离散随机模型降阶的最小条件信息损失方法

针对随机系统的模型降阶问题,从分析离散线性随机状态方程模型中的条件信息描述机制入手,讨论了模型状态集聚过程中系统的平均条件信息损失.运用在模式识别领域中获得成功应用的最小信息损失准则得出了一种新的模型降阶信息论方法———基于状态集聚的最小条件信息损失方法,并讨论了降阶模型阶次的选择.分析表明,当原系统是渐近稳定时,由该方法得出的降阶模型也是渐近稳定的.该方法运用简单,仿真研究也表明由该方法得出的降阶模型具有良好的近似性能.     

基于最小信息损失准则的降阶LQG控制器设计

从信息论的角度出发,研究了LQG控制器降阶问题。在考察系统内部状态信息描述的基础上,提出了两种基于交叉格莱姆矩阵最小信息损失的LQG控制器降阶方法。将由这两种方法得出的降阶LQG控制器分别与全阶LQG控制器、基于最小K-L信息距离的降阶控制器进行仿真对比研究,比较各闭环系统的控制性能。仿真结果表明,提出的降阶控制器能较好地逼近全阶控制器实现闭环系统性能。     

几种模型降阶方法的仿真对比研究

算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考.利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界.最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小.仿真算例证明了最小二乘法较前两者具有优越性.     

基于希尔伯特-施密特范数和交叉格莱姆的模型降阶方法

摘要：分析了模型降阶的发展历程和研究现状,重点研究基于交叉格莱姆信息的模型降阶方法的范数意义的误差性能指标和算法.分析指出了信息类模型降阶方法的信息损失指标的局限性——不满足非负性和不是范数意义的指标.利用Hankel奇异值以及交叉格莱姆的信息属性推导出Hilbert-Schmidt范数与交叉格莱姆的关系,从而通过理论推理运算得出Hilbert-Schmidt范数意义的误差指标,并提出了相应的降阶方法.最后,给出一个数值算例,验证了Hilbert-Schmidt范数意义的误差指标的合理性以及算法的良好降阶效果     

带约束条件的张量积Bézier曲面最佳降多阶

为了交换和存储不同造型系统中的数据,提出一种张量积Bézier曲面带约束条件的一次降多阶算法.该算法在保角点高阶插值情形下,利用原曲面顶点数组的降维方法和最小二乘法给出了Bézier曲面的最佳降多阶逼近;在给定降阶曲面的4条边界曲线的情形下,利用最小二乘法,对原曲面减去降阶曲面的4条边界曲线后所得到的新曲面进行无约束最佳降阶逼近;将保边界插值的降阶方法应用于拼接曲面,所得到的降阶曲面为整体C0连续.数值实验和逼近理论表明,文中算法比其他算法的精度高、效率高.     

基于最佳平方逼近的B样条曲线降阶

提出了一种基于带约束的最佳平方逼近的B样条曲线降阶的方法.首先讨论了降阶后曲线控制顶点个数以及节点向量的取法、保端点的B样条曲线降阶方法,并把带约束的最佳平方逼近技术引入到B样条曲线的降阶,即误差大的区域施加较大的权函数以降低最大误差.为满足给定误差限制下的降阶,提出了对原曲线插入节点的准则,即对不满足误差限制的区域插入节点.并用实例对新方法和基于扰动约束技术的降阶方法进行了比较.     

基于模型降阶的分数阶系统动态性能研究

由于大多数分数阶系统阶次过高,使得系统的控制器设计变得非常困难,会造成系统控制精度变差且动态性能降低等不利因素,而模型降阶技术是解决这一问题的有效工具.首先简要介绍了H2范数模型降阶的一般方法,并提出一种新的降阶模型结构,可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统.仿真结果证明,采用改进型H2范数模型降阶方法不仅保持了原有分数阶模型系统的动态性能而且还提升了原有整数阶模型系统的动态性能.     

基于遗传算法的H∞系统降阶方法

提出了基于H∞范数的系统降阶准则,并且利用遗传算法实现了基于该准则的系统降阶.这一方法的提出避免了传统方法的缺点,降阶系统达到了非常理想的性能.通过例子表明,该降阶方法优于目前普遍使用的其它降阶方法.     

基于非对称Lanczos 算法的线性分数阶系统模型降阶方法

采用非对称Lanczos 算法研究线性分数阶系统的模型降阶问题, 提出一种保持系统传递函数一定数量的分数阶矩的模型降阶方法. 根据Caputo 导数的运算法则给出线性分数阶系统的分数阶矩的计算方法; 利用非对称Lanczos 算法构造对应的非对称三对角矩阵; 根据非对称三对角矩阵的性质证明降阶系统与原系统具有相同的一定数量的分数阶矩; 给出降阶系统与原系统传递函数的误差估计, 为合理选择降阶系统的阶次提供理论依据. 数值实例的计算结果验证了所提出方法的有效性.

     

基于系统矩阵实Schur分解的集结法模型降阶

通过有序实Schur分解将系统矩阵变成分块对角阵,得到一种数值稳定的集结法模型降 阶,并给出降阶的L∞-误差界.降价系统保留了原系统的主导极点且为最小实现.     

Reduced-order observer-based finite-time control for one-sided Lipschitz nonlinear switched singular systems

The reduced-order observer-based finite-time control problem for one-sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced-order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse-freeness, have a unique solution and finite-time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced-order observer-based controller. Further, the lower finite-time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system.     

