结构可靠度分析FORM迭代算法的混沌控制

利用混沌控制原理对FORM收敛失败进行控制. 理清了全局性和局部性两类混沌反馈 控制各种方法的内在联系,说明稳定转换法和自适应调节法属于全局混沌反馈控制 方法,自适应调节法可视为稳定转换法的特例. 参 数调节混合法不过是松弛牛顿法的另一种表达形式,它们都属于局部混沌反馈控制方法. 阐 明了混沌反馈控制表达式与工程力学收敛控制迭代算法的对应关系. 也揭示了这些迭代算法 收敛控制措施的功效和局限性. 提出了一个以稳定转换法为主联合松弛牛顿法的混 沌反馈控制方法,对可靠度分析FORM迭代算法实现了周期振荡、分岔和混沌控制.     

亚音速气流作用下薄板结构混沌运动的时滞反馈控制

研究了亚音速气流下非线性二维薄板结构在横向周期载荷作用下的混沌运动及控制问题.基于von Karman板理论和分离变量法,建立了亚音速下薄板结构的运动控制方程.对于未控系统,采用Melnikov方法判断其混沌运动阈值,并用Runge-Kutta法进行数值验证.对处于混沌运动状态的系统,采用时滞反馈控制方法对混沌运动进行控制.结果表明,Melnikov方法可以有效地预测系统的混沌运动行为,时滞反馈控制方法可以有效地将系统的混沌运动转化为周期运动.     

受迫Duffing振子中混沌运动的控制

本文研究了受迫Ｄｕｆｆｉｎｇ振子发生混沌运动时的控制问题，通过周期激振力、自适应控制和连续反馈控制来抑制、控制其中的混沌运动，使系统从混沌运动状态转变变到规则运动状态。     

碰摩转子映射系统的延迟反馈混沌控制

将转子的碰摩映射在擦边轨道附近进行局部化,并通过实验数据去拟合局部映射,然后采用变量延迟反馈控制法对该系统进行控制.通过选取合适的控制增益,将转子系统的碰摩运动镇定到周期1转道上,从而实现对碰摩转子系统混沌运动的控制.     

时变切换时滞反馈镇定混沌系统不稳定周期轨线

为提高经典时滞反馈控制镇定不稳定周期轨线的效果, 扩大受控周期轨线的稳定区域, 本文基于时变切换策略对经典时滞反馈控制进行改进, 提出了时变切换时滞反馈控制. 时变切换时滞反馈控制的控制信号仅在特定的时段中存在, 而在其他时段上不存在控制信号, 这与经典时滞反馈控制中具有固定的控制信号是不同的. 通过实例分析, 研究了时变切换时滞反馈控制在镇定不稳定周期轨线中的具体性能. 以反馈增益系数为变量, 计算受控周期轨线的最大条件Lyapunov指数, 得到了受控周期轨线的稳定区域随切换频率变化的关系曲线. 结果表明, 随着切换频率增大, 受控周期轨线的稳定区域呈现非平滑地变化. 当选取恰当的切换频率时, 时变切换时滞反馈控制的稳定区域显著大于经典时滞反馈控制的稳定区域. 在混沌控制的工程实践中, 控制信号常常受到一定的限制. 要实现对目标周期轨线的稳定控制, 就需要受控周期轨线具有足够大的稳定区域. 因此, 与经典时滞反馈控制相比, 本文提出的时变切换时滞反馈控制具有更广泛的应用前景.      

