一类磁性刚体航天器的混沌控制研究

采用基于误差线性系统稳定性准则的混沌控制方法,控制具有结构内阻尼的磁性刚体航天器在重力场与磁场共同作用下在圆形轨道的混沌姿态运动.讨论了航天器姿态运动方程中部分参数的取值对于运动姿态的影响,给出了这些参数通过倍周期分岔或逆倍周期分岔通往混沌的途径.当参数使系统做混沌姿态运动时,采用上述方法将混沌运动控制至周期-4轨道,并实现周期-1、2、4轨道之间转换的灵活控制.此外,分析了控制参数的变化对于控制效果的影响,并分别给出了控制至不同轨道时的输入扰动范围及控制参数范围.仿真结果表明,该方法能够实现混沌姿态运动在预定周期轨道间的灵活控制,且输入扰动量小、控制速度快、具有高精度,从而验证了该方法在航天器混沌姿态运动控制方面的有效性.     

一个经济周期模型的分岔与混沌

在Goodwin与Puu的宏观经济思想基础上,得到了一个推广的非线性动力学经济周期系统．首先用数值方法研究了此系统在特定参数条件下的全局分岔行为．然后结合最大Lyapunov指数,详细讨论了系统在分岔过程中动力学特征的转变．通过分析分岔图形发现在某些参数区间内倍周期分岔导致了混沌;在混沌区域内嵌有多个周期窗口;“加速数”值的增加可以促进经济的周期性运动．最后介绍了分岔和混沌分析得到的动力学性质对理解经济波动的应用．     

粘弹性传动带的分岔特性和混沌振动分析

研究了粘弹性传动带横向振动的分岔特性和混沌动力学行为．将传动带视为沿轴向运动的抗弯刚度较 小的粘弹性梁模型,同时考虑变形的几何非线性和材料的非线性因素,运用弹性力学方法建立了其横向振动 的偏微分方程,利用 Galerkin 方法得到了时空坐标解耦的二阶非线性动力学方程,重点探讨了带速波动对系统 动态特性的影响．采用数值方法对系统的运动响应进行仿真,分岔图和 Poincaré图表明：随着平均带速和波动 幅值的变化,系统出现周期振动和混沌振动,倍周期分岔是产生混沌振动的途径．     

基于Kelvin模型的粘弹性浅拱的动力稳定性

研究了外激励作用下非线性粘弹性浅拱的动力行为．通过达朗贝尔原理和欧拉一贝努利假定建立了浅拱的动力学控制方程,其中采用Kelvin模型来表示非线性粘弹性材料的本构关系,并利用Galerkin法将方程简化用于数值分析．分析了粘弹性材料参数、浅拱矢高、外激励幅值和频率对系统分岔和混沌等非线性动力学行为的影响,结果表明各种参数条件下系统的非线性动力特性十分复杂,周期运动、准周期运动和混沌运动窗口在一定条件下交替出现．     

改进遗传神经网络控制混沌运动的研究

用最大Lyapunov指数构造遗传算法中的适应度函数,通过遗传算法优化神经网络的权系数．根据所得到的适应度函数和权系数来构造遗传神经网络控制器,从而提高神经网络控制效果．对离散系统Logistic映射和连续系统Rossler方程、AFM（原子力显微镜）悬臂梁振动系统的混沌运动分别进行了仿真控制．数值实验结果表明本文改进的遗传神经网络控制方法对离散或者连续的混沌系统都能控制到低周期轨道上去,证明了算法的有效性．     

Buck变换器频率引起的混沌及其控制

大多数关于变换器分岔和混沌的研究都是以直流电源电压作为变量进行分析和控制的。为了研究变换器开关频率对系统动力学行为和混沌控制效果的影响,以PWM模拟电压控制Buck变换器为研究对象,首先通过计算机仿真电路得到分岔图,分析了开关频率对系统的影响;然后利用硬件实验电路对单周期稳定、倍周期分岔和混沌3种不同状态进行相图分析,对分岔图进行验证;最后,采用参数扰动法实施混沌控制,研究了正弦谐波扰动信号幅值对控制效果的影响。通过选取特定的幅值比,经过计算机仿真电路得到新的分岔图,与混沌控制前的分岔图形成了鲜明的对比;通过选取特定的开关频率,经过混沌控制前后的电容电压和电感电流时域图,验证了混沌控制有利于提高变换器的稳态和暂态性能。有利于加深对变换器非线性动力学行为及其控制的认识和研究。     