Proper orthogonal decomposition and incompressible flow: An application to particle modeling

The proper orthogonal decomposition (POD) is a reduced-order modeling technique that is used to compactly represent unsteady flows. In this paper, we use the POD to capture the parametric variation of a flow with Reynolds number. We study incompressible, axisymmetric, steady flow over spherical particles at various Reynolds numbers in order to give an alternative to correlation-based approaches for predicting the drag on a sphere. In most previous applications of the POD for reduced-order modeling of incompressible flow, the POD modes typically have only described the velocity field; the pressure field was not directly modeled. Since we are interested in drag, which is dependent on the pressure, we formulate the method to directly include the pressure field of an incompressible flow. The POD modes are then derived from numerical flow solutions obtained using an hp-finite element method. A reduced-order model is created by performing a streamwise-upwind-Petrov-Galerkin (SUPG) projection of the incompressible Navier-Stokes equations onto the space spanned by the POD modes. The SUPG approach is taken because when pressure modes are included the Galerkin method fails to give unique solutions for incompressible flow. This is demonstrated for some simple test cases. An efficient numerical implementation is also developed using a Taylor expansion of the SUPG projection of the Navier-Stokes equations. Finally, values of drag are computed from the reduced-order model. Drag can be calculated to within 1.0% of the direct numerical simulations using only a small number of modes while still retaining all of the essential physics around the particle.     

Swarm intelligence algorithm for interconnect model order reduction with sub-block structure preserving

In this paper, we propose a generalised sub-block structure preservation interconnect model order reduction (MOR) technique based on the swarm intelligence method, that is, particle swarm optimisation (PSO). The swarm intelligence-based structure preservation MOR can be used for a standard model as a criterion for different structure preservation interconnect MOR methods. In the proposed technique, the PSO method is used for predicting the unknown elements of structure-preserving reduced-order modelling of interconnect circuits. The prediction is based on minimising the difference of transform function between the original full-order and desired reduced-order systems maintaining the full-order structure in the reduced-order model. The proposed swarm-intelligence-based structure-preserving MOR method is compared with published work on structure preservation MOR SPRIM techniques. Simulation and synthesis results verify the accuracy and validity of the new structure-preserving MOR technique.     

多标签学习中基于互信息的快速特征选择方法

针对传统的基于启发式搜索的多标记特征选择算法时间复杂度高的问题，提出一种简单快速的多标记特征选择（EF-MLFS）方法。首先使用互信息（MI）衡量每个维度的特征与每一维标记之间的相关性，然后将所得相关性相加并排序，最后按照总的相关性大小进行特征选择。将所提方法与六种现有的比较有代表性的多标记特征选择方法作对比，如最大依赖性最小冗余性（MDMR）算法和基于朴素贝叶斯的多标记特征选择（MLNB）方法等。实验结果表明，EF-MLFS方法进行特征选择并分类的结果在平均准确率、覆盖率、海明损失等常见的多标记分类评价指标上均达最优；该方法无需进行全局搜索，因此时间复杂度相较于MDMR、对偶多标记应用（PMU）等方法也有明显降低。     

互连线高效时域梯形差分模型降阶算法

为了进一步提高现有互连电路模型降阶方法的精度和效率,提出一种基于时域梯形法差分的互连线模型降阶方法.首先将互连电路的时域方程用梯形法差分离散后获得一种关于状态变量的递推关系,形成了一个非齐次Krylov子空间;然后利用非齐次Arnoldi算法求得非齐次Krylov子空间的正交基,再通过正交基对原始系统进行投影得到降阶系统.该算法可以保证时域差分后降阶系统和原始系统的状态变量在离散时间点的匹配,保证时域降阶精度,同时也保证了降阶过程的数值稳定性及降阶系统的无源性.与现有的时域模型降阶方法相比,文中算法可降低计算复杂度;与频域降阶方法相比,由于避免了时频域转换误差,其在时域具有更高的精度.     

Computer-aided methods for redesigning the stabilized pitch control system of a semi-active terminal homing missile

An unstable pitch control system of a terminal homing missile was formerly stabilized using a high order stabilization filter that was realized using active elements. A new dominant-data matching method is presented to redesign the high-order stabilization filter for obtaining reduced-order filters. As a result, the implementation cost is reduced and the reliability increased. An algebraic method is also applied to improve the performance of the redesigned pitch control system. In addition, the proposed dominant-data matching method can be applied to determine a reduced-order model of a high-order system. Unlike most existing model reduction methods, the reduced-order model has the exact assigned frequency-domain specifications of the original system. Computer-aided design methods can also be applied to design general control systems.     

具有单调性非线性项的非线性系统降维观测器设计

Based on the discussion about the existence and design method of full-order observer for systems with monotone nonlinearities, a reduced-order observer design method is developed under the assumption that a linear matrix inequality (LMI) has positive definite matrix solution and the reduced-order observer gain matrix is computed by the solution of LMI. By a linear transformation, a reduced-order observer which does not contain the information of the derivative of the system output is provided. A model is simulated and some conclusions are drawn based on the comparison of the results of reduced-order observer to that of full-order observer. The simulation shows that the design method developed by this paper has good performance.     

随机马尔可夫切换系统的H∞模型降阶

考虑一类带有时滞的不确定马尔可夫切换系统的H∞模型降阶问题.首先得到了一个矩阵不等式形式的充分条件,使该系统的H∞模型降阶问题对于满足条件的任意不确定性都是可解的;然后依据CCL(conecom plem entarity linearization)方法给出了该问题的求解算法,以及降阶模型的参数化方法.仿真算例说明该方法的有效性.