明渠网络中基于带权Lyapunov函数的边界反馈控制稳定性

以描述明渠非定常流的一维模型——Saint-Venant方程为基础, 对由两段渠道串联构成的梯级河道网络, 以加权熵函数构成其Lyaponov函数, 基于该Lyapunov函数证明了在一定的边界反馈控制作用下, 闭环系统在平衡点的一个邻域内是渐近稳定的.     

切换状态反馈控制系统的稳定性分析

研究了一类切换控制系统的稳定性分析问题,切换控制器由多个线性状态反馈控制器组成。运用Lyapunov方法得出了稳定性的时域判据,通过求解一个线性矩阵不等式的方法分析切换控制系统的稳定性,利用KYP引理得到了等价的频域判据;并且研究了一类含有参数不确定性的切换控制系统的鲁棒稳定性分析问题,给出了稳定性时域判据和频域判据。稳定性分析的主要结果是基于公共二次Lyapunov函数的,适用于切换系统任意切换的情形,该方法在工程实例中的应用表明了其有效性。     

带边界非线性干扰的反稳定波方程的镇定

本文研究了一类具有边界控制匹配非线性干扰的反稳定波动方程的镇定问题. 本文只用了两个量测, 构造了一个无限维干扰估计器来实时估计状态和总干扰, 该估计器既不要求干扰的导数有界, 也不需要高增益. 基于估计的总干扰和估计的状态, 本文设计了输出反馈控制律稳定原系统. 此外, 本文还证明了闭环系统的其他状态是有界的. 为了说明理论结果, 下文给出了一些数值模拟.     

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。     

具有动态边界阻尼的波方程的降阶型差分半离散化的一致指数稳定性

由于在最优控制的数值计算和可观性的反问题中,离散系统关于离散化参数的一致指数稳定性具有重要作用,因而一致指数稳定性得到广泛而深入的研究.众所周知,对指数稳定的波方程的空间变量用经典的有限差分或有限元离散化后,离散格式产生高频病态伪特征模,致使离散系统不是一致指数稳定的.为了恢复一致指数稳定性,学者们引入了添加数值粘性项法和滤波法等方法.然而对于具有动态边界条件的波方程的一致指数稳定性问题研究的较少.本文用降阶型差分方法对此问题进行研究,先对具有动态边界条件的波方程进行降阶处理,然后利用有限差分对其进行空间半离散化,不用再对其进行任何处理,引入合适的李雅普诺夫函数即可验证离散系统是一致指数稳定的.     

具有异维数子系统的切换系统稳定性分析

研究一类线性切换系统的稳定性问题.该类切换系统包含2个不同维数的线性子系统.首先根据原系统的结构,构造出它的比较切换系统;然后设计出比较系统的切换率,在保证每个线性子系统的被激活时间均大于某一数值τ(＞0)的情况下,构造出2个子系统的Lyapunov函数;随后利用线性矩阵不等式(LMI)的方法给出每个子系统渐近稳定的条件.进一步利用Lyapunov稳定性理论的方法,保证整个比较系统的渐进稳定性,进而给出了原切换系统达到渐近稳定的一个充分条件.最后,一个数值例子说明文中方法的有效性.     

分布参数切换系统的稳定性分析

将切换系统的概念引入到分布参数系统中，提出分布参数切换系统的概念．结合切换系统和分布参数系统的建模方法，建立了两类分布参数切换系统的模型．运用切换系统的稳定性分析方法，对两类分布参数切换系统的稳定性进行分析，得出了指数稳定的充分条件．仿真示例验证了定理的正确性．     

具有边界控制的线性Timoshenko型系统的指数稳定性

本文研究多孔弹性材料在实际应用中的镇定问题.多孔物体的动力学行为由线性Timoshenko型方程描述,这样的系统一般只是渐近稳定但不指数稳定.假定系统两端都是自由的,在自由端对系统施加边界速度反馈控制,本文讨论闭环系统的适定性和指数稳定性.首先,利用有界线性算子半群理论得到了系统的适定性.进一步对系统算子的本征值的渐近值估计,得到算子谱分布在一个带域,相互分离的,模充分大的本征值都是简单本征值.通过引入一个辅助算子,利用它的谱性质以及有界线性算子的扰动理论,得到系统的广义本征向量的完整性以及Riesz基性质.最后利用Riesz基性质和谱分布得到闭环系统的指数稳定性.     

