基于谱分解的中立型延时系统控制器设计

针对线性中立型延时系统, 提出一种基于算子半群谱分解理论的控制器设计方法. 在中立型项的范数小于1的情况下, 利用谱理论并结合投影算子, 将系统无穷维解空间分解为有限维不稳定广义特征子空间和无限维稳定子空间的直和. 通过对有限维子系统的研究, 得到系统状态反馈控制律, 并通过投影算子证明了状态反馈控制闭环系统的渐近稳定性. 最后数值例子验证了所提方法的有效性.     

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.     

基于观测器的移动执行器对二维分布参数系统的控制

研究二维分布参数系统在传感器执行器网络下的控制问题.传感器执行器网络由二维平面上固定的传感器与移动的执行器组成.首先,利用传感器对二维分布参数系统的测量信息设计观测器,用来估计二维分布参数系统的状态,并在观测器的基础上给出相应的控制器;然后,利用算子半群理论并结合Lyapunov方法,得到平面上移动的执行器的水平运动速度和垂直运动速度,该速度依赖于观测器的信息;最后,数值仿真表明,二维分布参数系统在该移动执行器控制下的性能得到了有效的提高.     

Hilbert空间中广义分布参数系统的精确能控性

首先,应用泛函分析和算子理论研究了Hilbert空间中广义算子半群的一些性质,并应用广义算子半群理论给出了Hilbert空间中广义分布参数系统的解的存在唯一性及解的构造性表达式;其次,应用泛函分析及广义算子半群理论讨论了Hilbert空间中广义分布参数系统的精确能控性。给出了精确能控的必要及充分条件。说明了广义分布参数系统精确能控性和稳定性之间的关系。所得结果对广义分布参数的研究有重要的理论意义。     

Lurie广义系统基于观测器的控制器设计

研究了Lurie广义系统基于状态观测器的控制器设计问题.通过使用Lyapunov稳定性理论,线性矩阵不等式方法,分别给出了状态反馈控制器和观测器的设计方法,并建立了分离原理,进而得到了基于观测器的控制器设计方法.所得结论对广义系统理论本身的发展和实际应用都有非常重要的意义.最后给出了仿真实例.     

基于移动传感器/执行器网络的时滞分布参数系统镇定控制

考虑一类基于移动传感器/执行器网络具有状态时滞的分布参数系统,在系统中加入扰动因子,分析移动传感器/执行器的动力学行为,研究系统出现扰动时如何设计反馈控制器和移动控制力.首先利用无穷维抽象发展方程理论将时滞分布参数系统在Hilbert空间中进行方程演变;其次,结合工程实际应用进行合理的假设以便于问题的解决;接着利用算子半群理论,通过Lyapunov稳定性定理证明系统的状态在反馈控制器的作用下能够趋于稳态,且系统在移动控制力的作用下渐近稳定;最后,通过数值仿真实验表明所设计控制策略的有效性.     

基于多重分形和小波变换的声目标信号特征提取

研究了基于关联积分的广义维数谱的定量计算方法,提出了声目标信号的多重分形特 征,并对其特征即广义维数谱的有效性进行了分析;同时利用小波变换分析既能反映信号在变 换域特性又保留其时域信息的特点,提出基于小波变换的子空间能量及主要能量集中子空间时 域信息的特征提取方法,并通过模糊神经网络识别系统对声目标信号的广义维数谱、子空间能 量及时域信息的组合特征进行了验证.     

中立型非线性不确定时滞系统的控制器设计

研究了一类中立型非线性不确定时滞系统的稳定性分析和状态观测器设计问题,系统包含状态时滞和非线性不确定性,基于Lyapunov稳定性理论,给出了该类时滞系统在非线性不确定性满足增益有界的条件下状态观测器存在的充分条件,并通过线性矩阵不等式(LMI)方法构造得出基于状态观测器的动态输出反馈控制器,最后给出一个数值算例验证了本文结果的有效性.     

