基于小波算法的二阶线性定常分布参数系统的辨识

本文基于正交函数逼近方法,借助于小波变换,并利用其运算矩阵及其运算性质,研究了分布参数系统的辨识问题。将Haar小波正交基应用于分布参数系统的辨识中,经正交小波逼近变换,将原偏微分描述的分布参数系统转化为代数矩阵方程,并且,考虑了初始条件和边界条件,获得了算法简单、计算方便、具有较高精度的辨识算法,简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法。仿真实例表明了本文所提出的算法的有效性。     

时变非线性分布参数控制系统的小波辨识算法

基于正交函数逼近理论,在Haar小波正交规范基的基础上,总结并推导出了其积分运算矩阵、微分运算矩阵、乘积运算矩阵及其运算性质,并应用于一类时变非线性分布参数系统的辨识.借助于正交小波函数逼近方法对分布参数系统进行辨识,经正交小波逼近变换转化为代数矩阵方程,因此该方法可以不考虑初始条件和边界条件,较其他辨识方法要简单得多.该算法简单、计算量小、简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法.     

分布式反应器模型的小波逼近辨识方法

小波变换作为一种有效的函数逼近工具,为其应用于分布参数系统的逼近提供了理论根据.以一大类复杂化学反应器分布参数模型为研究对象,采用Hear正交小波函数逼近非线性分布参数模型,然后采用多变量最小二乘递推辨识算法求解集总化的多变量状态空间模型参数.不仅考虑实际过程中状态量、控制量或变参数的乘积非线性特征.而且将反应过程的传质系数当作空同变参数进行辨识,为此,提出了一种便于逼近计算的新的Haar小波运算矩阵--平方积分运算矩阵,并得到了计算通式.通过仿真实例说明了通过提高Haar小波逼近阶数可极大地改善辨识效果.同时运用变尺度分段逼近方法,以较低的阶数较好地逼近平稳过程,说明了该方法的有效性.     

基于小波逼近变换的非线性分布参数系统辨识

利用Haar小波正交规范基的微分运算矩阵及其运算性质,将描述一类非线性分布参数系统的偏微分方程转化为代数矩阵方程,结合最小二乘法,确定出待辨识的系统参数,避免了对偏微分方程进行多重积分运算的繁琐;并且,可以不考虑初始条件和边界条件,较其他采用积分运算矩阵的辨识方法要简单得多,简化了分布参数系统辨识的求解过程。该方法简单,计算量小,辨识精度高。仿真结果表明了该算法应用在非线性分布参数系统辨识中的有效性。     

基于小波变换的二阶线性分布参数系统预测控制

分布参数系统由于其复杂性,控制系统设计一直是控制理论的难点.寻求解决分布参数系统控制的新思路,本文提出了基于正交小波变换的线性离散时间分布参数系统预测控制概念,应用正交小波变换将二阶线性分布参数系统预测控制命题变换为集总参数系统预测控制问题,并设计预测控制器,将控制律进行反演获得原系统的具有分布特性的控制律.仿真研究表明,本文提出的分布参数系统预测控制算法取得了理想的控制效果,对系统模型失配和扰动具有较好的鲁棒性,验证了算法的有效性.     

一类有输入噪声扰动的逆系统无偏参数辨识算法研究

对逆系统建模时,原系统的输出作为逆系统参数辨识时的输入.由于原系统输出存在测量噪声,且噪声方差未知,采用普通最小二乘法辨识,无法得到逆系统参数的一致无偏估计.为此,本文研究了一种有输入扰动的的逆系统无偏参数辨识算法,该算法先通过小波变换估计输入信号噪声的方差,再由估计得到的方差,通过偏差消除的递推最小_乘法,对逆系统的参数进行无偏辨识.该算法降低了对输入辨识信号为白噪声的要求,具有较强的实用性.由于采用递推运算,该算法也可以用于逆系统参数的在线辨识.最后,通过实验验证了该算法的有效性.     

蚁群算法在系统辨识中的应用

将传统用于离散空间问题求解的蚁群算法引入连续空间内的系统参数辨识问题求解, 定义了各智能单蚁的信息量分布函数和相应的系统辨识求解算法,并在线性系统参数辨识的实 例仿真中得到了很好的结果,显示了蚁群算法在连续空间优化问题中的应用前景.最后,对蚁群 算法在连续空间优化领域中的适用特征作了总结,并指出了今后进一步工作的方向.     

一个新混沌系统的参数辨识

基于稳定性理论,对一个新混沌系统设计了合适的参数辨识观测器,并选择适当的未知参数初值,达到该系统所有参数能准确和快速的辨识,同时结合小波降噪法,提高参数的辨识精度．数值仿真结果表明了所设计的参数辨识观测器的有效性．     

基于强跟踪滤波器及小波变换的非线性系统参数辨识及应用

本文采用强跟踪滤波器为主要框架, 通过线性化和状态扩展解决非线性系统时变参数和状态的估计问题. 在普通强跟踪滤波器的基础上, 以小波变换估计量测噪声, 采用滤波增益调整系数解决过跟踪问题, 给出了主要的计算公式和参数的取值方法, Monte Carlo仿真和在弹道方程参数辨识中的应用结果表明, 本方法不但对突变参数具有强跟踪能力, 在噪声方差发生变化的情况下, 仍可以对非线性参数进行准确的辨识, 状态与参数估计精度高于 普通的强跟踪滤波器.     

