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.     

双回路复杂波网络的镇定

本文研究双回路的复杂波网络系统,主要探索带回路系统的控制问题,通过设计反馈控制器使得闭环系统稳定.同时借助于谱分析方法讨论了相应闭环系统算子谱的分布情况并证明了系统算子的(广义)本征向量构成状态空间上的一组加括号Riesz基,得到了闭环系统特征模态的展开.     

弹性梁点控制、点测量与指数镇定

运用近年来发展的基理论对弹性梁点测量、点控制做一个系统的处理, 得到了用速度线性反馈可实现系统的指数镇定的条件且指数镇定当且仅当系统精确可控, 在指数镇定的情况下闭环系统的广义本征函数生成能量空间的Riesz基且谱确定增长条件成立.     

串联弦系统的控制器和补偿器的设计及其Riesz基

针对一类串联弦系统,在两端自由,内部连接点处力连续而位移不连续的条件下,论文先在内部连接点处构造补偿器对位移进行补偿,然后在两端设计控制器对系统进行控制.于是得到一个闭环控制系统.利用半群理论证明了这一系统的适定性.通过算子的谱分析,推出了该系统的谱由重数有限的孤立本征值构成并且谱分布在左半复平面,平行于虚轴的一个带域内.因此该系统存在Riesz基,满足谱确定增长条件并且是渐近稳定的.     

广义动态系统的微分算子矩阵方法

本文用微分算子矩阵方法讨论了一类广义动态系统的结构性质,并且用微分算子多项式 矩阵的系数阵,给出了各类动态系统能控(观)性的直接判据.它是用微分算子矩阵方法研究 广义动态系统的开端.     

多维分段广义正交多项式算子及其在分布参数系统辨识中的应用

在一维分段广义正交多项式的基础上，提出多维分段广义正交多项式及其相应的正交多项式算子的定义，总结归纳了多维分段广义正交多项式算子的基本性质和主要运算规则，并将二维分段广义正交多项式算子法应用于一类非线性分布参数系统的辨识，数值算例表明，即使在存在量测噪声的情况下，使用较小的分段数和正交基项数也能得到较好的辨识效果。     

基于广义径向基函数的神经网络分类预测

径向基函数网络是神经网络中一种广泛使用的设计方法.它把神经网络的设计看作是一个高维空间的曲线逼近问题.相对于其他的神经网络方法.径向基函数神经网络除了具有一般神经网络的优点,如多维非线性映射能力、泛化能力、并行信息处理能力等,还具有很强的聚类分析能力,学习算法简单方便等优点.针对一个实际分类问题,利用广义径向基函数网络的思想训练一个网络并实现对测试数据集的分类预测.本算法采用k-均值聚类算法训练广义径向基函数网络中心,使用奇异值分解计算输出层权值.对该网络的实现细节及待改进之处进行简要分析.实验表明广义径向基函数神经网络的思想具有很强的聚类分析能力,学习算法简单方便等优点.     

基于多重广义算子的复杂网络建模方法的研究

复杂网络的研究显示,不同系统在经历时空演化从最初简单状态涌现出同样结构特征的现象.针对不同的内在结构却表现出同样外部特征的特点,比较符合于广义算子模型的研究思路.提出一种适合复杂网络的普适建模方法,在分析融合多重广义算子模型和复杂网络的研究成果基础上,将广义算子模型应用于复杂网络的建模中.建模过程采用“分解-联结”的方式.首先根据系统的结构特征进行分解,分别建立广义算子和关系算子,然后联结形成复杂网络的广义算子模型.最后可用于Internet的建模中,证明了模型的简单性、灵活性和有效性.     

Riesz回火分数阶平流-扩散方程的隐式中点方法

本文针对Riesz回火分数阶平流-扩散方程,采用隐式中点方法离散一阶时间偏导数,用修正的二阶Lubich回火差分算子逼近Riesz空间回火分数阶偏导数,并对平流项采用中心差商进行离散,构造出新的数值方法,获得了数值方法的稳定性和收敛性,该方法的收敛阶在空间和时间方向均达到二阶精度.数值试验验证了数值方法的有效性.     

主被动关节柔性树形机器人系统动力学建模与仿真

进一步完善空间算子代数理论体系,研究了带有主被动关节的树形柔性机器人系统符号动力学高效率建模的方法.利用拓扑结构和低序体阵列的方法描述了树型机器人系统.采用空间算子研究了欠驱动树型多体系统的描述方法.根据系统中铰的驱动情况分别对铰链定义为主动铰和被动铰,建立树形机器人系统的运动学,然后通过铰链的类型分别按照两次从系统的顶端到基座的顺序、一次从基座到顶端的顺序进行了系统铰接体惯量的递推、系统冗余力的递推、广义加速度和广义主动力的递推,最后将分叉处的广义力和广义加速度矢量相加得到树形机器人系统的广义动力学模型.通过上述递推过程建立动力学模型,实现了高效率O(N)(N为系统自由度)次的计算效率.最后以加拿大树形空间机械臂为例做仿真验证了本研究内容的正确性和高效性.     

