具有对称初始数据的二维反应扩散方程的边界镇定

研究了二维圆盘上具有对称初始数据的反应扩散方程的边界控制. 由于初始条件和边界条件关于圆心旋转对称, 系统可以转化为等价的极坐标系下的一维抛物方程. 此时, 极点的奇异性成为了控制器设计中的难点. 本文设计了一系列方程变换, 消除了核函数方程中极点奇异性的影响, 将其转化为修正的Bessel方程, 求出了显式的核函数表达式和精确的边界反馈控制律, 扩展了偏微分方程的backstepping方法. 系统的收敛速度可通过改变控制器中的一个参数来调节. 然后用Lyapunov函数法证明了闭环系统在H1范数下指数稳定, 表明了系统对初值的连续依赖. 最后用数值仿真验证了方法的有效性.     

基于Cosserat 弹性杆理论的柔性线缆物理建模方法

针对虚拟环境中线缆敷设过程仿真的线缆建模问题,提出一种基于Cosserat 弹性 杆理论的柔性线缆物理建模方法。该方法在线缆离散模型的基础上根据Cosserat 弹性杆理论导 出线缆的总体势能,并通过优化算法得到线缆总体势能最小时的线缆形态,即线缆的平衡状态。 模型考虑到线缆的柔性和连续性,能够模拟线缆的弯曲和扭转变形;通过对线缆进行离散表达, 实现了对线缆总体势能的数值求解;引入罚函数将求解线缆总体势能最小值问题转化为非线性 无约束优化问题;非线性无约束优化问题的求解采用信赖域方法,提高了求解的稳定性。设计 并开发了虚拟环境中的线缆敷设过程仿真原型系统,并进行实例验证,证明该方法的可行性。     

Swing‐Stabilization Up for a Rotatory‐Elastic Pendulum Via Nonlinear Sub‐Optimal Control

This paper deals with the smooth control design for Swing‐Stabilization Up of underactuated pendular robot. The considered system has, at least, two different no actuated links, one of them is pendular like elbow, the other one is prismatic and elastic. Thus, the control aim is to swing‐up and stabilize the underactuated system by using non‐switched control algorithm. To this, the control algorithm summarizes the concept of sub‐optimal control, the energy based control and the Kalman's canonical decomposition to unify the Swing‐Up and Stabilization of the considered underactuated system. In order to test the designed control algorithm, experimental results are presented for the non‐conventional rotatory elastic‐pendulum system.     

基于Cosserat理论的头发动态模拟*

针对基于弹性杆理论的超螺旋模型中对动力学方程的求解影响头发模拟实时性的问题,采用Cosserat弹性杆理论对头发建模,引入角速度变量,并加入头发运动平衡的固有约束,得到改进的拉格朗日动力学运动方程;然后,将头发单体离散化,用角速度和四元数作为状态变量简化动力学方程,用半显式的欧拉方程加速方程的执行,大大降低了系统的运行时间,提高了模拟的速度,在满足实时性要求的同时提高了头发模拟的真实度。     

具有耗散边界反馈的Timoshenko梁的镇定

研究了具有线性耗散边界控制的Timoshenko梁的边界反馈镇定问题。首先,在反馈系数矩阵B正定的前提下,我们证明了所论闭环系统是指数稳定的。然后,对于反馈系数矩阵B半正定的情况,得到了闭环系统渐近稳定的几个充要条件。     

Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control

This paper derives a feedback controlf(t), ‖f(t)‖_E≦r,r>0, which forces the infinite-dimensional control systemdu/dt=Au+Bf, u(0)=u _o ≠H to have the asymptotic behavioru(t)→0 ast→∞ inH. HereA is the infinitesimal generator of aC _o semigroup of contractionse ^At on a real Hilbert spaceH andB is a bounded linear operator mapping a Hilbert space of controlsE intoH. An application to the boundary feedback control of a vibrating beam is provided in detail and an application to the stabilization of the NASA Spacecraft Control Laboratory is sketched. This research was sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF Contract/Grants AFOSR 81-0172 and AFOSR 87-0315.     

Universal Adaptive Stabilization of Nonlinear Systems

Mårtensson's result The order of a stabilizing regulator issufficient a priori information for adaptive stabilization is proved to bevalid also for a class of nonlinear, time–varying systems and thefeedback strategy is simplified.     

具有一般耗散边界反馈的Euler-Bernoulli梁的指数镇定问题

讨论具有一般线性耗散边界反馈的Euler-Bernoulli梁的指数镇定问题.首先将所讨论的系统化为抽象空间中的发展方程,并利用G0半群理论给出闭环系统解的存在唯一性.其次,对相应的闭环系统特征方程进行详尽的讨论计算,得到了系统本征值的分布特性,从而利用Lassel不变原理得到了闭环系统渐近稳定的充分必要条件.最后通过对闭环系统的本征值及其相应的本征函数进行估计,导出了相应的闭环系统指数稳定的充分必要条件.     

