Robust D-Stability Test of LTI General Fractional Order Control Systems

This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.     

Adaptive guidance law design based on characteristic model for reentry vehicles

In this paper an adaptive guidance law based on the characteristic model is designed to track a reference drag acceleration for reentry vehicles like the Shuttle. The characteristic modeling method of linear constant systems is extended for single-input and single-output （SlSO） linear time-varying systems so that the characteristic model can be established for reentry vehicles. A new nonlinear differential golden-section adaptive control law is presented. When the coefficients belong to a bounded closed convex set and their rate of change meets some constraints, the uniformly asymptotic stability of the nonlinear differential golden-section adaptive control system is proved. The tracking control law, the nonlinear differential golden-section control law, and the revised logical integral control law are integrated to design an adaptive guidance law based on the characteristic model. This guidance law overcomes the disadvantage of the feedback linearization method which needs the precise model. Simulation results show that the proposed method has better performance of tracking the reference drag acceleration than the feedback linearizaUon one.     

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control design methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.     

Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks

This paper addresses two kinds of optimal control problems of probabilistic mix-valued logical control networks by using the semi-tensor product of matrices, and presents a number of new results on the optimal finite-horizon control and the first-passage model based control problems, respectively. Firstly, the probabilistic mix-valued logical control network is expressed in an algebraic form by the semi-tensor product method, based on which the optimal finite-horizon control problem is studied and a new algorithm for choosing a sequence of control actions is established to minimize a given cost functional over finite steps. Secondly, the first-passage model of probabilistic mix-valued logical networks is given and a new algorithm for designing the optimal control scheme is proposed to maximize the corresponding probability criterion. FinMly, an illustrative example is studied to support our new results/algorithms.     

Adaptive control of linear multivariable systems with high frequency gain matrix hurwitz

A new adaptive control scheme is proposed for multivariable model reference adaptive control （MRAC） systems based on the nonlinear backstepplng approach with vector form. The assumption on a priori knowledge of the high frequency gain matrix in existing results is relaxed and the new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. This control scheme guarantees the global stability of the closed-loop systems and the tracking error can be arbitrary small. The simulation result for an application example shows the validity of the proposed nonlinear adaptive scheme.     

Modeling and control for wireless networked control system

In this paper, the stabilization problem is considered for the class of wireless networked control systems (WNCS). An indicator is introduced in the WNCS model. The packet drop sequences in the indicator are represented as states of a Markov chain. A new discrete Markov switching system model integrating 802.11 protocol and new scheduling approach for wireless networks with control systems are constructed. The variable controller can be obtained easily by solving the linear matrix inequality (LMI) with the use of the Matlab toolbox. Both the known and unknown dropout probabilities are considered. Finally, a simulation is given to show the feasibility of the proposed method.     

Controllability for single-input mechanical control systems with dissipation

Within the affane connection framework of Lagrangian control systems, based on the results of Sussmann on small-time locally controllability of single-input affine nonlinear control systems, the controllability results for mechanical control systems with single-input are extended to the case of the systems with isotropic damping, where the Lagrangian is the kinetic energy associated with a Riemannian metric, A sufficient condition of negative small-time locally controllability for the system is obtained.Then,it is demonstrated that such systems are small-time locally configuration controllable if and only if the dimemion of the configuration manifold is one. Finally, two examples are given to illustrate the results. Lie bracketting of vector fields and the symmetric product show the advantages in the discussion.     

Editorial

Nowadays control systems can find applications in many areas, like aerospace, motion tracking, chemical engineering, physics, biology, economics. To improve control performance is a perpetual goal. With recent progresses of computing technologies, better control performance can be achieved by more judicious control strategies based on more precise and more complicated, such as time-varying, nonlinear, models. Another trend to improve control performance is built upon the divide-and-conquer philosophy, i.e., a complicated control task is cooperatively accomplished by multiple controllers/agents, instead of a single super-powerful controller. This trend is made possible due to great advances in communication, which enable the information exchange among agents and may unite the less powerful agents. The cost for such control performance improvement is higher spatial complexity of control systems. Although high model complexity and spatial complexity can be physically handled by current powerful controllers/agents, the lack of efficient analysis and synthesis methods prevents the performance improvement of control systems with high model or/and spatial complexity. As we know, conventional control methods are mainly developed under the assumptions of linear, time-invariant and centralized models. In order to resolve the issues due to the aforementioned two types of complexities, new methods are expected, which is exactly the major aim of the present special issue.     

Semi-tensor product of matrices and its application to Morgen''''s problem

This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional da-ta; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgan's problem for control systems is formulated as a numerically solvable problem.     

H-infinity control for switched and impulsive singular systems

A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.     

