多自由度非线性振动系统的多频分叉

本文研究自治和非自治多目由度非线性振动系统当其线化系统有多个特征值同时经过虚轴时产生的多频分叉问题,提出了用于分析多频分叉问题的平均摄动解法,得到了在共振和非共振情形的多频分叉渐近摄动解和稳定性判据,我们还将本文方法用在分析机车轮对动力系统的Hopf分叉中和Van der PolDuffing耦合非线性振子的双频分叉中。     

随机窄带噪声作用下非线性碰撞振动系统的稳态响应研究

研究了随机参激作用下一个非线性碰撞振动系统的随机响应.基于Krylov-Bogoliubov平均法,借助第一类改进的Bessel函数,得到了决定平凡解的几乎确定稳定性的最大Lyapunov指数.模拟结果发现,碰撞振动系统的最大Lyapunov指数特性不同于一般的非碰撞系统,其最小值为负.同时,在确定性情形下,得到了骨架曲线方程和不稳定区域的临界方程.进一步,利用矩方法,讨论了系统的一阶和二阶非平凡稳态矩,发现了碰撞振动系统中有频率岛现象的存在.最后,借助FokkerPlanck-Kolmogorov方程,利用有限差分法,讨论了碰撞振动系统中存在的随机跳现象.在随机强度较小时,稳态概率密度集中于响应振幅的非平凡分支;但是随着随机强度的增加,平凡稳态解的概率会变大.     

W-模型辨识及其统计特性

本文选用三位式伪随机序列作为输入 ,充分利用其激励信号的各种特性 ,辨识非线性系统 Wiener模型的线性子系统脉冲响应函数 ,对非线性增益环节 ,则由其奇数和偶数项多项式系数分别进行估计 .同时研究线性与非线性子系统辨识的统计特性 ,给出各部分参数估计的置信区间 .     

基于神经网络的一类非仿射非线性系统自适应控制

针对一类带有不确定性的非仿射非线性系统,利用Backstepping设计方法,设计了一种神经网络自适应控制器．该控制器可以实现跟踪特性．基于Lyapunov函数,得出稳定的权学习算法．并利用Lyapunov稳定性理论证明了闭环系统是一致最终有界的．仿真结果表明,这种控制器具有良好的鲁棒性和跟踪特性．     

基于观测器的非严格反馈时滞非线性系统的神经网络自适应控制

针对一类非严格反馈的时滞非线性系统, 研究了一类基于观测器的自适应神经网络控制问题.针对系统中存在未知状态变量的问题, 设计了一个状态观测器.利用反步法和径向基神经网络的逼近特性, 提出了一种自适应神经网络输出反馈控制方法.所设计的控制器保证了闭环系统中所有信号的半全局一致有界性.最后, 通过仿真验证了所提控制方法的有效性.     

几类非线性系统对白噪声参激与／或外激平稳响应的精确解

用福克-普朗克-柯尔莫哥洛夫方程方法构造了一类二阶、三类高阶非线性系统对白噪声参激与/或外激的平稳响应的精确解.讨论了解的存在与唯一性及解的性态.所考虑的系统的共同特点是非保守力依赖于相应保守系统的首次积分,因此可称为广义能量依赖系统.文中指出,对每个广义能量依赖系统,存在一族与之随机等价的非广义能量依赖系统,它们有相同的平稳概率密度.并指出对一给定广义能量依赖系统,如何找到其等价随机系统.作为例子,给出了二阶广义能量依赖随机系统的等价随机系统.最后指出并用例子说明,许多非广义能量依赖非线性随机系统的精确平稳解可通过寻求其等价广义能量依赖系统而找到.     

Gauss白噪声激励下分数阶导数系统的非平稳响应

研究了Gauss(高斯)白噪声激励下具有分数阶导数阻尼的非线性随机动力系统的非平稳响应.应用等价线性化方法将非线性系统转化为等价的线性系统,之后采用随机平均法获得系统响应满足的FPK(Fokker-Planck-Kolmogorov)方程,其中分数阶导数近似为一个周期函数.使用Galerkin方法求解FPK方程进而得到系统的近似非平稳响应.数值结果验证了方法的正确性和有效性.     

一类非最小相位非线性系统的鲁棒输出调节

研究了一类具有非最小相位和非线性外部系统的非线性系统的全局鲁棒输出调节问题.首先,利用浸入系统设计了一个非线性内模.其次,把原系统的全局鲁棒输出调节问题转化为增广系统的全局鲁棒镇定问题.然后,利用改变能量函数和动态增益技巧设计了一个状态反馈控制器,使得闭环系统的解有界并且跟踪误差渐近趋于零.最后,利用仿真结果验证了所设计的控制器的有效性.     