快速预测混沌控制效果的一个量化指标

本文对Pyragas的时滞自反馈控制方法作了深入详细的研究，并从瞬态Lyapunov特性指数（ILCE）和短期平均Lyapunov特性指数（SLCE）的角度进一步揭示了该方法的控制机理，提出了一个利用瞬态Lyapunov特性指数实时反映混沌控制效果的量化指标P。     

概率约束评估的功能度量法的混沌控制

功能度量法是基于可靠度的结构优化设计中评估概率约束的一种方法,其改进均值(AMV)迭代格式具有简洁、高效的优点,但对一些非线性功能函数搜索最小功能目标点时可能陷入周期振荡或混沌解,本文利用混沌反馈控制的稳定转换法对功能度量法的AMV迭代格式实施收敛控制.首先展示一些功能函数应用功能度量法AMV格式迭代计算产生了周期解和混沌解现象,并对迭代算法进行了混沌动力学分析.然后利用稳定转换法对功能度量法迭代失败的参数区间进行混沌控制,使嵌入周期和混沌轨道的不稳定不动点稳定化,获得了稳定收敛解,实现了迭代解的周期振荡、分岔和混沌控制.     

非自治时滞反馈控制系统的周期解分岔和混沌

研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理,研究对应的线性平衡态失稳的临界边界,将时滞非线性控制方程化为泛函微分方程,给出由Hopf分岔产生的周期解的解析形式．通过分析周期解的稳定性得到周期解的失稳区域,使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路：倍周期分岔和环面破裂．其结果表明,时滞在控制系统中可以作为控制和产生系统的复杂运动的控制“开关”．     

带时滞的二元神经元网络的OPNCL控制和复杂网络的时间延迟反馈控制

针对一种带时滞的二元神经元网络和一种复杂网络的混沌控制问题,利用开环加非线性闭环(Open Plus Nonlinear Closed Loop,OPNCL)方法和时间延迟反馈控制(Time Delay FeedbackControl,TDFC)方法,分别设计了该混沌网络和混沌系统的控制器。从理论上证明了第一种控制器可使该网络系统的解稳定地传递到选定的目标,并通过数值模拟实验进一步验证了两种方法的有效性。结果表明:该方法避免了开环加非线性闭环控制的一些限制因素;对于任何目标,所控制混沌系统的传递域(Basins of Entrainment)是全局的,避免了有关确定传递域范围的繁琐计算。     

混沌系统的自适应延迟控制

本文结合Ｐｙｒａｇａｓ的延迟反旬控制思想，提出了镇定混沌吸引子中嵌入的不稳定周期轨道的自适应延迟控制法。避免了常规自适应控制方法需要设计参圪模型或确定目标状态的麻烦，字种自适应延迟控制方法，控制器简单，实时性好，数值仿真结果验证了这种方法的有效性。     

Suppression of chaos in a MEMS resonator by delayed position feedback

A delayed position feedback control is applied on DC voltage source for suppressing chaos of a typical MEMS resonator actuated by electrostatic forces. A theoretical necessary condition for chaotic oscillation of the controlled system is presented. Numerical results and the analytical prediction reveal the evolution of dynamical behavior of the system with AC voltage amplitude and the control effect of delayed feedback on reducing chaos of the system. It shows that the delayed feedback control is effective on suppressing chaos of the micro mechanical resonator.     

Delayed feedback control and bifurcation analysis of Rossler chaotic system

In this paper, from the view of stability and chaos control, we investigate the Rossler chaotic system with delayed feedback. At first, we consider the stability of one of the fixed points, verifying that Hopf bifurcation occurs as delay crosses some critical values. Then, for determining the stability and direction of Hopf bifurcation we derive explicit formulae by using the normal-form theory and center manifold theorem. By designing appropriate feedback strength and delay, one of the unstable equilibria of the Rossler chaotic system can be controlled to be stable, or stable bifurcating periodic solutions occur at the neighborhood of the equilibrium. Finally, some numerical simulations are carried out to support the analytic results.     

