非高斯列维噪声激励下非线性系统的Lyapunov指数

研究了非高斯列维噪声作用下非线性系统的渐近线性化方法和Lyapunov指数.利用渐近线性化方法将非线性系统线性化,通过系统的响应轨迹验证了该方法的有效性.通过广义的伊藤法则公式,推导出了列维噪声驱动下Lyapunov指数的一般表达式.给出当参数变化时,非线性系统的随机稳定性分析.     

Optimal robot‐environment interaction using inverse differential Riccati equation

An optimal robot‐environment interaction is designed by transforming an environment model into an optimal control problem. In the optimal control, the inverse differential Riccati equation is introduced as a fixed‐end‐point closed‐loop optimal control over a specific time interval. Then, the environment model, including interaction force, is formulated in a state equation, and the optimal trajectory is determined by minimizing a cost function. Position control is proposed, and the stability of the closed‐loop system is investigated using the Lyapunov direct method. Finally, theoretical developments are verified through numerical simulation.     

Experiment and numerical simulation of chaotic mixing performance enhanced by perturbed rigid-flexible impeller in stirred tank

To eliminate the isolated mixing regions in the stirred tank, factors associated with chaotic mixing performance were studied, including flow field structure and fluid velocity of rigid RT impeller (R-RT), perturbed rigid RT impeller (PR-RT) and perturbed rigid-flexible RT impeller (PRF-RT). The maximum Lyapunov exponent (LLE) and multi-scale entropy (MSE) were calculated by using Matlab software programming, and the differences in flow field structure and fluid velocity of the three blade systems were studied through computational fluid mechanics. The experimental and computational results showed that perturbed rigid-flexible RT impeller could destroy the boundary of the mesostatic flow field in the isolated mixing regions and the symmetry flow in the process of fluid mixing through the random disturbance of the flexible blade, eliminating the isolated mixing regions. At 90 r/min, the LLE of the perturbed rigid-flexible RT impeller is larger than that of rigid RT impeller and perturbed rigid RT impeller. The LLE of the rigid-flexible RT impeller compared with the rigid RT impeller and perturbed rigid RT impeller increases 13.29% and 7.25% respectively and the MSE of the perturbed rigid-flexible RT impeller is also larger than that of rigid RT impeller and perturbed rigid RT impeller. The perturbed rigid-flexible RT impeller enhances the flow field instability, forms an asymmetric flow field structure, and reduces the distribution range of isolated mixing regions. The perturbed rigid-flexible RT impeller enhances the energy dissipation of the blade, improves the fluid velocity at the bottom and top of the tank and the wall of the tank, and reduces the mixing time.     

基于观测器中立系统的时滞相关稳定性

研究了一类中立系统的稳定性问题,设计一个基于观测器的状态反馈器。采用描述器方法,利用Lypunov函数,不对V函数的导数放犬,而是引用一些恰当的0项,通过解两个LMI,获得了误差系统和原系统的时滞相关稳定性的充分条件。同时解决了系统增益问题。最后一个数值例子说明了设计方法的有效性和可行性。     

短群签名的高效批验证

进入普适通信的时代,从车辆到心脏监听器等大量设备都需要与它们的环境彼此交流信息,从而对验证和安全通信的要求不断上升：①密码费用较低;②能够快速验证大量不同来源的消息;③隐私保护。文章针对一个高效的短群签名体制提出了一个批验证算法,其中验证运算的主要部分只需要2个双线性对,就可满足上面的全部3个要求。     

红外小目标小波多尺度相关检测方法

提出一种基于小波多尺度相关的目标检测方法.该方法通过二进小波对图像进行多尺度分析;利用边缘和噪声具有不同的Lipschitz指数造成它们的小波变换模在不同尺度下的不同传播特性,根据小波变换尺度相关性计算相邻大尺度模相关量用来增强信号,抑制噪声,提取粗略边缘图;并结合小尺度检测,具有定位精确的特点,将粗略边缘图与小尺度模图相与,寻找模极大值点,得到最终的检测结果.实验结果表明,该方法较传统的小波多尺度边缘检测方法能更加有效地进行红外小目标检测.     

Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm

This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices. We choose the geodesic distance between -AHX - XA and P as the cost function, and put forward the Extended Hamiltonian algorithm (EHA) and Natural gradient algorithm (NGA) for the solution. Finally, several numerical experiments give you an idea about the effectiveness of the proposed algorithms. We also show the comparison between these two algorithms EHA and NGA. Obtained results are provided and analyzed graphically. We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm, whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm (NGA) as compared to Extended Hamiltonian Algorithm (EHA). The aim of this paper is to show that the Extended Hamiltonian algorithm (EHA) has superior convergence properties as compared to Natural gradient algorithm (NGA). Upto the best of author’s knowledge, no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.     

三波耦合非线性动力学行为的分析与计算

本文从Lyapunov指数、吸引子、时间序列及其功率谱等几方面对三波耦合的非线性行为进行了详细地分析与计算.指出随着正则线性频率和衰减系数在某些范围内变化,系统分别处于周期态和混沌态,并从倍周期进入混沌,或从混沌进入周期态.     

自主移动机器人的轨迹误差补偿方法

自主移动机器人现有轨迹控制器结构复杂且控制不稳定,本文设计出一种结构简洁且快速收敛的线性化轨迹误差补偿方法。首先将自主移动机器人在全局坐标系下X和Y方向的轨迹误差转换到局部坐标系下,然后得到切向误差、法向误差以及角度误差,最终设计线性化轨迹误差补偿方法,计算出两个驱动轮的运动补偿量。基于李雅普诺夫稳定判据,在该控制模型下整个线性化系统是渐进稳定且收敛的。实际试验测试证实基于所提出的轨迹误差补偿方法,自主移动机器人的运动精度能稳定控制在±5 mm之内。     

On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations

In this note we describe the maximal and the minimal values of Lyapunov exponents for second-order discrete time-invariant linear system perturbed by time-varying bounded perturbations. An interpretation of the results in terms of generalized spectral radius is given. An application of obtained formulas to the robust stability problem is demonstrated on a numerical example.