Special coordinate basis for multivariable linear systems—finite and infinite zero structure,squaring down and decoupling

A special coordinate basis for multivariable linear systems is introduced here. Several fundamental properties of linear systems regarding controllability (stabiliza-bility), observability (detectability), invariant zeros, decoupling zeros, infinite zero structure, effect of feedback on zero structure, squaring down, diagonal and triangular decoupling etc. can be directly displayed in terms of the special coordinate basis. Moreover, connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established.     

严格线性散播网络编码

针对线性广播和线性散播网络编码在保证节点或节点集解码空间维数方面的不足,提出了一类新的线性网络编码——严格线性散播网络编码.给出了严格线性散播的定义,并设计了相应的构造算法,此种网络编码增强了对网络中任意非源节点集的输入链路上的全局编码核的限制,但其构造所需的有限域的阶并不大于普通的线性散播.此外,还提出了多种转换矩阵的概念,并证明了普通线性散播到严格线性散播的转换矩阵的存在性.结合特殊的数据打包策略,论证了严格线性散播在异构网络中的应用优势:一方面,它能够利用单一网络编码会话实现异构网络中的多速率信息传输;另一方面,它能够为异构网络拓扑结构的扩展提供便利.     

各向同性线性系统理论研究综述

各向同性线性系统作为一类特殊的线性系统,不仅具有广泛的应用背景,还具备许多一般线性系统不具有的特殊性质.鉴于此,系统地归纳总结各向同性线性系统的特点,特别是这类系统与其对应的复系数线性系统之间的关联;此外,讨论对各向同性线性系统设计各向同性反馈的必要性,并以航天器姿态控制系统为例介绍各向同性线性系统的具体应用实例;结合几类常见的可用各向同性线性系统描述的工程控制系统,对现有的相关结果进行归纳和介绍;最后对各向同性线性系统进一步的研究方向进行简单的展望.     

Special decentralized control problems in discrete-time interconnected systems composed of two subsystems

In this paper, some special decentralized control problems are addressed for discrete-time interconnected systems. First it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases. Then a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. In addition, a decentralized controller design method based on linear matrix inequality is also given by using parameter-dependent Lyapunov function method developed for the study of robust stability. A special linear star coupled dynamical network is also considered. The central subsystem must be unstable to stabilize the whole network under a special coupling. Several examples are given to illustrate the results.     

Complete identification of some non-linear closed-loop systems†

The problem of complete identification of some non-linear closed-loop systems is dealt with in this paper. The basic system consists of two linear parts and a nonlinear one between them. Two special cases of this are produced by removing each one of the two linear parts. The nonlinear character of the systems is determined by static testing. Dynamic testing (.e. using entire input and output, signals) allows the linear transfer functions to be determined. Two procedures are suggested corresponding, one to one, to the two special cases. A theoretical procedure is also developed for the full basic system.     

A maximum modulus theorem for linear fractional transformations

A main result in the structured singular value theory is a maximum modulus-like theorem for a special case of linear fractional transformations. We extend that result to general linear fractional transformations.     

Matrix corrections minimal with respect to the Euclidean norm for linear programming problems

We consider special algebraic constructions, namely minimal matrix solutions and corrections of systems of linear algebraic equations and pairs of conjugate systems of linear algebraic equations. We build the corresponding mathematical apparatus that also lets us solve inverse linear programming problems (construct model linear programming problems with given properties), study and solve approximate and singular linear programming problems. We give statements of the theorems and numerical examples.     

均匀线列阵时域宽带波束形成方法研究

时域宽带恒定束宽波束形成技术一般采用特殊频率响应的FIR滤波器组实现对不同频率的加权.对水下常用的均匀线列阵,利用切比雪夫方法设计了形成宽带恒定束宽波束的权值.通过对切比雪夫方法设计权值特性的分析,推导出实现加权的FIR滤波器组的相位响应关系式.根据推导结果得出设计的FlR滤波器组应为一组斜率不同的线性相位响应FIR滤波器.推导了滤波器组相位响应的计算公式.给出三种特殊频率响应FIR滤波器设计算法.通过仿真结果比较了三种方法设计的用于实现均匀线列阵恒定束宽加权的FIR滤波器组的性能.     

Reduced-order estimation Part 2. Smoothing

A fixed-interval reduced-order linear smoother is presented for continuous-parameter Markov processes. The smoother is a combination of two reduced-order linear niters. The Mayne-Fraser full-order smoother is shown to be a special case of this reduced-order smoother.     

