基于LPV 方法的Stewart 平台关节空间分散控制

为了提高Stewart 平台关节空间分散控制系统的性能,提出一种基于线性变参数(Linear Parameter Varying,LPV) 方法的控制策略．首先建立了平台关节空间动力学模型;通过分析平台惯性矩阵,指出单支路 子系统等效负载变化以及子系统间的耦合干扰是分散控制需要处理的主要问题．然后将平台惯性矩阵分解为 一个对角阵与一个耦合阵之和,子系统间耦合作用视为对单支路的干扰,从而得到每个子系统的动力学方程． 最后针对子系统等效负载随着上平台运动而在较大范围内变化的特点,引入LPV 控制方法,使控制器参数能 够适应子系统负载变化,减少了保守性．仿真结果表明了所提方法的有效性．     

大系统块对角优分解

以系统状态方程为模型,提出将系统矩阵Ａ块三角分散后,通过非平衡补偿使其具有块对角优形式的分解该当。仿真实例证明该方法是可行的,它可简化模型为块对角型,为大系统分散控制设计与实现及并行处理提供了实用手段。     

干扰观测器补偿的四旋翼块对角控制器

针对四旋翼无人机大机动、强非线性、强耦合、多变量、易受外界干扰的特点,并考虑到其模型符合块对角结构,设计了干扰观测器补偿的块对角控制器.首先,针对前四个特点,并结合模型的特殊块对角结构,提出采用块对角理论对飞行控制器进行设计.然后,为提高块对角控制器的综合性能,提出将混合线性设计策略应用到控制器设计中.最后,为提高其在...     

有向网络下线性多个体系统的整体行为—–矩阵方法

研究了有向通讯网络条件下一阶和二阶线性多个体协同动力学系统整体行为的矩阵代数性质.利用矩阵分析的方法将系统的系数矩阵变换为Frobenius标准型,由此将系统分解为独立基本子系统和非独立基本子系统的组成结构.通过研究行和为零的对角占优矩阵的性质,得出了对线性多个体协同动力学系统整体行为起决定作用的系数矩阵的性质,从而将这一问题转换为普通线性代数问题.     

具有多图拓扑结构的同类智能体LQR控制

本文考虑具有一般线性时不变动态特性的多智能体系统优化控制问题. 将智能体之间的通讯拓扑结构建模成具有自环的无向多图, 每个子系统就是一个节点, 每个节点的控制行为只与本身及邻居节点有关. 由于反馈矩阵具有块对角结构约束, 本文研究的LQR控制问题本质上是一类结构优化问题. 最小化系统LQR性能指标等价于最小化单个智能体性能指标和. 基于线性矩阵不等式得到系统的次优性能指标, 指出LQR性能域是凸集. 由此多智能体系统的LQR控制转化为若干个子系统的LQR控制, 可以通过求解系数是Laplacian矩阵最小最大特征值的两个矩阵不等式得到反馈增益. 数值例子验证了方法的有效性.     

关联大系统的分散H∞/LTR控制

讨论关联大系统分散回路传递再生的设计问题.利用矩阵的奇异值分解技术,提出了对关联项进行块对角化处理的一种新方法.基于H∞理论,将多变量系统的回路传递再生方法推广于分散控制关联大系统,并避免了在所有可能的分散观测器增益构成的集合上,直接计算再生矩阵的H∞范数下确界的困难.     

基于扩张状态观测器的分散模型预测控制

针对复杂关联系统中分散控制方法无法有效解决子系统间的耦合和干扰问题, 提出一种基于扩张状态观测器的分散模型预测控制算法. 首先将复杂关联系统分解为多个状态维数较低、控制变量较少的子系统, 并为每个子系统设计本地预测控制器; 然后, 采用扩张状态观测器对子系统的耦合项以及干扰项进行估计, 进而利用估计值对子系统进行前馈补偿, 从而降低复杂关联系统的计算复杂度, 提高系统的稳定性和抗干扰能力; 最后, 利用液位控制系统验证了所提出算法的有效性.

