基于无味卡尔曼滤波的多雷达方位配准算法

将无味卡尔曼滤波（Unscented Kalman filter，UKF）应用于雷达配准，提出一种新的多雷达方位配准算法。在该算法中，目标的运动状态和方位误差由选定的采样点来近似，在每个更新过程中，采样点随着状态方程传播并随非线性测量方程变换，得到目标的运动状态和方位误差的均值，避免了对非线性方程的线性化，且具有较高的计算精度。与传统的扩展卡尔曼滤波（Extended Kalman filter，EKF）方法进行了仿真比较，结果表明UKF方法能有效地克服非线性跟踪问题中很容易出现的滤波发散问题，且估计精度高于UKF方法。     

反重力铸造装备的模糊建模与预测控制

工业中的反重力装备在铸造过程中具有时滞性、强非线性和时变性的特点,传统的控制算法难以达到满意的效果,由此提出了一种基于T-S模型的模糊预测控制方法.该方法根据T-S模型的描述来设计神经网络结构,利用误差反传算法离线辨识前件参数和后件参数,使用加权最小二乘递推方法进一步在线修正模型的后件参数,并将T-S模型转化为状态空间模型,使用丢番图方程推导出预测控制律.仿真结果表明此方法具有良好的动态特性.     

基于最大互信息和量子粒子群优化算法的医学图像配准研究*

研究了基于最大互信息的图像配准算法,在图像配准中引入了新的相似性测度,在分析具有量子行为的粒子群优化算法基础上,将量子粒子群算法作为优化策略用于图像配准并与Powell算法和PSO算法进行了仿真比较,对仿真结果进行了分析。     

基于RBF神经网络的直接广义预测控制

针对广义预测控制算法需要在线递推求解 Diophantine 方程及矩阵求逆等计算量大的缺陷,对参数未知多变量非线性系统提出一种径向基函数神经网络的直接广义预测控制算法.该算法将多变量非线性系统转化为多变量时变线性系统,用三次样条基函数逼近系统广义误差向量中的时变系数,然后利用径向基神经网络来逼近控制增量表达式,并基于广义误差估计值对控制器参数向量即网络权值向量θu和广义误差估计值中的未知向量θe进行自适应调整.仿真结果验证了此算法的有效性.     

非线性系统的RBF网络直接广义预测控制

针对广义预测控制(GPC)算法需要在线递推求解Diophantine方程及矩阵求逆等计算量大的缺陷,本文对参数未知非线性系统提出一种RBF网络的直接广义预测控制方法。该方法首先将非线性系统转化为时变线性系统,然后用三次样条基函数逼近系统广义误差中的时变系数,并基于广义误差估计值对控制器参数即网络权值和广义误差估计值中的未知向量进行自适应调整,然后利用RBF网络来逼近控制增量表达式。     

基于非线性薛定谔方程的时间序列去噪

针对噪声污染严重的时间序列,提出一种基于动态随机共振效应的去噪方法.通过具体分析非线性光学系统中的动态随机共振效应,推导出非线性薛定谔方程中的非线性扰动项,得到用于描述非线性系统中的信号传播模型,并应用于时间序列去噪.首先将归一化的时间序列信号输入模型系统,然后通过自适应粒子群优化算法确定系统传播方程中的各项参数,最后利用分步傅里叶方法求解传播方程的数值解,作为系统的输出.对于一些典型的时间序列信号,与现有的去噪方法相比,文中方法在信噪比上平均提高0.3～3.7 dB,在均方根误差上平均降低0.03～0.11,该方法在时间序列去噪上具有更好的效果.     

空基多平台多传感器时间空间数据配准与目标跟踪

研究多个空中移动平台的时间空间数据配准与目标跟踪问题.首先给出空中移动平台传感器数据空间配准几何坐标转换算法;然后采用最小二乘法对多传感器异步测量数据进行时间配准;最后将目标的运动模型和传感器配准误差模型组合在同一个状态方程中,利用扩展Kalman滤波方程进行估计.Monte-Carlo仿真表明,该方法能同时有效地估计目标运动状态和传感器配准误差,比传统配准方法具有更快的收敛速度和更高的精度.     