一类反应扩散系统的参数辨识与反演方法

研究具有两个未知参数D和k的一类反应扩散系统的参数辨识与反演问题 .对其中未知系数函数D =D(x) ,采用时空有限元数值方法进行辨识 ,给出其数值逼近解Dh.将此常数数值逼近解Dh 作为控制参数 ,利用反演方法确定系统的另一个未知参数k .     

分布参数系统边界控制的Haar小波算法

由于分布参数系统通常由偏微分方程描述,采用解析法求解分布参数系统最优边界控制问题,是非常难以解决的.正交函数逼近的方法在分布参数系统控制方面,已经取得了较好的效果.Haar小波作为正交基函数,利用小波的一些运算及变换矩阵,将分布参数系统转化为集总参数系统,再求其逼近解.仿真示例验证了所提出的算法是非常有效的.该方法为分布参数系统的控制算法提出了一条新的解决方案.     

Reduction of distributed system identification complexity using intelligent sensors

The identification problems of distributed-parameter systems (DPS) is dealt with, A special method of data collection by using moving sensors is proposed. The sensors are ‘intelligent’ in the sense that they are able to track the positions of the exiremum values of a system state at each time instant. It is shown how to reduce the identification problem for DPS to that of identifying a certain system described by ordinary differential equations (ODE). The proposed approach is applicable to the DPS described by quasi-linear partial differential equations of the hyperbolic type. Attention is focused on the problem of reduction, while the identification of the resulting ODE is not considered in detail, since it is an easier task.     

Trajectory planning for quasilinear parabolic distributed parameter systems based on finite-difference semi-discretisations

In this contribution, a flatness-based approach is considered for the solution of the trajectory planning problem for quasilinear parabolic distributed parameter systems (DPS) by making use of finite-difference semi-discretisations. It is shown that the method yields solutions which are equivalent to results known from the infinite-dimensional trajectory planning for a certain class of quasi-linear parabolic DPS. Furthermore, the methodology being proposed can also be applied to systems with general analytic nonlinearities. As analytical convergence results are not available in this case, a numerical test criterion for the convergence behaviour is suggested.     

Distributed parameter system identification using finite element differential neural networks

Most of the previous work on identification involves systems described by ordinary differential equations (ODEs). Many industrial processes and physical phenomena, however, should be modeled using partial differential equations (PDEs) which offer both spatial and temporal distributions that are simply not available with ODE models. Systems described by a PDE belong to a class of system called distributed parameter system (DPS). This article presents a method for solving the problem of identification of uncertain DPSs using a differential neural network (DNN). The DPS, assumed to be described by a PDE, is approximated using the finite element method (FEM). The FEM discretizes the domain into a set of distributed and connected nodes, thereby, allowing a representation of the DPS in a finite number of ODEs. The proposed DNN follows the same interconnection structure of the FEM, thus allowing the DNN to identify the FEM approximation of the DPS in both 2D and 3D domains. Lyapunov's second method was used to derive adaptive learning laws for the proposed DNN structure. The identification algorithm, here developed in Nvidia's CUDA/C to reduce the execution time, runs mostly on the graphics processing unit (GPU). A physical experiment served to validate the 2D case. In the experiment, the DNN followed the trajectory of 57 markers that were placed on an undulating square piece of silk. The proposed DNN is compared against a method based on principal component analysis and an artificial neural network trained with group search optimization. In addition to the 2D case, a simulation validated the 3D case, where input data for the DNN was generated by solving a PDE with appropriate initial and boundary conditions over an unitary domain. Results show that the proposed FEM-based DNN approximates the dynamic behavior of both a real 2D and a simulated 3D system.     

按段多重契比雪夫多项式系及其在线性时变系统辨识中的应用

本文在块脉冲函数系和契比雪夫多项式系基础上定义了一种新的正交函数系--按段多 重契比雪夫多项式系,研究该函数系的主要性质和基本运算法则,得出了积分运算矩阵、乘积 运算矩阵和元素乘积运算矩阵,并用此函数系研究线性时变系统的参数辨识问题,获得了简 单、快速、高精度的递推辨识算法.数值例子计算结果表明,当采用如伪随机信号一类的充分 激励的函数作为被辨识系统的试验信号,本文提出的算法所得结果的精度和计算时间都比一 般正交契比雪夫多项式算法所得结果为好.     

An efficient method based on the second kind Chebyshev wavelets for solving variable-order fractional convection diffusion equations

In this paper, a class of variable-order fractional convection diffusion equations have been solved with assistance of the second kind Chebyshev wavelets operational matrix. The operational matrix of variable-order fractional derivative is derived for the second kind Chebyshev wavelets. By implementing the second kind Chebyshev wavelets functions and also the associated operational matrix, the considered equations will be reduced to the corresponding Sylvester equation, which can be solved by some appropriate iterative solvers. Also, the convergence analysis of the proposed numerical method to the exact solutions and error estimation are given. A variety of numerical examples are considered to show the efficiency and accuracy of the presented technique.