Modeling,nonlinear dynamic analysis and control of fractional PMSG of wind turbine

This study aims to reveal the laws of the relationship between fractional-order system and integer-order system. Meanwhile, delayed feedback control is introduced to control the fractional-order PMSG (permanent magnet synchronous generator) model of a wind turbine. First, the fractional-order mathematical model of PMSG is established. Next, numerical simulations under different system orders are given and the system dynamic behaviors are analyzed in detail. Then, the delayed feedback control method is introduced to control the fractional-order PMSG and the control results when different parameters vary are analyzed. Complex dynamics are presented and some interesting phenomena are discovered. It is found that the system order influences the dynamics of the system in many aspects such as chaos pattern, bifurcation behavior, period window, shape and size of strange attractor. The delayed time, feedback gain, feedback limitation, system order can obviously influence the control result except the initial state of the system. Moreover, the feedback limitation has a minimum to successfully control the system to stable states and the system order also has a maximum to do so.     

Stability, bifurcation and chaos of a delayed oscillator with negative damping and delayed feedback control

This paper presents a detailed analysis on the dynamics of a delayed oscillator with negative damping and delayed feedback control. Firstly, a linear stability analysis for the trivial equilibrium is given. Then, the direction of Hopf bifurcation and stability of periodic solutions bifurcating from trivial equilibrium are determined by using the normal form theory and center manifold theorem. It shows that with properly chosen delay and gain in the delayed feedback path, this controlled delayed system may have stable equilibrium, or periodic solutions, or quasi-periodic solutions, or coexisting stable solutions. In addition, the controlled system may exhibit period-doubling bifurcation which eventually leads to chaos. Finally, some new interesting phenomena, such as the coexistence of periodic orbits and chaotic attractors, have been observed. The results indicate that delayed feedback control can make systems with state delay produce more complicated dynamics.     

Using the delayed feedback control and saturation control to suppress the vibration of the dynamical system

In the present paper, the delayed feedback control is applied to suppress or stabilize the vibration of the primary system in a two degree-of-freedom dynamical system with parametrically excited pendulum. The case of a 1:2 internal resonance between pendulum and primary system is studied. The method of multiple scales is applied to obtain second-order approximations of the response of the system. The system stability and bifurcations of equilibrium point of the averaged equations are computed. It is shown that the delayed feedback control can be used to suppress the vibration or stabilize the system when the saturation control is invalid. The vibration of the primary system can be suppressed by the delayed feedback control when the original system is in the single-mode motion. The effect of gain and delay on the vibration suppression is discussed. As the delay varies at a fixed value of the gain, the vibration of the primary system can be suppressed at some values of the delay. The vibration suppression performance of the system is improved at a large value of the gain. The vibration of the primary system could be suppressed about 56% compared with the original system by choosing the appropriate values of gain and delay. The delayed feedback control also can be used to stabilize the system when the original system is unstable. The gain and delay could be chosen as the controlling parameters. Numerical simulation is agreement with the analytical solutions well.     

一类忆阻神经元的电活动多模振荡及Hamilton 能量反馈控制

根据法拉第电磁感应定律,在离子穿越细胞膜或者在外界电磁辐射下,细胞内外的电生理环境会产生电磁感应效应,继而会影响神经元的电活动行为. 基于此,本文考虑电磁感应影响下的 Hindmarsh-Rose (HR) 神经元模型,研究了其混合模式振荡放电特征,并设计一个 Hamilton 能量反馈控制器,将其控制到不同的周期簇放电状态. 首先,通过理论分析发现磁通 HR 神经元系统的 Hopf 分岔使其平衡点的稳定性发生了改变,并产生极限环,进而研究了 Hopf 分岔点附近膜电压的放电特征. 基于双参数数值仿真发现该系统具有丰富的分岔结构,在不同的参数平面上存在倍周期分岔、伴有混沌的加周期分岔、无混沌的加周期分岔以及共存的混合模式振荡. 最后,为了有效控制膜电压的混合模式振荡,利用亥姆霍兹理论计算出磁通 HR 神经元系统的 Hamilton 能量函数并设计 Hamilton 能量反馈控制器,通过数值仿真分析了膜电压在不同反馈增益下的簇放电状态,发现该控制器能够有效地控制膜电压到不同的周期簇放电模式. 本文的研究结果为探究电磁感应下神经元的分岔结构及其能量控制领域提供了有用的理论支撑.