基于扩展KalIan滤波的空基多平台多传感器数据配准和目标跟踪算法

本文研究基于扩展Kalman滤波和多个空中移动平台的多传感器数据配准与目标跟踪问题.文中首先给出了空中移动平台传感器数据配准几何坐标转换算法;接着将目标运动模型和传感器配准误差模型组合在同一个状态方程中,然后利用扩展Kalman滤波方程进行估计.Monte-Carlo仿真表明,该方法能同时有效地估计目标运动状态和传感器配准误差.     

基于扩展Kalman滤波的空基多平台多传感器数据配准和目标跟踪算法

本文研究基于扩展Kalman滤波和多个空中移动平台的多传感器数据配准与目标跟踪问题.文中首先给出了空中移动平台传感器数据配准几何坐标转换算法;接着将目标运动模型和传感器配准误差模型组合在同一个状态方程中,然后利用扩展Kalman滤波方程进行估计.Monte-Carlo仿真表明,该方法能同时有效地估计目标运动状态和传感器配准误差.     

基于分片线性函数逼近的非线性观测器设计

综合分片线性函数模型辨识/逼近和鲁棒观测器设计方法,研究了一大类非线性鲁棒观测器设计方法.所提出的算法能有效解决非线性系统的辨识/建模问题,并保证在一定的逼近精度下观测误差可以控制在一定的范围内,且观测误差随着逼近精度的提高而减小.     

Two-grid methods for miscible displacement problem by Galerkin methods and mixed finite-element methods

The miscible displacement problem of one incompressible fluid is modelled by a nonlinear coupled system of two partial differential equations in porous media. One equation is elliptic form for the pressure and the other equation is parabolic form for the concentration of one of the fluids. In the paper, we present an efficient two-grid method for solving the miscible displacement problem by using mixed finite-element method for the approximation of the pressure equation and standard Galerkin method for concentration equation. We linearize the discretized equations based on the idea of Newton iteration in our methods, firstly, we solve an original nonlinear coupling problem on the coarse grid, then solve two linear systems on the fine grid. we obtain the error estimates for the two-grid algorithm, it is shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation. Moreover, numerical experimentation is given in this paper.     

Case studies on the application of the stable manifold approach for nonlinear optimal control design

This paper presents application results of a recently developed method for approximately solving the Hamilton–Jacobi equation in nonlinear control theory. The method is based on stable manifold theory and consists of a successive approximation algorithm which is suitable for computer calculations. Numerical approach for this algorithm is advantageous in that the computational complexity does not increase with respect to the accuracy of approximation and non-analytic nonlinearities such as saturation can be handled. First, the stable manifold approach for approximately solving the Hamilton–Jacobi equation is reviewed from the computational viewpoint and next, the detailed applications are reported for the problems such as swing up and stabilization of a 2-dimensional inverted pendulum (simulation), stabilization of systems with input saturation (simulation) and a (sub)optimal servo system design for magnetic levitation system (experiment).     

On efficient simulation of non-Newtonian flow in saturated porous media with a multigrid adaptive refinement solver

Flow of non-Newtonian fluid in saturated porous media can be described by the continuity equation and the generalized Darcy law. Here we discuss the efficient solution of the resulting second order nonlinear elliptic equation. The equation is discretized by the finite volume method on a cell-centered grid. Local adaptive refinement of the grid is introduced in order to reduce the number of unknowns. We develop a special implementation, that allows us to perform unstructured local refinement in conjunction with the finite volume discretization. Two residual based error indicators are exploited in the adaptive refinement criterion. Second order accurate discretization of the fluxes on the interfaces between refined and non-refined subdomains, as well as on the boundaries with Dirichlet boundary condition, are presented here as an essential part of an accurate and efficient algorithm. A nonlinear full approximation storage multigrid algorithm is developed especially for the above described composite (coarse plus locally refined) grid approach. In particular, second order approximation of the fluxes around interfaces is a result of a quadratic approximation of slave nodes in the multigrid-adaptive refinement (MG-AR) algorithm. Results from numerical solution of various academic and practice-induced problems are presented and the performance of the solver is discussed.     