     

空间连接系统的稳定与镇定

研究连续时间线性时不变空间连接系统的稳定性分析与镇定控制器设计问题,其具有不同动态特性的子系统之间的连接关系为任意且时不变的.推导空间连接系统稳定性分析易于计算的充分必要条件,并给出系统稳定的基于单个子系统参数的充分条件和必要条件;在此基础上,进行基于单个子系统状态反馈的镇定控制器设计.所提方法能够避免高维矩阵的求逆等运算,而且充分利用了系统参数矩阵的块对角结构和子系统连接矩阵的稀疏特性.仿真结果显示,所得到的条件在大规模网络化系统的分析与综合中,计算效率有很大的提高.     

基于包含原理一般动态互联系统的分解与分散控制

针对一般结构互联系统的动态变化, 通过系统结构的描述, 以包含原理的多重叠分解为基础, 构建出适用于一般结构互联系统对对分解与重叠分散控制的扩展收缩变换矩阵、置换矩阵及相关的补偿矩阵; 然后根据所提出的子系统对的删除与添加方式, 构建出相应的删除矩阵与添加矩阵, 并将两者结合得到用于完成结构变化后的互联系统对对分解与重叠分散控制的结构变化矩阵, 从而实现具有一般动态结构互联系统的分解与分散控制; 最后以四区域互联电力系统AGC为例对其进行详细说明.

     

动力学解耦的平面多自由度机构的设计

本文以简化动力学方程为目标提出了多自由度平面机构的设计方法。首先在开环机构上增加杆组得到相同自由度的闭环机构，进而设计杆组的质量和质心位置使闭环机构的惯性矩阵为对角阵，达到使动力学方程解耦的目的。该设计思想适用于任意自由度机构。本文从这一思想出发提出一种并行驱动的三自由度平面机构，其惯性矩阵不难设计成常量对角阵。由于这一特性，所提机构可望用于高速机器人。     

一类特殊系统的三对角解耦控制研究

针对一类典型的多变量耦合三对角工业系统,在研究（块）三对角矩阵计算的基础上,提出了一种新的三对角解耦算法。该算法关键在于构造两补偿矩阵,即前串联补偿阵L（s）和后串联补偿阵R（s）,从而使耦合三对角工业系统变为对角系统,实现解耦。考虑到三对角工业系统次对角线上可能存有零传递函数分量,在此讨论了两种L（s）和R（s）的构造算法。经仿真不仅证实了方法的有效性,而且得出了构造的L（s）和R（s）具有多分量相等的特点,这将大大减轻其在工业实现方面的工作量。     

块对角占优性与对称矩阵的块对角预条件

§1.引言 稀疏线性方程组的求解在科学计算与工程应用中非常重要。在材料模拟与设计、电磁场计算、计算流体力学和核爆数值模拟等领域中经常要求解微分方程,并通过有限元或有限差分与有限体积等方法进行离散,化为非线性方程组或稀疏线性方程组。非线性方程组的求解     

A method for computation of the discrete Fourier transform over a finite field

The discrete Fourier transform over a finite field finds applications in algebraic coding theory. The proposed computation method for the discrete Fourier transform is based on factorizing the transform matrix into a product of a binary block circulant matrix and a diagonal block circulant matrix.     

Dynamic simplification of three degree of freedom manipulators with closed chains

A method is presented for designing manipulators to have simplified dynamics. It is based on adding a link group to an open kinematic chain to form a closed chain without changing the degrees of freedom of the open chain. The mass property of the link group is designed to make the closed chain have a diagonal inertia matrix. The conditions of mass distribution are derived under which the inertia matrices become diagonal. The advantage of the proposed method is that the manipulator dynamics can be treated as a decoupled linear system thereby greatly simplifying the control implementation. As examples of the technique we apply it to the design of a 3 DOF planar manipulator and a 3 DOF spatial manipulator.     

