线性时滞系统依赖于时滞的H∞状态反馈控制

对具有纯滞后输入的线性时滞系统,在系统的状态时滞与控制输入时滞不同时,研 究了依赖时滞的H∞状态反馈控制器设计问题,其控制器存在的充分条件由一个线性矩阵不 等式(LMI)的形式给出,并给出了相应的H∞控制器的综合设计方法.     

不确定时滞系统保性能弹性控制器的设计

研究了一类不确定时滞系统的保性能控制问题, 其不确定性不仅存在于系统矩阵, 而且存在于控制器的增益中. 在控制器增益摄动具有加法和乘法两种结构形式下, 讨论了系统的弹性保性能控制器设计问题, 给出了弹性保性能控制器存在的充分必要条件. 数值算例说明了设计的可行性和有效性.     

随机不确定时滞系统的鲁棒H∞控制

本文研究了随机不确定时滞系统的鲁棒稳定性与鲁棒H∞控制问题,系统的不确性具有凸多面体形式.利用线性矩阵不等式方法,通过依赖于参数的Lyapunov函数,得到了此类系统鲁棒随机镇定的充分条件.在此基础上,又给出了H∞状态反馈控制器的设计.     

基于主动滑模控制实现一类含有非匹配不确定混沌系统的同步

讨论了一类非匹配不确定混沌系统的同步问题.基于主动控制思想,提出了一种主动滑模控制策略,使得从任意初始条件出发的不确定混沌系统在有限时间内到达滑模面.利用线性矩阵不等式(LMI)技术设计了一个鲁棒稳定的滑模面,以降低非匹配不确定对系统的影响.给出了线性矩阵不等式形式的稳定滑模面存在的充分条件.通过对Rssler系统的同步仿真,验证了该方法的可行性.     

一类不确定时滞系统的非线性H_∞控制

利用Lyapunov稳定性定理和线性矩阵不等式工具,讨论了一类不确定时滞系统的非线性H∞控制问题.设计的非线性H控制器可由线性矩阵不等式的解给出.进一步,建立一个具有线性矩阵不等式约束的凸优化问题,得到了不确定时滞系统的最优状态反馈H控制律,仿真示例表明了该方法的可行性.     

不确定Delta算子切换系统的鲁棒控制研究

研究了一类参数不确定线性Delta算子切换系统的鲁棒H∞控制问题.针对传统采用的Delta算子切换系统仅限于多Lyapunov函数方法,使系统仅实现渐进稳定,收敛速度慢.为了提高控制系统的稳定性,解决系统的状态反馈鲁棒H∞控制的难点问题,首次提出利用多Lyapunov函数和平均驻留时间方法,以线性矩阵不等式的形式给出了参数不确定Delta算子切换系统指数稳定性条件,并进行了H∞性能分析,从而进一步给出系统鲁棒H∞控制器的设计方法.所设计的控制器不但保证系统参数不确定时闭环系统指数稳定,而且满足所期望的H∞性能指标.仿真结果证明了设计方法的有效性和可行性.     

广义系统正实反馈控制的一种新方法

研究了广义连续系统的扩展严格正实的控制问题.首先,利用与原系统等价的增广系统和矩阵分解,给出了广义系统正则,无脉冲,稳定且扩展严格正实的一个新的充分必要条件.并且此条件是便于Matlab求解的严格线性矩阵不等式形式.其次,基于此定理和线性矩阵不等式的性质,给出了保证闭环系统是正则,无脉冲,稳定且ESPR的控制器设计方法.最后通过2个数值算例说明了所提出方法的有效性和可行性.     

二次型耗散线性离散系统的鲁棒性分析与控制

考虑一类不确定离散多变量系统的鲁棒二次型耗散性分析和控制,其中各不确定参数矩阵具有线性分式形式.首先对确定系统建立二次型耗散性与正实性之间的等价关系,由此导出线性系统二次型耗散的充分必要条件;然后证明不确定系统的鲁棒耗散性分析和控制可转化为确定系统的耗散性分析和设计,给出了这类不确定系统鲁棒耗散的充分必要条件以及鲁棒耗散控制问题的线性矩阵不等式解法.所得结果可将H∞控制与正实控制统一起来,提供一种较为灵活、保守性较小的系统设计方法.仿真例子说明了所提方法的有效性.     

具有结构不确定性的时滞系统的最优非脆弱保性能控制

对一类具有结构不确定性的线性时滞系统的最优非脆弱保性能控制问题进行了研究.以线性矩阵不等式的形式给出了设计非脆弱保性能控制律的一个充分条件.然后给出了在使性能指标上界最小的意义下,最优非脆弱保性能控制律的设计算法.最后用例子演示了方法的有效性.     

基于观测器的广义时滞系统弹性保成本控制

在同时考虑系统矩阵参数不确定性和控制器不确定性对系统性能影响的前提下,研究了一类基于观测器的不确定广义时滞系统的弹性保成本控制问题.基于Lvapunov稳定性理论,通过构造广义Lyapunov函数和广义二次性能指标函数,以线性矩阵不等式的形式给出了基于观测器状态反馈的弹性保成本控制器的设计方法.该控制器不仅保证了广义时滞系统是鲁棒稳定而且使其具有相应的性能指标上界.采用一种新方法将系统弹性保成本控制器设计和状态观测器增益矩阵求取转化为两组严格线性矩阵不等式的可行解问题.最后通过算例验证了该方法的可行性和有效性.     

