一个干摩擦Duffing振子的滑动分岔分析

分析了一个干摩擦Duffing振子在不同参数下混沌和周期轨及不同周期轨之间的共存与转换.干摩擦振子属于Filippov系统,会发生特有的粘滞现象.分析发现,从穿越轨线转换到粘滞--滑移轨线不仅可经穿越滑动分岔和切换滑动分岔实现,也可经两个相邻的穿越滑动分岔和多滑动分岔实现,而从粘滞-滑移轨线转换到非穿越轨线须经擦边滑动...     

一类几何非线性干摩擦振子的分岔研究

考虑了一个几何非线性干摩擦振子.介绍了如何利用事件驱动方法模拟该类具有不连续矢量场的Filippov系统,所介绍的算法是基于Filippov方法的扩展,从而可以精确地检测出滑动运动区域的入口和出口.用了两种不同的Poincaré截面,表示了随参数变化,不同类型含滑动过程的周期运动之间的转化过程,研究了不同类型的滑动分岔和周期倍化分岔,并发现了在倍化过程中多滑动段的存在.     

欠驱动两杆机器人的统一控制策略和全局稳定性分析

针对包括 Acrobot 和 Pendubot 在内的欠驱动两杆机器人, 提出了一种统一的运动控制策略. 欠驱动两杆机器人的整个运动空间分为两个区域: 摇起区和平衡区, 并对这两个区域分别设计控制律. 首先, 在摇起区, 应用一种基于弱控制 Lyapunov 函数 (Weak-control Lyapunov function, WCLF) 的控制方法, 来增加系统能量和控制驱动杆的姿势. 其次, 为了避免奇异值的出现, 选择弱控制 Lyapunov 函数中的一个参数为系统状态空间的非线性函数. 然后, 通过系统状态调节基于弱控制 Lyapunov 函数的控制律中的另一个设计参数, 来改进系统控制效果. 使用弱控制 Lyapunov 设计的摇起区控制律, 可基于最大不变集原理保证其稳定性; 而机器人离开摇起区后, 利用非光滑 Lyapunov 函数 (Non-smooth Lyapunov function, NSLF) 来保证其稳定. 最后, 结合 WCLF 和 NSLF 保证了控制系统的全局稳定.     

基于自稳定域和相依锥判据的一类二阶不确定系统的控制设计

针对一类二阶不确定系统,构造了以线性Lipschitz曲面作为边界的自稳定域,并依此设计控制律,利用Filippov解与空间非光滑曲面的相依锥判据,证明在该控制律的作用下系统轨迹将在有限时间到达所设计的自稳定域边界并进入其内部,从而系统轨迹将收敛到原点.所得结果放宽了对自稳定域边界光滑性的要求,提高了设计的灵活性.仿真结果验证了设计的正确性和有效性.     

双悬臂梁在简谐力作用下的碰撞动力学分析

对带集中端质量柔性悬臂梁进行了理论建模,在此基础上得到了双悬臂梁碰撞模型.通过对简谐激励力作用下悬臂梁碰撞运动的理论分析和实验论证,得到了该动力系统中被碰撞悬臂梁k=p/1型周期碰撞运动,典型的周期碰撞有k= 1/1,k=1/2,k=2/2等.此外,建立了该动力系统碰撞情况下的Poincare映射,运用半解析法得到了该...     

分析动力学三个问题的研究进展

分析力学的发展涉及理论的和应用的诸多方面.本文在分析力学与数学交缘的三个问题上综述分析力学的近代发展.第一是利用Lie群和Lie代数的一些成果来研究分析动力学方程的积分问题.第二是将分析力学的经典和近代积分方法应用于一般微分方程的积分问题.第三是将分析动力学方程在一定条件下化成梯度系统的方程,再用梯度系统的性质来研究力学系统的动力学行为.     

