Risk-sensitive filtering for discrete-time systems with time-varying delay

In this paper, the risk-sensitive filtering problem with time-varying delay is investigated. The problem is transformed into Krein space as an equivalent optimisation problem. The observations with time-varying delays are restructured as ones with multiple constant delays by defining a binary variable model with respect to the arrival process of observations, containing the same state information as the original. Finally, the reorganised innovation analysis approach in Krein space allows the solution to the proposed risk-sensitive filtering in terms of the solutions to Riccati and matrix difference equations.     

Swarm stability for high-order linear time-invariant singular multi-agent systems

Swarm-stability and swarm-stabilisation problems for high-order linear time-invariant singular multi-agent systems with directed networks are investigated. First, necessary and sufficient conditions for swarm stability and asymptotic swarm stability are proposed, which are independent of the dimensions of Jordan blocks of the Laplacian matrix of the interaction topology. Then, an approach is given to determine the absolute motion as a whole, and it is shown that the absolute motion is completely determined by initial states if the interaction topology is balanced. Furthermore, an approach is presented to determine gain matrices for asymptotic swarm stabilisation. Moreover, leader-following swarm-stability and swarm-stabilisation problems are investigated. Finally, numerical examples are given to demonstrate theoretical results.     

Singular perturbation analysis of a flexible beam used in underwater exploration

This article focuses on the analysis of a flexible beam based on two approaches of singular perturbations and feedback linearisation. First, a model is obtained for a flexible beam consisting of flexible joints and actuators for underwater positioning and/or tracking control leading to a singularly perturbed structure based on the slow phenomena due to the rigid portion and fast phenomena due to the flexible part of the system. Next, two ways are given for introducing the small parameter responsible for time-scale behaviour, one using a separate small parameter for each beam joint and beam link and the second using a single small parameter with appropriate scaling. Using the singular perturbation approach, the original systems are decoupled into slow and fast subsystems. The main objective is to use a feedback linearisation approach and design a proportional-integral-derivative computed-torque, composite (slow and fast) controller for improving the tracking performance. An illustrative example is provided.     

模型的快速降阶技术

为快速进行模型的降阶,结合平衡截断（Balanced Truncation,BT）方法和特征正交分解（Proper Orthogonal Decomposition,POD）方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解（Singular Value Decomposition,SVD）提取BT＋POD模态,对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶模型（Reduced Order Model,ROM）;该模型就成为全阶模型（Full Order Model,FOM）的ROM.通过对阶数n=406的LTI SISO系统和阶数n=9的2区间电力系统进行的验证表明,在保留BT方法输入输出平衡特性的基础上,该方法效率高于BT方法.     

线性广义系统基于一般形式观测器的严格耗散控制

本文主要研究线性广义系统基于一般形式状态观测器的严格耗散控制器的设计问题,其中关于状态观测器需要同时设计3个系数矩阵.利用线性矩阵不等式方法,分别得到了满足要求的状态观测器及严格耗散控制器的存在条件及设计方法,保证观测器能够渐近地跟踪系统状态并且闭环广义系统容许且严格耗散.最后给出两个数值算例说明本文设计方法的有效性.     

一类具有漂移、扩散及停时的奇异型随机控制

以随机分析的知识和最优控制理论为基础,推广了一类带停时的奇异型随机控制中的折扣费用模型,主要在受控状态过程中增加了漂移因子和扩散因子,使其为一随机微分方程的解,并将费用函数一般化.通过求解一组变分方程,证明了最优控制及最优停时的存在性,并给出了最优费用函数的解析表达式.     

基于时标分离的飞行器姿态双环控制器设计方法

基于时标分离思想,将飞行器姿态控制系统分为慢变化的姿态角回路和快变化的角速度回路分别设计。外环采用精确线性化方法设计控制器。考虑到飞行器转动惯量的大范围时变或摄动,内环采用模型参考自适应控制方法设计控制器。仿真验证了方法的有效性。     

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.     

基于时频空间奇异值分解的多分量线性调频信号分离与增强

针对加性色噪声背景下的多分量线性调频信号的分离和增强问题,提出了一种新的基于时频空间奇异值分解的算法,该方法对加性噪声有较好的抑制能力.同时,对于线性调频信号的最佳分数阶傅里叶变换域估计问题提出了在低信噪比下更为有效的基于信号四阶分数阶傅里叶变换中心矩的方法.仿真实验证明了本文方法的有效性.     

基于奇异谱分析与PSO优化SVM的混凝土坝变形监控模型

针对混凝土坝自动化变形监测数据存在噪声成分,且变形与环境影响因素间呈现出复杂的非线性关系等问题,提出了基于奇异谱分析(SSA)与粒子群算法(PSO)优化支持向量机(SVM)的混凝土坝变形监控模型。模型利用SSA对实测变形进行分解,提取其蕴含的趋势与周期性成分并对变形加以重构;在此基础上,采用基于PSO优化的SVM对重构变形与环境影响因素间复杂的非线性函数关系进行挖掘。实例验证结果表明,该模型具有较好的拟合与预测精度,可以有效地挖掘实测变形蕴含的数据特征,减小噪声成分对建模精度的影响,具有一定的工程应用价值。