Stabilization of a Heat‐ODE System Cascaded at a Boundary Point and an Intermediate Point

This paper considers the stabilization of a heat‐ODE system cascaded at a boundary point and an intermediate point. The stabilizing feedback control law is designed by the backstepping method. Based on a novel transformation, we prove that all the kernel functions in the forward and inverse transformations are of the class C². Moreover, the effectiveness of controller design is shown with a numerical simulation. Finally, we show the coherence between the controllability assumption of the main theorem in this paper and the known one for a special case with λ=0.     

使用多控制器结构的可靠镇定

采用因子化方法研究了具有强镇定被控对象的可靠镇定问题.证明了几种可靠镇定问题定义之间的等价关系,并表征了可靠控制器的结构.给出了对于任意给定的控制器,存在另一个控制器使其共同解决可靠镇定问题的充要条件,该条件提供了一种选择可靠控制器的方法.     

基于采样控制的一类本质非线性系统的全局镇定

针对一类含不确定参数的本质非线性系统,基于非光滑控制技术,提出了 一种基于采样控制的全局非光滑镇定方案. 首先,基于加幂积分技术和递归设计方法,提出了一类采样状态反馈控制器构造性设计方法.然后,通过合理地构造Lyapunvo泛函,严格地证明了存在一个最大采样周期 可以保证闭环系统的全局渐近稳定性. 由于控制器是离散形式的,所以在实际中易于用计算机来实现. 仿真结果验证了该方法的有效 性.     

一类关联大系统的分散强镇定

研究由子系统通过输入输出通道实现连接的关联大系统的分散强镇定问题，对于静态连接或的动态连接的情形，给出了大系统可以实现分散强镇定的条件，这些条件的检验只在子系统一级进行，具有较低的计算维数。     

非线性系统基于增益观测器的全局输出反馈镇定

讨论几类非线性控制系统可输出反馈指数镇定的充分条件;特别地,在可输出反馈指数镇定的条件下讨论控制器参数的有效范围;数值模拟证实所设计的控制器厦其调节参数的有效性。     

Grasping impact force control of a flexible robotic gripper using a piezoelectric actuator

This paper presents robust force tracking control of a flexible beam during a grasping operation using a piezoceramic actuator. Equations describing the motion of the gripper in conditions of contact and noncontact are derived based on the cantilever beam. In this study, contact force is regulated, in addition to the impact force generated at the instant of contact, based on variable structure model reference adaptive control theory using only force measurements. For the derivation of the control law, it is assumed that parameters of the beam and the stiffness of the object are unknown. Computer simulations show the effectiveness the controller. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

一类不确定热方程自适应边界控制

研究了一类含有不确定控制系数和边界扰动的热方程自适应状态反馈边界控制设计问题. 通过Lyapunov方法, 显式地得到了仅需系统边界状态信息的自适应控制器. 证明了闭环系统状态是L2[0,1]稳定的, 特别是当边界扰动消逝时, 该状态收敛到0. 此外, 通过灵活选取参数调节律的初始条件, 适当放宽了相关文献中相容性条件对系统初始条件的限制. 仿真算例验证了本文方法的有效性.     

一类非完整约束系统的镇定与能控性

考虑非完整约束系统的镇定与能控性问题. 文中首先证明了虽然一般地说这类系统不能由光滑反馈镇定, 但它的存在性依赖于初值. 当初值在一个零测集外时, 这种反馈镇定确实存在. 然后我们证明了这类系统在分段光滑控制下全局可控. 由于证明是构造性的, 它给出了相应的控制.     

Stabilization analysis of a generalized nonlinear axially moving string by boundary velocity feedback

This paper addresses vibration suppression of an axially moving nonlinear string subject to boundary control at either the downstream or the upstream end. The equation of motion and the boundary conditions are derived from Hamilton's Principle, using the exact expression of the strain to describe the geometrical nonlinearity due to the finite transverse deformation. We can approximate this model by various simpler models found in the literature. We show that the oscillations of the moving string can be stabilized exponentially via linear negative velocity feedback acting at one end of the string. Our proofs rely on Lyapunov's direct method, using a carefully constructed energy functional.     

一类不确定非线性系统的输出反馈半全局镇定

研究了一类不确定非线性系统的输出反馈半全局镇定问题. 不同于现有文献,本文研究的控制系统具有更强的非线性和未知控制系数,这增加了设计输出反馈控制器的难度. 基于反推方法和输出反馈占优方法,设计了输出反馈半全局控制器. 通过选取适当的设计参数,该控制器可以保证闭环系统的半全局渐近稳定. 仿真实例验证了理论结果的有效性.     

一类非线性奇异摄动控制系统的镇定性*

本文讨论了一类非线性奇异摄动控制系统，文中我们运用动态分析的办法，结合处理非线性的技巧，着重研究了该系统的局部光滑反馈镇定性。     

一类二阶非完整系统的镇定

研究一类二阶非完整系统的镇定问题. 通过状态和输入反馈变换将系统模型转换为二阶链式标准型, 并对标准型给出一种时变光滑指数镇定控制律. 所得结果应用于欠驱动平面刚体的镇定.