切换多项式非线性系统的输入-状态稳定性

利用耗散不等式研究了切换多项式非线性系统的输入-状态稳定性分析问题,在任意切换信号下,给出了使得切换多项式非线性系统输入-状态稳定的充分条件.采用平方和分解方法来寻找切换多项式非线性系统的输入-状态稳定共同Lyapunov函数.数值算例验证了所提方法的可行性.     

具有奇异非线性项的抛物系统的非同时熄灭与同时熄灭[英文]

本文研究具有奇异非线性项的一维拟线性抛物系统解的熄灭性质. 首先, 利用标准正则化方法得到该系统弱解的局部存在性. 然后对解的同时熄灭和非同时熄灭进行区分, 并按照熄灭速率参数进行了详细分类.     

平稳随机过程的小波分析方法

利用小波变换对平稳随机过程进行了谱分析,在小波变换的基础上给出了平稳随机过程的时—频功率谱及联合平稳随机过程的时—频互功率谱的概念,并详尽地研究了它们所具有的性质及与传统功率谱的关系。     

On the numerical determination of optimal inputs

The design of optimal inputs for linear and nonlinear system identification involves the maximization of a quadratic performance index subject to an input energy constraint. In the classical approach, a Lagrange multiplier is introduced whose value is an unknown constant. In recent papers, the Lagrange multiplier has been determined by plotting a curve of the Lagrange multiplier as a function of the critical interval length or a curve of input energy versus the interval length. A new approach is presented in this paper in which the Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimal input. Numerical results are given for both a linear and a nonlinear dynamic system.     

Controller design for stabilizing bilinear systems with state-based switching

Some nonlinear systems can be approximated by switching bilinear systems. In this paper, we proposed a method to design state-based stabilizing controller for switching bilinear systems. Based on the similarity between switching bilinear systems and switching linear systems, corresponding switching linear systems are obtained for switching bilinear systems by applying state-based feedback control laws. Instead, we consider asymptotically stabilizing the corresponding switching linear system through solving a number of relaxed LMI conditions. Stabilizing controllers for switching bilinear systems can be derived based on the results of the corresponding switching linear systems. The stability of the controller is proved step by step through the decreasing of the multiple Lyapunov functions along the state trajectory. The effectiveness of the method is demonstrated by both a theoretical example and an example of urban traffic network with traffic signals.     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

以函数为参量的间歇发酵非线性动力系统及其辨识

建立以连续分段线性函数为参量的间歇发酵非线性动力系统,证明该动力系统的主要性质及解的存在性.以实验数据拟合得到的光滑曲线为依据,提出了连续分段线性函数为优化变量的辨识模型,论述可辨识性.依状态变量与辨识函数的相关性,构造求解辨识模型的优化算法,并给出优化算法的收敛性分析及数值结果.     

非线性系统周期解不动点迭代法

本文提出一种求解非线性系统周期解的数值方法。首先对非线性自治系统和非自治系统给出不同的点映射定义。其次指出用线性映射逼近原非线性映射,而线性映射是由非线性映射插值获得的。继而求取线性映射的不动点,作为原系统不动点的近似解。如不满足精度则作为下次映射的初始点。本文还提出了研究周期解稳定性的相应方法。     

A Simulation-free Nonlinear Model Order-reduction Approach and Comparison Study

In this paper, a new approach to the model order reduction of nonlinear systems is presented. This approach does not need a simulation of the original system, and therefore, it is suitable for large systems. By separating the linear and nonlinear parts of the original nonlinear model, the idea is to consider the nonlinearities of the resulting system as additional inputs. Based on the linear system from the last step, a known order-reduction method can be applied to find the coefficients of the nonlinear and the linear parts of a reduced-order model. Two different methods from linear-order reduction (balancing and truncation and Eitelberg's method with some modification) are used for this purpose, and their advantages and disadvantages are discussed. For comparison with some known methods in order reduction of nonlinear systems, three other methods are discussed briefly. Finally, a technical nonlinear system is reduced, and different methods are compared.     

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We propose a new estimation method for the parameters of a partial functional linear model when the parameter curve is subject to monotone constraint. The proposed estimators are implemented under the nonlinear mixed effects model framework. The small sample properties are illustrated through a simulation experiment.     

A note on a conjecture for the critical curve of a weakly coupled system of semilinear wave equations with scale-invariant lower order terms

In this note, two blow-up results are proved for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms both in the subcritical case and in the critical case when the damping and the mass terms make both equations in some sense “wave-like.” In the proof of the subcritical case, an iteration argument is used. This approach is based on a coupled system of nonlinear ordinary integral inequalities and lower bound estimates for the spatial integral of the nonlinearities. In the critical case, we employ a test function-type method that has been developed recently by Ikeda-Sobajima-Wakasa and relies strongly on a family of certain self-similar solutions of the adjoint linear equation. Therefore, as critical curve in the p−q plane of the exponents of the power nonlinearities for this weakly coupled system, we conjecture a shift of the critical curve for the corresponding weakly coupled system of semilinear wave equations.     

A Probe Method of Gradient Projection Type

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