横向流中细长圆柱的热弹性颤振

研究了细长圆柱体在热环境下的横向流致振动.应用迦辽金法将非线性运动控制偏微分方程离散为常微分方程组,首先分析了热载荷对系统临界流速的影响,然后采用数值方法得到了系统分岔区,以及它在参数空间的分布情况.应用分岔图、相图对系统的运动性质进行了判定.系统随着参数的变化呈现周期运动,温度增加,系统发生颤振的临界速度减小.当温度载荷不变时,流速增加,系统周期振动的振幅越来越大,系统发生极限环振动,周期3运动、拟周期运动和混沌运动.     

基于最大Lyapunov指数的行星齿轮传动系统混沌特性分析

为了分析行星齿轮系统的混沌特性,基于集中参数理论,考虑时变啮合刚度、齿隙和综合啮合误差等非线性因素,建立行星齿轮系统扭转振动模型.采用Runge-Kutta数值解法求解振动方程,利用分岔图和最大Lyapunov指数图分析系统随各种参数变化的分岔与混沌特性.数值仿真得出:随激励频率的增加,系统首先从周期运动进入阵发性混沌,再通过逆倍化分岔由混沌回到周期运动,之后再次通过跳跃激变和倍化分岔由周期运动进入混沌运动,最后通过逆倍化分岔稳定到1周期运动.随阻尼比的增加,系统通过逆倍化分岔由混沌运动进入周期运动.随综合啮合误差幅值、齿隙和刚度幅值分别增加的三种情况下,系统都是通过倍化分岔由周期运动进入混沌运动.随荷载的增加,系统通过跳跃激变和逆倍化分岔由混沌运动进入周期运动.以上分析结果可为行星齿轮系统参数设计提供理论依据.     

Host-Parasitoid系统的分岔与混沌控制

用数值模拟的方法,研究了Host-Parasitoid模型.该模型是一类非线性离散系统,反映了在一定的时间和空间内,寄生虫和寄宿主之间的生存状态.通过调节各种影响下的分岔参数,可以观察到系统具有周期泡,倍周期分叉,间歇混沌和Hopf分岔等复杂非线性动力学现象,揭示了系统通向混沌的途径.利用不同周期遍历下的奇怪吸引子和具有分形边界的吸引盆对系统的非线性特性进行了深入的探讨.最后利用参数开闭环控制法对系统的混沌状态进行了有效的控制.数值仿真和理论分析表明,选择相应的控制参数可将该系统的混沌状态控制到不同的稳定周期运动.     

一种带绝对值项系统的分岔、激变与混沌

研究了一种含有绝对值项的三维微分动力系统,用李雅普诺夫方法得到了系统发生第一次Hopf分岔的条件.利用相轨迹图、分岔图、最大李雅普诺夫指数谱等非线性动力学分析方法,分析了该系统从规则运动转化到混沌运动的规律.该系统是按照Feigenbaum途径(倍周期分岔)通向混沌的,在混沌区域存在周期窗口.当参数达到激变临界点时,混沌吸引子和不稳周期轨道在吸引子边界上碰撞,发生边界激变,激变临界值的领域内还存在相对长时间的瞬态混沌过程.     

Gait generation and control for biped robots with underactuation degree one

The paper develops a unified feedback control law for n degree-of-freedom biped robots with one degree of underactuation so as to generate periodic orbits on different slopes. The periodic orbits on different slopes are produced from an original periodic orbit, which is either a natural passive limit cycle on a specific slope or a stable periodic walking gait on level ground generated with active control. First, inspired by the controlled symmetries approach, a general result on gait generation on different slopes based on a periodic orbit on a specific slope is obtained. Second, the time-scaling control approach is integrated to reproduce geometrically same periodic orbits for biped robots with one degree of underactuation. The degree of underactuation is compensated by one degree-of-freedom in the temporal evolution that scales the original periodic orbit. Necessary and sufficient conditions are investigated for the existence and stability properties of periodic orbits on different slopes with the proposed control law. Finally, the proposed approach is illustrated by two kinds of underactuated biped robots: one has a passive gait on a specific ground slope and the other does not have a natural passive gait.     