基于小波分解的非线性系统多模型自适应控制

提出了一种改进的基于小波分解的非线性系统辨识算法,利用小波函数的逼近能力在线辨识被控对象的非线性项.针对基于小波分解的辨识算法缺乏预测能力,提出了根据线性鲁棒自适应控制器提供的当前控制信息预测未来的非线性项值新方法,并结合多模型方法,根据所定义的切换指标自动切换到当前最优控制器.仿真结果表明,改进的基于小波分解的辨识算法能够有效逼近非线性系统,基于小波分解的非线性系统多模型自适应控制方法改善了系统性能,随着系统运行跟踪误差明显减小,说明了该方法的有效性和可行性.     

Lanczos–Chebyshev pseudospectral methods for wave-propagation problems

The pseudospectral approach is a well-established method for studies of the wave propagation in various settings. In this paper, we report that the implementation of the pseudospectral approach can be simplified if power-series expansions are used. There is also an added advantage of an improved computational efficiency. We demonstrate how this approach can be implemented for two-dimensional (2D) models that may include material inhomogeneities. Physically relevant examples, taken from optics, are presented to show that, using collocations at Chebyshev points, the power-series approximation may give very accurate 2D soliton solutions of the nonlinear Schrödinger (NLS) equation. To find highly accurate numerical periodic solutions in models including periodic modulations of material parameters, a real-time evolution method (RTEM) is used. A variant of RTEM is applied to a system involving the copropagation of two pulses with different carrier frequencies, that cannot be easily solved by other existing methods.     

Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems

A problem of stabilisation of the randomly forced periodic and quasiperiodic modes for nonlinear dynamic systems is considered. For this problem solution, we propose a new theoretical approach to consider these modes as invariant manifolds of the stochastic differential equations with control. The aim of the control is to provide the exponential mean square (EMS) stability for these manifolds. A general method of the stabilisation based on the algebraic criterion of the EMS-stability is elaborated. A constructive technique for the design of the feedback regulators stabilising various types of oscillatory regimes is proposed. A detailed parametric analysis of the problem of the stabilisation for stochastically forced periodic and quasiperiodic modes is given. An illustrative example of stochastic Hopf system is included to demonstrate the effectiveness of the proposed technique.     

The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations

In this paper based on a system of Riccati equations with variable coefficients, we present a new Riccati equation with variable coefficients expansion method and its algorithm, which are direct and more powerful than the tanh-function method, sine-cosine method, the generalized hyperbolic-function method and the generalized Riccati equation with constant coefficient expansion method to construct more new exact solutions of nonlinear differential equations in mathematical physics. A pair of generalized Hamiltonian equations is chosen to illustrate our algorithm such that more families of new exact solutions are obtained which contain soliton-like solution and periodic solutions. This algorithm can also be applied to other nonlinear differential equations.     

Theoretical study of electronic transport through quasicrystalline nanotubes using mesh inflation approach

This work introduces the mesh inflation method to construct (dodecagonal) quasicrystalline shell structures, and investigates the properties and functions of quantum transport through quasiperiodic components, e.g. the nanotube device. We model the quantum dynamics of a system described by a nearest neighbor tight-binding formulism, and apply the non-equilibrium Green’s function technique to calculate the electronic transport properties, in which the non-equilibrium (transmitted) electronic density is self-consistently determined by solving Poisson’s equation in capacitive network modeling. Numerical results find that the transmission spectrum of the quasicrystalline nanotube illustrates crossover characteristics from local order (like in periodic lattices) to global disorder (like in amorphous solids) with varying energy. Moreover, the electronic transport properties of nanoprobes through multiple atomic channels follow the rule of Landauer’s formula.     

Finite Element Methods for a System of Dispersive Equations

The present study is concerned with the numerical approximation of periodic solutions of systems of Korteweg–de Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate two types of schemes that differ in their treatment of the third derivatives appearing in the system. One approach preserves a certain important invariant of the system, up to round-off error, while the other, somewhat more standard method introduces a measure of dissipation. For both methods, we prove convergence of a semi-discrete approximation and highlight differences in the basic assumptions required for each. Numerical experiments are also conducted with the aim of ascertaining the accuracy of the two schemes when integrations are made over long time intervals.