具有脉冲作用的切换线性广义系统的稳定性

本文引入一类新的系统模型—具有脉冲作用的切换线性广义系统. 应用驻留时间(Dwell time)方法和平均驻留时间(Average dwell time)方法研究其稳定性问题, 并给出系统指数稳定性的充分条件. 证明了当平均驻留时间足够大且重设律是允许的, 那么系统是指数稳定的. 利用广义系统的受限等价性质, 具体给出允许的重设律的设计方法. 数值例子说明本文方法的有效性.     

具有松弛条件的一类切换模糊系统的稳定性分析

使用切换技术以及多Lyapuriov函数方法．研究一类切换模糊系统的稳定性问题．给出了有连续控制输入时该切换模糊系统的一种松弛稳定性条件,避免了并行分配补偿法中固模糊规则数较多而求解公共矩阵P的困难,同时给出了实现系统全局渐近稳定的切换策略．主要条件以LMI的形式给出,具有较强的可解性．空气调节系统的设计实例表明了所提出设计方法的可行性和有效性．     

Stability analysis of Euler‐Bernoulli beam with input delay in the boundary control

In this paper, we investigate an Euler‐Bernoulli system with input delay in the boundary control. Suppose that there is no delay in observation, y(t), of the system, and a partial input delay in the boundary control. The collocated boundary feedback control law u(t) = αy(t) + βy(t ? τ) is applied to obtain the closed loop system. By spectral analysis and Lyapunov method, we show that: when α>|β|, the closed loop system is exponentially stable for any τ>0; when α<|β|, the system is unstable for any τ>0; when α = |β|, the system is asymptotically stable for almost all τ>0. Finally, we provide numerical simulations to show the spectral distribution for different values of α and β. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output feedback stabilization of an unstable wave equation with general corrupted boundary observation

We consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback. By the approach, the disturbance is first estimated by a relatively independent estimator; it is then canceled in the feedback loop. As a result, the control law can be designed almost as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent, and that all subsystems in the closed-loop are asymptotically stable in the energy state space. We also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction.     

Adaptive error feedback regulation problem for 1D wave equation

By using the adaptive control approach, we solve the error feedback regulator problem for the one‐dimensional wave equation with a general harmonic disturbance anticollocated with control and with two types of disturbed measurements, ie, one collocated with control and the other anti‐collocated with control. Different from the classical error feedback regulator design, which is based on the internal mode principle, we give the adaptive servomechanism design for the system by making use of the measured tracking error (and its time derivative) and the estimation mechanism for the parameters of the disturbance and of the unknown reference. Constructing auxiliary systems and observer and applying the backstepping method for infinite‐dimensional system play important roles in the design. The control objective, which is to regulate the tracking error to zero and to keep the states bounded, is achieved.     

Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control

In this paper we are concerned with the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations (also known as stochastic differential equations with the Markovian switching) by discrete-time feedback controls. Although the stabilization by continuous-time feedback controls for such equations has been discussed by several authors (see e.g. , , ,  and ), there is so far no result on the stabilization by discrete-time feedback controls. Our aim here is to initiate the study in this area by establishing some new results.     

具有边界扰动的不确定Euler-Bernoulli梁方程输出反馈控制

针对带有边界扰动、内部不确定扰动和外部扰动的Euler-Bernoulli梁方程,为克服传统扰动观测器引入的高增益及未知扰动导数难以准确求解问题,本文将主动干扰抑制控制(ADRC)技术应用到Euler-Bernoulli梁方程这个偏微分方程(PDE)系统上,提出并设计了一种新的在线扰动观测器,可实时估计扰动值.依据估计扰动值,设计了一个边界输出反馈控制器.仿真结果表明,本文所提出的方法可很好地实现对内部不确定扰动和外部扰动的估计,配合输出反馈控制器,可对边界扰动进行有效抑制,进而实现系统的指数稳定.     

State feedback control of networked systems with uncertain plant

This article, considers the problem of state feedback control of networked systems with an uncertain plant. The signals for feedback periodically switch between the plant state and the state of a model of the plant according to whether the plant state is available from the communication network or not. The model is used to generate control signals when the plant state is not available from the network. A sufficient condition for the robust exponential stability of the closed-loop system is derived in terms of the network dwell time and the system parameters. Examples are also worked out to demonstrate numerical procedures for designing state feedback controller of the system based on the obtained results. Simulations show the feasibility and efficiency of the proposed methods.