一般阻尼动力系统非奇异摄动法

借助矩阵摄动理论,将模态叠加法运用于一般阻尼矩阵的动力学方程求解结构的动响应是一种较为理想的方法.但当系统的外荷载激振频率接近于系统的固有频率时,直接将阻尼矩阵作为摄动矩阵,会使解产生奇异,并导致求解失败或误差过大,这是因为模态坐标下的动力学方程是无阻尼方程.为了解决这一问题,本文考虑在模态坐标的动力学方程中保留一定的阻尼.即将阻尼做分解,代入振动方程,得到不同阶次摄动方程,再将摄动方程变换到模态坐标,即采用非奇异摄动方法.最后通过数值算例,得到一阶、二阶摄动,将其与精确解进行比较.精度明显得到改善,基本趋于精确解.从而验证了本方法的精确性和有效性.     

两自由度非线性系统1:3内共振的渐近摄动分析

提出了一种改进的渐近摄动法,并用该方法研究了同时含平方项和立方项的两自由度非线性系统在1:3内共振情况下的非线性动力学行为.分别在平均方程和原方程的基础上得到了幅频响应曲线和分叉图,对比表明两种结果基本吻合.改进后的渐近摄动法比原有渐近摄动法更容易应用于1:3内共振情况.     

摄动离散Riccati方程解的上下界估计

讨论摄动离散Riccati方程正定解的估计问题。针对摄动参数满足范数有界不确定性情形,获得了正定解的上界和下界,且界的计算通过确定的离散Riccati方程的解给出,避免高阶代数方程的求解,同时得到基于Riccati方程的摄动离散系统稳定性分析的新方法,所给出的数值算例验证了方法的可行性。     

一类非线性奇异摄动系统的近似最优控制

针对一类非线性奇异摄动系统,基于自适应动态规划算法提出了一种新型的近似最优控制设计方法.该方法基于奇异摄动系统的快、慢Hamilton-Jacobi-Bellman(HJB)方程,从初始性能指标开始,通过神经网络的近似和控制律与性能指标的逐步更新迭代,最终收敛到最优的性能指标,而不用直接求解复杂的HJB方程.同时给出了...     

非线性末制导系统参数灵敏度分析

末制导系统参数随着飞行环境及飞行条件的改变而存在摄动,针对这一问题本文提出根据动态灵敏度来分析参数摄动对脱靶量的影响.基于伴随法推导出与系统动态方程相同规模的伴随方程,并通过一次伴随求解计算得到脱靶量对所有可调参数及摄动参数的动态灵敏度,有效的提高了计算效率.传统的直接分析法是将系统状态变量直接对参数变量进行微分,需要对每个参数变量求解一组代数或微分方程,对于状态变量及参数变量较多的情况效率较低.本文基于两种方法对末制导系统的参数灵敏度进行分析,分析结果揭示了参数摄动对脱靶量的影响程度,较小的参数灵敏度为提高系统的鲁棒性提供了依据.     

面向复用的航天器轨道计算仿真分析

研究航天器轨道计算,提高精度,航天器轨道摄动方程中的模型复用性差,精度不高.为解决上述问题,改进了利用四阶龙格-库塔法求解三维二阶常微分方程组的过程,使仿真程序更易于实现和移植.采用改进的算法进行航天器轨道摄动方程的积分运算,求解出实时的航天器三维位置和速度进而算出星下点经纬度,分析了仿真的时间开销.仿真结果表明,长期的航天器运行仿真需要考虑摄动的影响,推导的四阶龙格-库塔法具有较好的可复用性,能方便地用于航天器轨道仿真中,满足仿真的精度和实时性要求.     

非线性末制导系统参数灵敏度分析（英文）

末制导系统参数随着飞行环境及飞行条件的改变而存在摄动,针对这一问题本文提出根据动态灵敏度来分析参数摄动对脱靶量的影响.基于伴随法推导出与系统动态方程相同规模的伴随方程,并通过一次伴随求解计算得到脱靶量对所有可调参数及摄动参数的动态灵敏度,有效的提高了计算效率.传统的直接分析法是将系统状态变量直接对参数变量进行微分,需要对每个参数变量求解一组代数或微分方程,对于状态变量及参数变量较多的情况效率较低.本文基于两种方法对末制导系统的参数灵敏度进行分析,分析结果揭示了参数摄动对脱靶量的影响程度,较小的参数灵敏度为提高系统的鲁棒性提供了依据.     