Riesz bases and exact controllability of C0-groups with one-dimensional input operators

This paper considers linear infinite dimensional systems with C₀-group generators and one-dimensional admissible input operators. The exact controllability and Riesz basis generation property are discussed. The corresponding results of Jacob and Zwart (Advances in Mathematical Systems Theory, Birkhäuser, Boston, MA, 2000) under the assumption of algebraic simplicity for eigenvalues of the generator are generalized to the case in which the eigenvalues are allowed to be algebraically multiple but with a uniform bound on the multiplicity.     

Identification of finite dimensional models of infinite dimensional dynamical systems

The identification of finite dimensional discrete-time models of deterministic linear and nonlinear infinite dimensional systems from pointwise observations is investigated. The input and output observations are used to construct finite dimensional approximations of the solution and the forcing function which are expanded in terms of a finite element basis. An algorithm to determine a minimal basis to approximate the data is introduced. Subsequently, the resulting coordinate vectors are used to identify a finite dimensional discrete-time model. Theoretical results concerning the existence, stability and convergence of the finite dimensional representation are established. Numerical results involving identification of finite dimensional models for both linear and nonlinear infinite dimensional systems are presented.     

Flatness-based trajectory planning for diffusion–reaction systems in a parallelepipedon—A spectral approach

Spectral analysis is considered for the flatness-based solution of the trajectory planning problem for a boundary controlled diffusion–reaction system defined on a 1≤r-dimensional parallelepipedon. By exploiting the Riesz spectral properties of the system operator, it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output, which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order. Their convergence is verified for both infinite-dimensional and finite-dimensional actuator configurations by restricting the basic output to certain Gevrey classes involving non-analytic functions. With this, a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite-time transitions between stationary profiles.     

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.     

On input/output maps for nonlinear systems via continuity in a locally convex topology

In this paper we show that the output of a nonlinear system with inputs in ( ) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results.     

On the L2-gain of a double integrator with feedback loopsaturation nonlinearity

We consider the open problem of whether there exists finite L₂ gain in each channel of a double integrator in feedback interconnection with a saturation nonlinearity. It has been shown by Liu-Chitour-Sontag (1996) that the L₂ gain from input to the output of the first integrator is infinite. In this paper, by constructing a special excitation, we show that the L₂ gain from input to the output of the second integrator is also infinite     

Stabilization of strict‐feedback nonlinear systems with input delay using closed‐loop predictors

In this paper, we consider the control problem of strict‐feedback nonlinear systems with time‐varying input and output delays. The approach is based on the usual observer/predictor/feedback approach, but the novelty is the use of the closed‐loop dynamics in the predictor. This approach allows to develop two designs, an instantaneous predictor and a delay differential equation‐based predictor, that both attain the same performance in terms of system trajectories and input signal as in the case with no delays. The design based on delay differential equations allows to build a cascade of predictors to deal with arbitrarily large delay bounds. The resulting controller is much simpler to implement than classical infinite‐dimensional predictors, and it is robust with respect to actuation and measurement disturbances. We illustrate the approach with an application to the control of a chaotic system with input delay. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust controller design for infinite‐dimensional exosystems

In this paper, we consider robust output regulation of distributed parameter systems with infinite‐dimensional exosystems capable of generating polynomially growing signals. We design an observer‐based error feedback controller solving the control problem. The controller is chosen in such a way that it incorporates an internal model of the infinite‐dimensional exosystem. The remaining parameters of the controller are chosen to stabilize the closed‐loop system strongly. We also analyze the classes of signals generated by the exosystem. In particular, we explore the connection between the smoothness properties of the reference and disturbance signals and the strictness of the conditions required for the existence of a controller solving the robust output regulation problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Output Regulation for a Class of Infinite Dimensional Systems with an Unknown Exosystem

This paper is about solving the output regulation problem for a class of infinite dimensional systems with an unknown exosystem. First, under the unit relative degree assumption, the infinite dimensional system is decomposed into a cascaded one composed of a one‐dimensional system and an infinite dimensional system. Then, the problem is solved by combining an adaptive internal model and an adaptive control. The presented results are illustrated via a periodic tracking problem of a heat equation.     

Sufficient and necessary conditions for the solvability of the state feedback regulation problem

In this paper, we discuss the state feedback output regulation problem (SFRP) for infinite‐dimensional linear control systems with infinite‐dimensional exosystems. Under the polynomial stabilizability assumption, sufficient and necessary conditions are given for the solvability of the SFRP. The solvability of this problem is characterized in terms of the solvability of a pair of linear regulator equations. An application of the solvability of the SFRP for polynomial stable SISO system is given. Copyright © 2013 John Wiley & Sons, Ltd.