压缩矢量图形的两个算法的比较和分析

文章在介绍矢量图形压缩的意义后,分别介绍了矢量图形压缩的分治算法和线性算法,并对这两个算法进行了分析和比较。在选取适当的控制数据压缩的阈值后,分治算法和线性算法的压缩效果接近,但线性算法所需存储空间比分治算法的少,而且线性算法的时间复杂度从分治算法的O(nlogn)降低到O(n)。     

用好两个技术——WLAN和千兆的网络建设实例分析

国前,WLAN和千兆成为网络建设中采用最为普及的两项技术,前者将灵活、方便这一核心竞争力充分发挥,成为不适合布线的用户“必然的选择”;后者以平滑升级、保护投资为最大卖点,赢得了广大以太网用户“继续的选择”。     

两个标准模型下可证明安全的代理签名方案分析和改进

对最近冀会芳等学者和于义科等学者提出的基于Waters的两个标准模型下可证明安全的代理签名方案进行了安全分析,指出了这两个方案中存在的不足和缺陷,即存在授权伪造,任何人可以伪装成原始签名者向代理签名者发出有效的代理授权证书;存在代理签名伪造,任何人在不知道代理签名密钥的情况下,可伪造代理签名者的签名。提出了一个能克服缺陷的、改进的代理签名方案,并对改进方案的正确性、有效性和安全性进行了详细分析。分析显示,与两个原方案相比,改进的方案具有同样的签名长度、几乎一样的执行效率,但是更加安全。     

Two-stop-two-slip motions of a dry friction oscillator

This paper presents the investigation on the two-stop-two-slip (TSTS) motions in a dry friction oscillator.Friction is a kind of dissipated force.Simple dry friction oscillator implies complicated stick-slip motions.Due to its nonlinear non-smooth characters,it is difficult to analyze the stick-slip motions.First,TSTS motion is analyzed in this paper.A closed form solution of the TSTS motions is presented.In addition,parameter domain for the motion is studied.In general,there are no explicit solutions to tr...     

一个粘弹性振子的动力学与控制

本文详细分析了一个具有粘弹性项的非线性振子的动力学与控制.首先研究了系统平衡点的稳定性,表明系统存在复杂的无界动力学行为.然后引入时滞速度反馈对这个不稳定系统进行控制.研究结果表明速度反馈控制能镇定此不稳定的粘弹性系统.适当的选择控制增益和控制时滞,控制系统有稳定的平衡点,由Hopf分岔产生的周期解,拟周期解,并能展现出复杂的混沌解.数值模拟验证了结论的正确性.     

一类双悬臂含间隙振动系统的混沌控制策略研究

由于一类双悬臂含间隙振动系统具有典型非光滑特性和有明显的非线性,这直接导致了系统发生分叉与混沌现象的可能性.为此针对该系统的混沌现象,利用基于能量的开环控制策略,构造有界控制器对混沌行为进行控制,混沌运动可被引导到稳定的目标周期轨道,并对控制的收敛速度进行分析,数值模拟结果表明了该控制策略的有效性与可行性,可为碰振系统的优化设计,振动控制和安全运行提供了理论参考.     

Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation

The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol s...     

Complex instabilities near codimension-2 bifurcation and torus breakdown in a Cuk converter with an inductive impedance load

Power switching converters exhibit a wide range of nonlinear behavior, such as bifurcation and chaos. Complex instabilities near the codimension-2 bifurcation point are shown in some nonlinear higher order systems. In this study, codimension-2 bifurcation and complex instabilities in a single inner current loop controlled Cuk converter with an inductive impedance load are analyzed by studying the Floquet multipliers and switching modes of the system. The periodl orbit loses its stability by period-doubling and subcritical Neimark- Sacker bifurcations. The period2 orbit enters a two-loop torus orbit via border collision and Neimark-Saeker bifurcations. The dynamic behavior of the system near the eodimension-2 bifurcation points is clearly studied. The mechanism of the coexisting phenomenon from the subcritical Neimark-Sacker bifurcation is explained. Finally, chaos from torus breakdown is detected in this higher order switching converter with an inductive impedance load and its phase shift characteristics to different initial conditions are investigated.     