基于双曲方程特征分解的水生态数据挖掘

提出一种基于非线性双曲方程广义特征分解的离群数据挖掘方法,并应用于大型分布式数据库离群数据挖掘。采用广义特征分解的方法求解数据集的离群因子,求解非线性双曲方程广义特征Taylor展开。对离群数据的线性部分进行隐格式逼近,对非线性部分进行显格式逼近,挖掘到的离群数据深度和方位信息。构建水生态环境并进行仿真实验。实验结果表明,该算法在对大型分布式数据库的离群数据挖掘中,能很好地挖掘到离群数据张成子空间谱信息,具有较好的数据特征挖掘性能。     

单变量控制系统设计的多项式方法(二)

三 基本原理在这一节里,我们介绍单输入单输出的线性控制系统理论中的状态反馈,kx-观测器、kx-降维观测器、动态反馈、跟踪系统、抗干扰系统、最优状态反馈、最优状态估计、最优随机控制等问题的多项式表示法。我们将看到,上述这些问题均可化成求解多项式方程及多项式谱分解方程的问题。     

Quadratic optimal control of stable systems through spectral factorization

We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, because such time delays force both the control operator and the observation operator to be unbounded at the same time. In order to be able to include this case we take an alternative approach. We work in an input-output framework, and reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. In a standard shift semigroup realization this amounts to factorizations of the Riccati operator and the feedback operator into convolution operators and projections. Our approach leads to a new significant discovery: in the case where the impulse response of the system contains discrete time delays, the standard Riccati equation is incorrect; to get the correct Riccati equation the feed-through matrix of the system must be partially replaced by the feed-through matrix of the spectral factor. This means that, before it is even possible to write down the correct Riccati equation, a spectral factorization problem must first be solved to find one of the weighting matrices in this equation.     

Boundary and Distributed Control for a Nonlinear Three‐Dimensional Euler‐Bernoulli Beam Based On Infinite Dimensional Disturbance Observer

Control problems in spatially distributed systems are challenging because the disturbance is of infinite dimensions. To this end, this paper discusses an infinite dimensional disturbance observer design, which is illustrated based on a partial differential equation (PDE) model of a nonlinear three‐dimensional Euler‐Bernoulli beam. The basic idea of the observer design is to modify the estimations based on the difference between the estimated output and actual output. Moreover, an auxiliary parameter system is established to help with the analysis. Then a Lyapunov function candidate consisting of the energy of the system, the observer error and an auxiliary term is given. After a series of analyses of the function, distributed controllers and boundary controllers based on the proposed observer are given to restrain vibration. Finally, by numerical simulations, the convergence of the observer is demonstrated, and the efficacy of control performance is also shown.     

Observer theory for distributed-parameter systems

This paper examines the problem of the approximate reconstruction of the unknown state variables in distributed-parameter systems. New results on the observer theory for important classes of linear and non-linear operator, partial differential, and partial differential-integral equations in describing distributed-parameter systems are presented. The specific developments employ the recent results on Lyapunov stability theory, along with the theory of linear and non-linear semigroup operators, and their infinitesimal generators. The questions of observability, stability of the state reconstruction error dynamics associated with the proposed observer structure are discussed. The theoretical results are illustrated with some applications to problems of the kinetic lumping of complex distributed-parameter chemical reaction systems, as well as the observer design for linear and non-linear distributed-parameter diffusion systems.     

Uniform controllability of semidiscrete approximations of parabolic control systems

Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the present paper, under the main assumptions that the discretized semigroup is uniformly analytic, and that the control operator is mildly unbounded, we prove that the semidiscrete approximation models are uniformly controllable. Moreover, we provide a computationally efficient way to compute the approximation controls. An example of application is implemented for the one- and two-dimensional heat equation with Neumann boundary control.     

Infinite dimensional and reduced order observers for Burgers equation

Obtaining a representative model in feedback control system design problems is a key step and is generally a challenge. For spatially continuous systems, it becomes more difficult as the dynamics is infinite dimensional and the well known techniques of systems and control engineering are difficult to apply directly. In this paper, observer design is reported for one-dimensional Burgers equation, which is a non-linear partial differential equation. An infinite dimensional form of the observer is demonstrated to converge asymptotically to the target dynamics, and proper orthogonal decomposition is used to obtain the reduced order observer. When this is done, the corresponding observer is shown to be successful under certain circumstances. The paper unfolds the connections between target dynamics, observer and their finite dimensional counterparts. A set of simulation results has been presented to justify the theoretical claims of the paper.     