Necessary conditions for Hadamard factorizations of Hurwitz polynomials

A property of Hurwitz polynomials is related with the Hadamard product. Garloff and Wagner proved that Hadamard products of Hurwitz polynomials are Hurwitz polynomials, and Garloff and Shrinivasan shown that there are Hurwitz polynomials of degree 4 which do not have a Hadamard factorization into two Hurwitz polynomials of the same degree 4. In this paper, we give necessary conditions for an even-degree Hurwitz polynomial to have a Hadamard factorization into two even-degree Hurwitz polynomials; such conditions are given in terms of the coefficients of the given polynomial alone. Furthermore, we show that if an odd-degree Hurwitz polynomial has a Hadamard factorization then a system of nonlinear inequalities has at least one solution.     

LS-SVM算法在近红外光谱煤质分析中的应用

针对目前电力行业煤质分析的需求,提出了基于Hadamard近红外光谱的煤质分析技术,对Hadamard近红外光谱仪研制、控制分析软件设计、煤炭光谱信号采集、指标特征信息提取、定量模型建立五个环节综合考虑,研发了Hadamard近红外煤质分析系统.研究中,对41个不同质量指标的标准煤样进行了定量分析预测,考察了在相同粒径的条件下Hadamard近红外光谱对煤炭指标的预测能力,提出了基于ICA+LS-SVM算法的的煤炭指标预测方法,光谱数据与煤炭指标具有很好的相关性,相关系数普遍在0.9以上,取得了较好预测效果.     

Image coding using vector quantization in the transform domain

Two new image-coding systems are proposed. In the first system a one-dimensional Hadamard transform is applied on each row of image data, and a vector-quantization process along the columns of the transformed image data. In the second system a two-dimensional Hadamard transform is carried out on sub-blocks of an image followed by a vector-quantization process on the neighbouring sub-blocks.     

Estimation of 3-D translational motion parameters via hadamard transform

A new method based on spatial-temporal Hadamard transform is proposed to estimate the 3-D translational motion parameters. This method has no restriction on the magnitude of displacement. Moreover, for an image of size 2ⁿ × 2ⁿ, only 2n + 1 coefficients need to be computed. Experimental results are demonstrated for this powerful method.     

Hadamard matrices of Williamson type: A challenge for Computer Algebra

We describe new families of challenging polynomial systems of equations arising in the construction of Hadamard matrices of Williamson type. These systems depend on a parameter and exhibit a number of symmetries. We demonstrate that Genetic Algorithms form a suitable tool to apply to these systems, for which the traditional Computer Algebra methods seem to be inappropriate.     

图像Hadamard变换域鲁棒水印算法

提出了一种基于分块Hadamard变换的鲁棒图像水印算法。水印图像先进行置乱和扩展得到水印序列。原始图像进行8×8分块的Hadamard变换,在中频系数里按不同强度嵌入水印。水印提取时,先计算与原始图像在对应的变换域系数的差值,再计算该差值与水印编码的相关性来确定每个水印像素。实验表明,该算法对原始图像的视觉影响小,具有良好的鲁棒性。     

医疗大数据隐私保护多关键词范围搜索方案

随着医疗信息系统的急速发展,基于医疗云的信息系统将大量电子健康记录（EHRs）存储在医疗云系统中,利用医疗云强大的存储能力和计算能力对EHRs数据进行安全与统一的管理.尽管传统加密机制可以保证医疗数据在半诚实云服务器中的机密性,但对加密后的EHRs数据执行安全、快速、有效的范围搜索,仍是一个有待解决的关键问题.提出一种支持多关键词范围搜索的可搜索加密方案：利用向量积保持加密机制实现复杂查询结构的可搜索加密,可支持连接关键词查询、范围查询以及通配符的查询;通过随机化构建搜索索引和搜索陷门,实现搜索模式隐藏,达到搜索语句的隐私保护;采用矩阵哈达马积缩小所需密钥矩阵的维度.理论分析和实验结果表明：该方案在达到医疗数据隐私保证的同时,对用户的检索策略也进行了有效的隐私性保护,有效提高了检索效率,降低了创建索引及陷门所用时间,实现了多用户多文件下医疗数据的范围搜索能力.     

Constructions of Complex Hadamard Matrices via Tiling Abelian Groups

Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling of Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent, very general construction of complex Hadamard matrices due to Dita [2] via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szabó [8], we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita’s construction. These new families complement the recent catalogue [10] of complex Hadamard matrices of small order.     

A note on commutative multivariate rational series

Direct arguments are presented showing that for rational series in several commuting variables, the rational series problem is undecidable, and closure under Hadamard product fails.     

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation. Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.