The Effect of System Stochastic Noise on SINS Initial Alignment

捷联惯导系统初始对准系统状态方程所描述的状态统计信息,受系统随机噪声驱动,系统随机噪声通过噪声驱动阵作用于状态。常用系统状态方程的系统噪声驱动阵为单位阵。经过分析发现系统噪声驱动阵为单位阵是有条件的;通过推导给出了系统状态方程可以简化此种形式的条件;指出了在水平陀螺、加速度计随机噪声水平不同时,若使用简化系统模型会引起状态估计误差;并通过单轴旋转多位置对准仿真实验进行了验证。仿真结果表明：若水平陀螺随机噪声水平不同,采用简化模型进行初始对准会引起状态估计误差。     

Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized Sylvester matrix equation

The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system theory.     

改进的强跟踪SVD-UKF算法在组合导航中的应用

针对无迹卡尔曼滤波（Unscented Kalman Filter,UKF）在系统强非线性或状态模型不精确的情况下,存在滤波精度降低甚至发散的问题,提出一种改进的强跟踪SVD-UKF算法。该算法采用奇异值分解（Singular Value Decomposition,SVD）的方法改进UKF中状态协方差矩阵的迭代,保证协方差矩阵的非负定性及迭代的稳定性;算法基于强跟踪滤波（Strong Tracking filter,STF）理论框架,对改进的SVD-UKF引入多重渐消因子自适应调整状态协方差矩阵,在系统状态发生突变的情况下,实现系统真实状态的强跟踪。将该算法在BDS/INS组合导航中仿真验证,结果表明了该算法的有效性。     

Achieving diagonal interactor matrix for multivariable linear systems with uncertain parameters

The notion of interactor matrix or equivalently the Hermite normal form, is a generalization of relative degree to multivariable systems, and is crucial in problems such as decoupling, inverse dynamics, and adaptive control. In order for a system to be input-output decoupled using static state feedback, the existence of a diagonal interactor matrix must first be established. For a multivariable linear system which does not have a diagonal interactor matrix, dynamic precompensation or dynamic state feedback is required for achieving a diagonal interactor matrix for the compensated system. Such precompensation often depends on the parameters of system, and is thus difficult to implement with accuracy when the system is subject to parameter uncertainty. In this paper we characterize a class of linear systems which can be precompensated to achieve a diagonal interactor matrix without the exact knowledge of the system parameters. More precisely, we present necessary and sufficient conditions on the transfer matrix of the system under which there exists a diagonal dynamic precompensator such that the compensated system has a diagonal interactor matrix. These conditions are associated with the so-called (non)generic singularity of certain matrix related to the system structure but independent of the system parameters. The result of this paper is expected to be useful in robust and adaptive designs.     

基于拓扑结构和个体动态层面的多智能体系统可控性分析

针对一般线性多智能体系统中网络拓扑及个体动态这两个层面的可控性对系统整体可控性的关系进行了研究，提出了一种新的描述一般线性多智能体系统的模型。利用PBH(Popov-Belevitch-Hautus)判据，得到并证明了在此模型下多智能体系统可控性在网络拓扑结构与个体动态层面的充要条件。结合具体的例子解释了系统矩阵中出现重复特征值时对定理2充分性的影响，并且提供了一种避免重复特征值出现的方法。特别地，推导出了此模型下系统矩阵为实对称矩阵这一特殊情况时可以判定该系统不可控的两种判定条件，即比较系统矩阵中最大的特征值代数重数与控制矩阵中1元素的个数，满足条件即判定系统不可控。     

Transformations between some special matrices

Special matrices are very useful in signal processing and control systems. This paper studies the transformations and relationships between some special matrices. The conditions that a matrix is similar to a companion matrix are derived. It is proved that a companion matrix is similar to a diagonal matrix or Jordan matrix, and the transformation matrices between them are given. Finally, we apply the similarity transformation and the companion matrix to system identification.     

随机线性系统模型的集结简化

讨论集结法在简化随机线性系统模型中的应用,它可将n维状态空间模型的主要特征集结简化到r维（r〈n）状态空间模型上,优化地再现原系统的基本性能和模裂数据。在简化模型中,动态系统集结矩阵选定为原系统矩阵特征值的子集。这种方法既适用于离散系统,也适用于连续系统。高阶系统动态模型的这种简化处理方法,不仅克服与避免了对这类系统进行仿真分析时,占用较大内存空间与耗费大量机时的缺陷,而且提高厂仿真与控制过程的稳定性和结果的准确性。     

Feedback stabilization of linear autonomous time lag systems

A stabilization theory which employs well-established finite-dimensional control system tools is developed for the stabilization of linear autonomous time lag systems. The main ideas include 1) a set whose elements are matrices each of which is a left zero of the system characteristic quasi-polynomial matrix, and 2) a linear transformation which reduces the delay system to a delay-free system whose state matrix is a direct sum ofNelements of the matrix set whereNis some positive integer. From the definition of this matrix set, it is shown that each of its elements inherits its spectrum from that of the delay system so that by design, the system unstable poles may be embedded in the spectrum of the delay-free system. Under the assumption of spectral stabilizability, it is then shown how to obtain a stabilizing feedback control law on the basis of the delay-free system. Numerical examples are presented to confirm the theory.     

Identification of stable models in subspace identification by usingregularization

In subspace identification methods, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For a finite number of data points, the estimated system matrix is not guaranteed to be stable, even when the true linear system is known to be stable. In this paper, stability is imposed by using regularization. The regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi) definite weighting matrix. The amount of regularization can be determined from a generalized eigenvalue problem. The data augmentation method of Chui and Maciejowski (1996) is obtained by using specific choices for the weighting matrix in the regularization term