车桥耦合振动的摄动分析方法

基于结构摄动理论,推导车桥耦合动力系统的摄动方程,将原有的车桥耦合动力方程变成一组车辆和桥梁之间不相互耦合的方程组,实现车辆与桥梁的之间的解耦．理论上基于摄动分析方法进行严格推导,以简支梁为例,采用1／4车辆模型,验证了方法的可靠性．提出了该方法在大型有限元软件中的应用方法．     

船舶航向非线性H∞逆优化输出反馈控制

为抑制船舶航向非线性优化控制中模型参数摄动和由状态观测器引入的不确定观测误差,提出了一种非线性H∞逆优化控制算法.首先,基于无源理论设计观测器以实现海浪滤波,该观测器无需海浪扰动的方差信息从而减少了观测器参数数量.然后,考虑模型参数摄动对观测误差的影响,给出了描述系统局部(全局)性态的局部(全局)H∞优化性能指标.在以广义黎卡提方程(GARE)对局部优化问题的求解的基础上,应用逆优化方法将全局H∞优化问题转化为构造闭环系统的Lyapunov函数问题,得到同时满足两种指标的优化控制器,并证明了稳定性.仿真结果证明了该算法的有效性.     

轨道摄动对航天器角动量管理的影响和补偿

三轴主惯量接近的航天器长期在轨采用惯性系的角动量管理,使用垂直于轨道面的某一主惯性轴为Y轴,建立参考的惯性系进行控制器设计,轨道摄动使轨道长周期项与时间呈近似线性关系,导致控制器输出线性累加.针对此问题,分析轨道摄动导致控制律失效的原因,参考内模原理扩维方程,重新设计最优控制方法进行惯性系的角动量管理.通过半物理仿真表明了摄动补偿方法的可行性,且角动量和姿态长期稳定性均优于补偿前.     

摄动离散矩阵Lyapunov方程解的估计

研究摄动离散矩阵Lyapunov方程解的估计问题,利用矩阵运算性质及Lyapunov稳定性理论,给出在结构不确定性假设下方程解的存在条件及解的上下界估计,估计结果由一个线性矩阵不等式(LMI)和两个矩阵代数Riccati方程确定．针对几种不确定性假设,进一步给出矩阵代数Riccati方程的具体形式．最后通过一个算例说明了所得结果的有效性．     

基于动态补偿的线性系统最优干扰抑制

本文针对受外部干扰的线性时不变系统研究了基于动态补偿的最优干扰抑制问题,其中干扰信号为已知动态特性的扰动信号.首先,将原系统与扰动系统联立构成增广系统,进而转化为无扰动的标准线性二次最优问题.其次,给出了经具有适当动态阶的补偿器补偿后的闭环系统渐近稳定并且相关的Lyapunov方程正定对称解存在的条件,进一步给定的二次性能指标可写成一个与该解和闭环系统初值相关的表达式.为了得到系统的最优解,将该Lyapunov方程转化为一个双线性矩阵不等式形式,并给出了相应的路径跟踪算法以求得性能指标最小值以及补偿器参数.最后,通过数值算例说明应用本文方法可以不仅能够最小化线性二次指标,而且能够使得系统的干扰得到抑制.     

切换系统输出反馈镇定的特征结构配置方法

考虑由单输入--单输出线性子系统构成的切换系统, 通过解析方法设计输出反馈控制, 使闭环子系统具有公共二次Lyapunov函数. 基于可解Lie代数条件及广义Sylvester方程的通解, 利用特征结构配置方法建立了反馈控制的存在性准则, 并由此给出了控制器的设计形式. 仿真算例实现了设计过程并验证了方法的有效性.     