Implementation of repetitive controller for rejection of position-based periodic disturbances

Time-varying periodic motions have appeared in many industrial processes, such as cam-follower systems, in that the control system has to operate at a periodic variable velocity specified in terms of the angular position-domain. This paper employs a repetitive control for rejecting the time-varying periodic disturbances, and presents an implementation technique based on angular position which can generate a fixed number of cycles in real-time. This control technique can accommodate the period variation in a time-varying periodic signal such that variable samples per period for synchronization can be achieved by the regular fixed-time sampling rate. A technique using position information to manipulate the delayed data and an interpolation scheme to properly access data in the buffer memory is proposed. An anti-vibration control system with time-varying periodic disturbances is studied to illustrate control performance. The experimental results are given to illustrate that time-varying repetitive control can effectively eliminate steady-state errors within a few cycles.     

Application of the singular control test to periodic control problems of a continuous distillation process

The singular control test is applied to periodic control problems of a continuous distillation process in order to determine if the optimal periodic control is proper. It is also shown that the singular control test is easier to apply than the w-teat for the problems of concern. Some numerical calculations are carried out for seeking the optimal periodic controls.     

Control and state observation of periodic linear multimodal systems

This paper investigates the control and state observation problem for periodic linear controllable and observable multimodal systems. For a controllable periodic linear multimodal system, this paper proposes an alternative minimum-norm dynamic state feedback control scheme for state transition matrix assignment. Also presented is a new design of state observers for an observable periodic linear multimodal system. Finally, an analysis of closed-loop behaviour of controlled periodic linear multimodal systems using a state-estimate is given     

Periodic stabilizability of switched linear control systems

Stabilizability via direct/observer-based state feedback control for discrete-time switched linear control systems (SLCSs) is investigated in this paper. For an SLCS, the control factors are not only the control input but also the switching signal, and they need to be designed in order to stabilize the system. As a result, stabilization design for SLCSs is more complicated than that for non-switched ones. Differently from the existing approaches, a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems. It is highlighted that multiple feedback controllers need to be designed for one subsystem. For discrete-time SLCSs, it is proved that reachability implies periodic stabilizability via state feedback. A necessary and sufficient criterion for periodic stabilizability is also established. Two stabilization design algorithms are presented for real application. Moreover, it is proved that reachability and observability imply periodic stabilizability via observer-based feedback for discrete-time SLCSs. Periodic detectability, as the dual concept of periodic stabilizability, is discussed and the stabilization design algorithms via observer-based feedback are presented as well.     

一类脉冲动力系统的状态反馈控制

对一类具有状态反馈控制的脉冲动力系统的动力学性质进行了研究．由周期解的扰动解得到了一个Poincare映射，利用Poincare映射讨论了系统周期解的分岔，并得到了半平凡周期解和正周期-1解存在和稳定的充分条件．定性分析和数学模拟表明，半平凡周期解通过fold分岔分钻出正周期-1解，正周期-1解通过flip分岔分岔出正周期-2解，再通过一系列flip分岔通向混沌，此外，讨论了脉冲状态反馈控制的效果．     

Neighboring optimal control for periodic tasks for systems with discontinuous dynamics

We propose a trajectory-based optimal control method for periodic tasks for systems with discontinuous dynamics. A general method, dynamic programming, suffers from the problem of dimensionality. We use local models of the optimal control law to construct a local controller. We combine a parametric trajectory optimization method and differential dynamic programming (DDP) to find the optimal periodic trajectory in a periodic task. By formulating the optimal control problem with an infinite time horizon, DDP ...     

Satisfactory control of discrete-time linear periodic systems

In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.     

Attractor switching by neural control of chaotic neurodynamics

Chaotic attractors of discrete-time neural networks include infinitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically, a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between different stabilized periodic orbits. For chaotic modules with noise, random switching between different periodic orbits is observed.     

线性离散周期系统输出反馈参数化极点配置

采用周期输出反馈的途径, 考虑了线性离散时间周期系统的极点配置问题. 通过将闭环单值性矩阵进行一系列转化, 周期输出反馈律的求解问题可以转化为一类Sylvester矩阵方程的求解问题. 利用Sylvester矩阵方程的最新结果, 可以将输出反馈增益表示为参数化形式, 从而得到了能够实现极点配置的所有输出反馈控制器. 数值算例验证了方法的有效性.