problem of nonlinear–nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances. Specifically, we transform a given nonlinear–nonquadratic hybrid performance criterion to account for system disturbances. As a consequence, the disturbance rejection problem is translated into an optimal hybrid control problem. Furthermore, the resulting optimal hybrid control law is shown to render the closed-loop nonlinear input–output map dissipative with respect to general supply rates. In addition, the Lyapunov function guaranteeing closed-loop stability is shown to be a solution to a steady-state hybrid Hamilton–Jacobi–Isaacs equation and thus guaranteeing optimality.