双轮共轴移动式倒立摆动力学建模与状态反馈控制

应用第一类拉格朗日方法对系统进行力学分析,建立了以电机转矩为输入且轮在轴向无滑移的非完整约束下系统的数学模型.双轮共轴移动式倒立摆的运动控制目标是移动式倒立摆在二维平面内按指定的方向和速度运动,同时保持摆杆平衡.利用状态反馈,构造闭环系统的状态方程,通过极点配置求得控制量.仿真结果验证了系统状态方程的正确性和控制方法的合理性.     

具Cauchy-Ventcel边界的阻尼波方程的对数衰减性

本文研究有界区域上具Cauchy-Ventcel边界条件的波动方程的解的衰减性质。在不要求耗散区域满足几何控制条件的情形下,我们得到了波方程的对数衰减结果。 主要结果的证明依赖于具Cauchy-Ventcel边界条件的椭圆方程的插值不等式以及关于该椭圆方程的预解式估计。为得到期望的插值不等式, 我们采用的工具是整体Carleman估计。     

模糊非线性奇偶方程故障诊断方法

研究基于模糊模型和奇偶(一致性)方程的非线性系统执行器故障诊断方法.讨论了全解耦奇偶方程的产生方法,并给出了全解耦奇偶向量存在的条件.由全解耦奇偶方程产生的残差仅对特定执行器故障敏感,而与系统状态、扰动输入和其它执行器输入无关.用T-S模糊模型描述非线性系统,并与全解耦奇偶方程相结合得到了模糊奇偶方程,解决了奇偶方程在非线性系统中的应用问题.将执行器故障模型用刻度因子和偏差表示,用模糊奇偶方程产生残差,从而可以估计故障模型的参数.文章给出了某飞机非线性模型的仿真实例.     

广义Birkhoff方程的平衡稳定性

广义Birkhoff方程是一类更为普遍的约束功学系统的方程．研究定常广义Birkhoff方程的平衡稳定性．建立平衡方程，给出系统的能量变化方程，根据Birkhoff函数的定号性质，建立平衡稳定性的判据．举例说明结果的应用．     

基于状态观测器的双模控制方法

对于状态不可测的输入受限线性时不变系统,提出一种基于状态观测器的控制方法.该方法采用双模控制策略,将不变椭圆集概念同时应用于观测器的状态方程和误差方程,给出估计状态不变性和控制输入可行性条件并给出了闭环系统的稳定性定理.仿真结果表明了所提方法的有效性.     

非线性受控系统状态方程的任意阶近似解

针对工作在理想状态附近的受控系统,通过对其非线性状态方程进行Taylor展开,使之变为无穷级数形式的常微分方程组;然后在线性状态方程组解的基础上采用常数变异法,使之变换成积分方程;最后采用逐次逼近法求得非线性状态方程的任意阶近似解,并进一步讨论了系统状态的方均包络矩阵的转移规律.     

热—板传输系统的稳定性分析

本文研究由处于相邻区域的板方程和热方程构成的耦合系统的稳定性质, 其中耦合来自两个区域的交界 面上的传输边界条件. 在该传输系统中, 热方程起着控制器的作用, 且耗散通过交界面传输并影响板方程. 文献[1] 证明了在板方程上施加额外的控制器时, 该二维传输系统的能量呈指数衰减. 通过应用频域方法, 椭圆方程的正则 性理论等, 可以得到: 仅由热方程的耗散即可使得闭环系统指数稳定. 这一指数稳定的结论与相应的一维传输系统 的性质吻合. 最后, 文章还分析了不同传输边界条件下的板–热耦合系统的稳定性.     

多项式非线性系统的并行分布辨识

在状态空间方程中引入输入和状态的多项式函数,以此多项式函数表示非线性因素.为了辨识多项式非线性系统中的各系统矩阵,对于矢量化各系统矩阵组成的未知参数矢量,分别在无约束和有约束条件下采用两并行分布算法求解.在以状态方程等式为约束条件时,将各状态瞬时刻值与由系统矩阵组成的未知参数矢量合并为一个新的优化矢量.对于优化矢量的辨识,给出了并行分布算法的求解过程和迭代式.最后,通过仿真算例验证了所提出方法的有效性.     

一种实时手写数学方程编辑器

该文所述的数学方程编辑器,用户可用笔和书写板输入手写的数学公式,系统通过实时字符、符号识别和图形语法分析软件产生与输入相对应的语法分析树,并由此转换成诸如Latex、数学的或LISP-like符号等输出形式,与基于特殊方程描述语言的编辑系统相比,该手写方程编辑器相对简单且使用方便。     

时变时滞不确定性系统的状态反馈控制器设计

研究一类不确定性动态系统.这类系统具有多重时变状态时滞和多重时变控制输入时滞,其不确定性满足范数有界条件.采用黎卡提方程方法,得到了这类不确定性时滞系统可状态反馈镇定的充分条件.通过解一个特定的黎卡提不等式,即可得到镇定已知系统的控制器.     

Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin–Voigt damping

We consider the beam equation coupled by a transmission condition with a wave equation in an elastic beam. The beam has clamped boundary conditions and the wave equation has Dirichlet boundary conditions. The damping which is locally distributed acts through one of the equations only; its effect is transmitted to the other equation through the coupling. First, we consider the case where the dissipation acts through the beam equation. We show that in this case the coupled system is polynomially stable by using a recent result of Borichev and Tomilov on polynomial decay characterisation of bounded semigroups, we provide precise decay estimates showing that the energy of this coupled system decays polynomially as the time variable goes to infinity. Second, we discuss the case where the damping acts through the wave equation. Proceeding as in the first case, we prove that this system is also polynomially stable and we provide precise polynomial decay estimates for its energy. Finally, we show the lack of uniform exponential decay of solutions for both models.     

Boundary stabilisation of the wave equation in the presence of singularities

We study the boundary stabilisation of the wave equation by a nonlinear feedback active on a part of the boundary in geometric situations for which the solutions have singularities. These singularities appear at the interfaces at which the mixed Neumann–Dirichlet boundary conditions meet. Under a simple geometrical condition concerning the orientation of the boundary, we obtain sharp energy decay rates under a general growth assumption on the feedback. We show that the singularities do not affect the energy decay rates and give examples.     

线性奇异时滞系统的状态与不确定输入估计

研究了含不确定输入的线性奇异时滞系统的观测器设计.在一定秩条件下,通过引入两个广义坐标变换,先将系统等价变换为不含不确定输入的正常状态空间时滞系统,再变换为在系统描述中滞后项仅与输入和输出有关的系统.通过设计等价系统的状态观测器来获得原系统的观测器,实现对原系统的状态与不确定输入的指数逼近.     

Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.     

Stabilization of the Euler–Bernoulli plate with variable coefficients by nonlinear internal feedback

We consider the energy decay for solutions of the Euler–Bernoulli plate equation with variable coefficients where a nonlinear internal feedback acts in a suitable subregion of the domain. The Riemannian geometric method is used to deal with variable coefficient problems. When the feedback region has a structure similar to that for the wave equation with constant coefficients, we establish the stabilization of the system in the case of fixed boundary conditions. Several energy decay rates are established according to various growth restrictions on the nonlinear feedback near the origin and at infinity. We further show that, unlike for the case of constant coefficients, choices of such feedback regions depend not only on the type of boundary conditions but also on the curvature of a Riemannian metric, based on the coefficients of the system.     

线性离散时变系统的状态和输入混合估计: 一种对策方法

本文研究了线性离散时变系统的混合估计问题, 估计信号是状态和输入的线性组合. 设计目标要求满足一个最坏性能指标, 即从扰动到估计误差的能量增益小于一个给定值. 混合估计问题的最优解是二人零和微分对策的鞍点解. 基于微分对策方法, 混合估计问题有解的充要条件表达为 Riccati 微分方程的可解性. 在问题有解时, 给出了符合要求的估计器. 估计器的结构表达为一个增益矩阵和一个输出映射矩阵, 后者反映了未知输入与输出估计误差之间的内在联系. 最后, 通过数值例子证明了本文方法的有效性.     

线性连续时变系统的状态和输入混合估计:一种对策方法

The $H_\infty$ hybrid estimation problem for linear continuous time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. Based on the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in\hfill terms\hfill of\hfill solutions\hfill to\hfill a\hfill Riccati\hfill diffe-\\rential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix that reflects the internal relations between the unknown input and output estimation error. Both state and unknown inputs estimation are realized by the proposed estimator. Thus, the results in this paper are also capable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numerical example is provided to illustrate the proposed approach.     

Decay Rates for a Beam with Pointwise Force and Moment Feedback

We consider the Rayleigh beam equation and the Euler–Bernoulli beam equation with pointwise feedback shear force and bending moment at the position ξ in a bounded domain (0,π) with certain boundary conditions. The energy decay rate in both cases is investigated. In the case of the Rayleigh beam, we show that the decay rate is exponential if and only if ξ/π is a rational number with coprime factorization ξ/π=p/q, where q is odd. Moreover, for any other location of the actuator we give explicit polynomial decay estimates valid for regular initial data. In the case of the Euler–Bernoulli beam, even for a nonhomogeneous material, exponential decay of the energy is proved, independently of the position of the actuator. Date received: October 30, 2000. Date revised: December 20, 2001.     

General decay of a von Karman plate equation with memory on the boundary

We investigate the influence of boundary dissipation on the decay property of the solutions for a von Karman plate equation with a memory condition on one part of the boundary. Dropping the condition $u_0=0$ on one part of the boundary, we show a general stability result for the equation via setting modified energy functionals which are equivalent to the energy of the equation and using some properties of convex functions. This result allows a wider class of relaxation functions and improve earlier results of Mustafa and Abusharkh (2015) and Park and Park (2005).