On the Lyapunov matrix differential equation

A lower bound for the determinant of the solution to the Lyapunov matrix differential equation is derived. It is shown that this bound is obtained as a solution to a simple scalar differential equation. In the limiting case where the solution to the Lyapunov differential equation becomes stationary, the result reduces to one of the existing bounds for the algebraic equation.     

广义系统具有正定解的Lyapunov方程

本文研究线性广义系统有正定解的Lyapunov方程，给出广义系统稳定等价于Lyapunov方程有正定解，进一步研究了广义系统R－能观，稳定和Lyapunov方程存在正定解三者之间的关系。基于该Lyapunov方程，给出广义系统允许（正则，稳定，无脉冲）的等价条件。     

Stabilization of stochastic nonlinear systems driven by noise ofunknown covariance

This paper poses and solves a new problem of stochastic (nonlinear) disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise. This is a natural stochastic counterpart of the problem of input-to-state stabilization in the sense of Sontag (1989). Our development starts with a set of new global stochastic Lyapunov theorems. For an exemplary class of stochastic strict-feedback systems with vanishing nonlinearities, where the equilibrium is preserved in the presence of noise, we develop an adaptive stabilization scheme (based on tuning functions) that requires no a priori knowledge of a bound on the covariance. Next, we introduce a control Lyapunov function formula for stochastic disturbance attenuation. Finally, we address optimality and solve a differential game problem with the control and the noise covariance as opposing players; for strict-feedback systems the resulting Isaacs equation has a closed-form solution     

Learning and convergence analysis of neural-type structurednetworks

A class of feedforward neural networks, structured networks, has recently been introduced as a method for solving matrix algebra problems in an inherently parallel formulation. A convergence analysis for the training of structured networks is presented. Since the learning techniques used in structured networks are also employed in the training of neural networks, the issue of convergence is discussed not only from a numerical algebra perspective but also as a means of deriving insight into connectionist learning. Bounds on the learning rate are developed under which exponential convergence of the weights to their correct values is proved for a class of matrix algebra problems that includes linear equation solving, matrix inversion, and Lyapunov equation solving. For a special class of problems, the orthogonalized back-propagation algorithm, an optimal recursive update law for minimizing a least-squares cost functional, is introduced. It guarantees exact convergence in one epoch. Several learning issues are investigated.     

The Lyapunov approach to boundary stabilization of an anti‐stable one‐dimensional wave equation with boundary disturbance

In this paper, we are concerned with the boundary stabilization of a one‐dimensional anti‐stable wave equation with the boundary external disturbance. The backstepping method is first applied to transform the anti‐stability from the free end to the control end. A variable structure feedback stabilizing controller is designed by the Lyapunov function approach. It is shown that the resulting closed‐loop system is associated with a nonlinear semigroup and is asymptotically stable. In addition, we show that this controller is robust to the external disturbance in the sense that the vibrating energy of the closed‐loop system is also convergent to zero as time goes to infinity in the presence of bounded deterministic disturbance at the control end. The existence and uniqueness of the solution are also developed by the Galerkin approximation scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Matrix bounds of the discrete ARE solution

This paper provides new lower and upper matrix bounds of the solution to the discrete algebraic Riccati equation. The lower bound always works if the solution exists. The upper bounds are presented in terms of the solution of the discrete Lyapunov equation and its upper matrix bound. The upper bounds are always calculated if the solution of the Lyapunov equation exists. A numerical example shows that the new bounds are tighter than previous results in many cases.     

基于收缩反步的不确定机械臂轨迹跟踪控制

针对不确定机械臂系统的轨迹跟踪控制问题,基于干扰观测器原理,提出了一种收缩反步控制算法.首先,采用非线性观测器对系统的模型不确定项和未知外部干扰部分进行观测.然后,使用收缩反步控制求解出控制输入力矩,从而实现对参考轨迹的精确跟踪,并分析二阶闭环系统的增量稳定性和Lyapunov方程解的原点指数稳定性.最后,将上述所提控制律应用于2-DOF机械臂,通过收缩反步与滑模控制的对比仿真,证明其有效性.