On the mechanism and control for the ultra-low frequency oscillation in NY Power Grid with large-scale hydropower

The power grid with large proportion of hydropower may engage the ultra-low frequency oscillation (ULFO), which threatening the operation of system. To the NY Power Grid system, whose dimension is over thousands, this paper reveals the cause of ULFO with the phase portrait method, i.e., lies in the saturation of the different limits of the governor system of the generators, in other words, the occurrence of limit cycle is due to the non-smooth bifurcation. And furthermore, it proposes two methods to suppress ULFO with the philosophy of destroying the condition of non-smooth bifurcation. In detail, first, the phenomenon of ULFO in NY Power Grid, the damping characteristics and the limits in the governor system of the hydropower units are presented. Second, based on the non-smooth bifurcation theory, the mathematical basis of the oscillation in the non-smooth system caused by the saturation of limits is introduced. And then, the non-oscillation and oscillation dynamic of the system corresponding to without/with limits in the governor system are analyzed. Furthermore, it discusses the influence of the saturation of single limit on the characteristics of ULFO with the phase portraits. Moreover, the phase portraits of the ULFO under different faults is analyzed, and it shows that the limiting saturation occurs with a large enough disturbance. Thus, the ULFO is resulting from the negative damping of generation and the saturation of multiple limits under a large enough disturbance. In addition, according to the above mechanism, two strategies to suppress the ULFO, i.e., the governor parameters tuning and the fault strength relief are designed. The simulation shows the effectiveness of proposed strategies.     

Dynamical analysis of bursting oscillations in the Chay-Keizer model with three time scales

Based on the Chay-Keizer model with three time scales, we investigate the role of the slowest variable in generating bursting oscillations in pancreaticcells. It is shown that both of the two slow processes can interact to drive fast, medium and slow bursting oscillations typically observed in pancreaticcells. Moreover, diverse patterns of electrical bursting are presented, including the fold/fold bursting, fold/homoclinic bursting, fold/Hopf bursting via fold/fold hysteresis loop, and the fold/fold burstin...     

Dynamical Analysis of a Tri‐Neuron Fractional Network

The present paper concerns with the dynamics of a fractional neural network involving three neurons. Firstly, the bifurcation point is identified for which Hopf bifurcations may occur by taking the system parameter as a bifurcation parameter via the stability analysis of fractional systems. It is indicated that the system parameter can significantly affect the dynamical properties of such network. Secondly, the impact of the order on the bifurcation point is carefully examined. It is found that the occurrence of bifurcation is delayed as the order increases as long as the other system parameters are established. Finally, a numerical example is exploited to verify the efficiency of theoretical results.     

Adaptive control design for a class of nonsmooth nonlinear systems with matched and linearly parameterized uncertainty

This paper presents an adaptive control design for a class of nonsmooth nonlinear systems with matched uncertainty, which is linearly parameterized with a known discontinuous function. The design framework is based on the concept of the Filippov solution as the classical Lyapunov theory for smooth systems cannot be applied to establish the stability of the adaptive control system due to the presence of the discontinuity. It is proved that as an adaptive control system, the global Lyapunov stability with the convergence of the state of the controlled system to the origin can be achieved by evaluating the monotonicity of the Lyapunov function in the state space, particularly on the discontinuous surface, while the uniqueness of the solution of the closed‐loop system is not necessarily guaranteed. Some interesting numerical examples are demonstrated with simulation results. Copyright © 2008 John Wiley & Sons, Ltd.     

带干摩擦的非光滑动力系统Lyapunov指数的数值计算

对带干摩擦的非光滑动力系统,在不连续点利用闭上链(cocycle)得到一个传递矩阵,由此给出一种非光滑动力系统Lyapunov指数的数值计算方法.该方法是根据计算光滑动力系统Lyapunov指数的数值方法而提出的.通过对带干摩擦的动力系统进行Lyapunov指数的数值计算,结合时间历程图和Poincare映射对其动力学特性进行了分析.数值结果表明该方法的可行性和有效性,与一般的计算非光滑动力系统Lyapunov指数的数值算法相比,该方法更便于数值计算.