Small gain problem in coupled differential‐difference equations,time‐varying delays,and direct Lyapunov method

This article presents a Lyapunov–Krasovskii formulation of scaled small gain problem for systems described by coupled differential‐difference equations. This problem includes H_∞ problem with block‐diagonal uncertainty as a special case. A discretization may be applied to reduce the conditions into linear matrix inequalities. As an application, the stability problem of systems with time‐varying delays is transformed into the scaled small gain problem through a process of either one‐term approximation or two‐term approximation. The cases of time‐varying delays with and without derivative upper‐bound are compared. Finally, it is shown that similar conditions can also be obtained by a direct Lyapunov–Krasovskii functional method for coupled differential‐functional equations. Numerical examples are presented to illustrate the effectiveness of the method in tackling systems with time‐varying delays. Copyright © 2010 John Wiley & Sons, Ltd.     

LMI optimization approach to robust decentralized controller design

A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

压缩感知二进制测量矩阵的构造

针对现有二进制测量矩阵重构性能和硬件实现的负相关性,提出了一种新型压缩感知二进制测量矩阵,伪随机块对角矩阵(PRBD)。PRBD矩阵使用平衡正交Gold序列、块对角矩阵和降采样矩阵,通过结构化的方法构造,不仅保留了确定性矩阵易于硬件实现和计算复杂度低的优点,而且利于贪婪追踪算法进行图像重构。实验结果表明,PRBD测量矩阵具有良好的重构性能,在峰值信噪比(PSNR)的指标上比常用的二进制测量矩阵提高0.5dB以上。特别地,PRBD测量矩阵可采用图像分块重构的方法,在保证重构性能良好的情况下,图像重构需要的时间较短。     

一种基于DCT和SVD的音频水印算法

提出一种基于离散余弦变换(DCT)和奇异值分解(SVD)的音频水印算法.该算法将原始音频进行分段后再分块,对每一块进行DCT 变换,利用Zig-Zag算法将变换后的系数分成4个象限,通过对每个象限进行SVD变换得到对角阵,并在对角阵的第1个元素内嵌入水印.实验结果证明,该算法具有良好的透明性,在嵌入强度为0.2时峰值信噪比较高,同时可以抵抗重采样、回声、噪声等攻击,具有较高的鲁棒性.     

An efficient preconditioned iterative solver for solving a coupled fluid structure interaction problem

Modelling the interaction of an acoustic field in a fluid and an elastic structure submerged in the fluid leads to a system of complex linear equations with a complicated sparsity structure and, for higher wavenumbers and adequate modelling, the systems are very large. Direct methods are not practical. Preconditioned iterative methods, which are suitable for single operator equations, are not immediately applicable to the coupled case. This article proposes a block diagonal preconditioner of the sparse approximate inverse (SPAI) type that can accelerate the convergence of Krylov iterative solvers for the coupled system. Moreover, the proposed preconditioner can properly and implicitly scale the coupled matrix. Some numerical results are presented to demonstrate the effectiveness of the new method.     

Global optimization for robust control synthesis based on the Matrix Product Eigenvalue Problem

In this paper, we propose a new formulation for a class of optimization problems which occur in general robust control synthesis, called the Matrix Product Eigenvalue Problem (MPEP): Minimize the maximum eigenvalue of the product of two block‐diagonal positive‐definite symmetric matrices under convex constraints. This optimization class falls between methods of guaranteed low complexity such as the linear matrix inequality (LMI) optimization and methods known to be NP‐hard such as the bilinear matrix inequality (BMI) formulation, while still addressing most robust control synthesis problems involving BMIs encountered in applications. The objective of this paper is to provide an algorithm to find a global solution within any specified tolerance ε for the MPEP. We show that a finite number of LMI problems suffice to find the global solution and analyse its computational complexity in terms of the iteration number. We prove that the worst‐case iteration number grows no faster than a polynomial of the inverse of the tolerance given a fixed size of the block‐diagonal matrices in the eigenvalue condition. Copyright 2001 © John Wiley & Sons, Ltd.