Frequency-domain stability conditions for hybrid systems

Consideration was given to a special class of the hybrid systems with switchings of time-invariant linear right-hand sides. A narrower subclass of such systems, that of connected switched linear systems, was specified among them. The necessary and sufficient frequencydomain conditions (criteria) for the existence of a common quadratic Lyapunov function providing stability of the switched systems were proposed for them. The specified subclass includes control systems with several nonstationary nonlinearities from the finite sectors that are the matter at issue of the theory of absolute stability. For the connected switched linear systems of a special kind (triangular type systems), the separate necessary and separate sufficient existence conditions were obtained for such Lyapunov functions. The interrelations between these conditions were discussed in the example.     

基于特殊线性群的自同构群的签名

基于特殊线性群的自同构群上的离散对数问题,提出一种非交换群上的签名方案;分析特殊线性群的自同构群上的离散对数问题的困难性。通过适当地选取参数,表明新签名方案的安全性高于有限域上的DSA算法,甚至等同于椭圆曲线上的DSA算法。结果表明,采用Leedham-Green算法计算矩阵的幂运算,使得新方案的运行效率得到提高。     

Polynomial invariants for linear loops

The problem of generating polynomial invariants of special type for iterative loops with a linear mapping in the loop body is considered. A technique is proposed to generate such invariants based on the analysis of characteristic polynomials of linear mappings.     

一般线性滞后系统的稳定性及反馈镇定

本文建立一般线性滞后微分系统的简洁稳定性定理，给出一般时不变线性系统的一种反馈镇定方法，这种方法以线性时不变系统的LQ反馈为特例，取得了以往文献难以达到的结果．     

On an approach to the solution of nonlinear programming problems in inexact information on criterion importance coefficients and scale gradation in the additive value function

It is shown that the well-known approach to solving the problem of the minimization of the bilinear aim function with linear limitations on the criterion importance coefficients and values in terms of reducing it to linear programming via a special variable substitution is erroneous.     

正倒向随机微分方程与一类线性二次随机最优控制问题

讨论一类正倒向随机微分方程解的存在唯一性及其对应的一类线性二次随机最优控制问题,利用单调性方法证明了一类特殊的正倒向随机微分方程解的存在唯一性定理,利用该结果研究一类耦合了一个倒向随机微分方程的线性随机控制系统广义最优指标随机控制问题,得到由正倒向随机微分方程的解所表示的唯一最优控制的显式表达式,并得到精确的线性反馈及其对应的Riccati方程.     

垂直运动永磁直线同步电动机的Fuzzy-PID控制研究

由于垂直运动永磁直线同步电动机的特殊结构及特殊的边端效应 ,其精确的数学模型不容易建立。针对垂直运动永磁直线同步电动机 (PMLSM )的特点 ,设计了一个Fuzzy -PID控制器 ,通过仿真 ,取得了较好的控制效果     

Synthesis of concurrent multibeam and conical beam antenna arrays

An approach is presented to synthesize linear and planar antenna arrays to have concurrent multibeam radiation patterns as well as desired sidelobe levels. This approach is based on zeros perturbation of the pattern of linear arrays. Multibeam planar arrays are synthesized by both multiplying and transforming multibeam linear arrays. Besides, planar arrays having conical or ring type beam are synthesized by applying a special transformation to dual‐beam linear arrays. Some examples are brought to verify the effectiveness of the proposed approach for both linear and planar arrays.     

线性系统按转移矩阵配置的统一算式

本文讨论了线性状态反馈系统按转移矩阵进行配置的问题,导出了反馈矩阵的统一算式.该算式适用于时不变和时变的线性系统.本文的推导表明,常用的极点配置公式只是这个统一算式的一个特殊情况.     

A computational study on the quadratic knapsack problem with multiple constraints

The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint.In this paper we provide a comparison of quadratic and linear representations of QKP based on test problems with multiple knapsack constraints and up to eight hundred variables. For the linear representations, three standard linearizations are investigated. Both the quadratic and linear models are solved by standard branch-and-cut optimizers available via CPLEX. Our results show that the linear models perform well on small problem instances but for larger problems the quadratic model outperforms the linear models tested both in terms of solution quality and solution time by a wide margin. Moreover, our results demonstrate that QKP instances larger than those previously addressed in the literature as well as instances with multiple constraints can be successfully and efficiently solved by branch and cut methodologies.