Active Vibration Control for a Flexible‐Link Manipulator with Input Constraint Based on a Disturbance Observer

This paper mainly focuses on designing an active vibration control for a flexible‐link manipulator in the presence of input constraint and unknown spatially infinite dimensional disturbances. The manipulator we studied can be taken as an Euler–Bernoulli beam, the dynamic model of which has the form of partial differential equations. As the existence of spatially infinite dimensional disturbances on the beam, we first design a disturbance observer to estimate infinite dimensional disturbances. The proposed disturbance observer is guaranteed exponentially stable. Then, taking input saturation into account, a novel disturbance‐observer‐based controller is developed to regulate the joint angular position and rapidly suppress vibrations on the beam, which is the main contribution of this study. The closed‐loop system is validated asymptotically stable by theoretical analysis. The effectiveness of the proposed scheme is demonstrated by numerical simulations.     

挠性智能梁的振动控制

研究采用共位配置的压电敏感器和致动器的挠性是臂梁的振动控制问题,建立了智能梁的模型,设计了一种线性反馈控制律,并应用无空维空间的ＬａＳａｌｌｅ不变原理和线性半群理论证明了当敏感器和控制器的分布使得系统能镇条件成立时,所设计的控制抑制了梁的振动。     

Low dimensional disturbance observer‐based control for nonlinear parabolic PDE systems with spatio‐temporal disturbances

In this paper, a design problem of low dimensional disturbance observer‐based control (DOBC) is considered for a class of nonlinear parabolic partial differential equation (PDE) systems with the spatio‐temporal disturbance modeled by an infinite dimensional exosystem of parabolic PDE. Motivated by the fact that the dominant structure of the parabolic PDE is usually characterized by a finite number of degrees of freedom, the modal decomposition method is initially applied to both the PDE system and the PDE exosystem to derive a low dimensional slow system and a low dimensional slow exosystem, which accurately capture the dominant dynamics of the PDE system and the PDE exosystem, respectively. Then, the definition of input‐to‐state stability for the PDE system with the spatio‐temporal disturbance is given to formulate the design objective. Subsequently, based on the derived slow system and slow exosystem, a low dimensional disturbance observer (DO) is constructed to estimate the state of the slow exosystem, and then a low dimensional DOBC is given to compensate the effect of the slow exosystem in order to reject approximately the spatio‐temporal disturbance. Then, a design method of low dimensional DOBC is developed in terms of linear matrix inequality to guarantee that not only the closed‐loop slow system is exponentially stable in the presence of the slow exosystem but also the closed‐loop PDE system is input‐to‐state stable in the presence of the spatio‐temporal disturbance. Finally, simulation results on the control of temperature profile for catalytic rod demonstrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of finite dimensional robust H ∞ distributed consensus filters for dissipative PDE systems with sensor networks

This paper presents a design method of finite dimensional robust H _∞ distributed consensus filters (DCFs) for a class of dissipative nonlinear partial differential equation (PDE) systems with a sensor network, for which the eigenvalue spectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement. Initially, the modal decomposition technique is applied to the PDE system to derive a finite dimensional ordinary differential equation system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Then, based on the slow subsystem, a set of finite dimensional robust H _∞ DCFs are developed to enforce the consensus of the slow mode estimates and state estimates of all local filters for all admissible nonlinear dynamics and observation spillover, while attenuating the effect of external disturbances. The Luenberger and consensus gains of the proposed DCFs can be obtained by solving a set of linear matrix inequalities (LMIs). Furthermore, by the existing LMI optimization technique, a suboptimal design of robust H _∞ DCFs is proposed in the sense of minimizing the attenuation level. Finally, the effectiveness of the proposed DCFs is demonstrated on the state estimation of one dimensional Kuramoto–Sivashinsky equation system with a sensor network. Copyright © 2014 John Wiley & Sons, Ltd.