Continuity properties of solutions to H2 and H∞ Riccati equations

In H₂ and H_∞ optimal control (semi-)stabilizing solutions of algebraic Riccati equations play an essential role. It is well-known that these solutions might have discontinuities as a function of the system parameters. The paper shows that these discontinuities are directly linked to non-left-invertibility and, in contrast to what one might think, unrelated to zeros on the imaginary axis.     

Monotonicity of maximal solutions of algebraic Riccati equations

A monotonicity result for the maximal solution of the equation XBB^*X − A^*X − XA − Q = 0, Q = Q^*, (A, B) stabilizable, is proved.     

On parameter dependence of solutions of algebraic riccati equations

We study the behavior of Hermitian solutions, especially the maximal ones, of algebraic Riccati equations whose coefficients depend on real parameters. The cases of analytic dependence on one parameter andC′ dependence (0≤r≤∞) on many parameters are considered. The basic assumption made is stabilizability. Partially supported by an NSF grant.     

Convolutional solutions of partial difference equations

A significant part of the theory of one-dimensional linear shift-invariant systems is based on the concept of weighting function (or impulse response): the output is the convolution of the weighting function with the input. This paper introduces the concept of linear translation-invariant systems and uses this notion in studying impulse response, z-transforms, and transfer functions for multidimensional systems.     

Remarks on the time-varying H∞ Riccati equations

In this paper we establish some useful properties of three Riccati equations appearing in the standard H_∞-control problems for continuous and discrete-time time-varying systems. We then give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent Riccati equations with a coupling inequality.     

代数约简的条件信息熵表示及其高效约简算法

给出如何保持正区域不变的语义分析,提出一种修正条件信息熵计算公式,证明保持修正条件信息熵不变与保持正区域不变相互等价。在此基础上,给出代数约简概念的修正条件信息熵表示。给出反例说明修正条件信息熵不具有单调性,导致没法给出自底向上的启发式约简算法,证明了代数协调集中不可删除属性的不可逆性质,提出一种自顶向下直接删除属性的高效约简算法。它从所有条件属性集出发,逐步删除不必要的属性,只需遍历各属性一次,即可保证得到原始决策表的一个代数约简。数值算例和实验验证了该算法的正确性和高效性。     

一种新颖的混沌分组密码算法

在研究已经提出的一些混沌加密算法的基础上,提出了一种新的混沌分组密码算法.算法的密钥包含64位的外部比特流K和Logistic映射的初值x0两部分,同时也用这个混沌映射定义了一个双射映射.然后通过3种代数运算和由双射映射确定的置换运算还用在64比特的明文上,产生64比特的密文.理论与实验分析表明该算法克服了一些纯混沌密码系统的固有缺陷,同时也具有较高的性能.     

Closed-form solution for a class of continuous-time algebraic Riccati equations

In the present paper we obtain a closed-form solution for a class of continuous-time algebraic Riccati equations (AREs) with vanishing state weight. The ARE in such a class solves a minimum energy control problem. The obtained closed-form solution is used to prove a link between two independent fundamental limitation results in control over networks.     

On the geometry of symplectic pencils arising from discrete-time matrix equations

In this paper general symplectic matrix pencils are considered disregarding the particular matrix equations from which they arise. A parameterization of the Lagrangian deflating subspaces is given with the only assumption of regularity of the matrix pencil.     

A geometric index reduction method for implicit systems of differential algebraic equations

This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE (a differential Kronecker representation) in as many variables as the order of the input system. This can be done by means of a Kronecker-type algorithm with bounded complexity.     

交通矢量地图离散非线性校正算法

该文从交通矢量地图的基本特征出发,在深入分析矢量地图的网络拓扑结构的基础上提出了一种新的矢量地图自动校正算法,即：离散非线性校正算法。算法的关键在于离散块的选取以及所选取离散块内各节点的相应调整。通过对整个地图平面的分块非线性校正,在合理选取校正样本的情况下能够对整个地图的所有局部区域达到最优的校正。与传统的线性自动校正算法相比,这种算法可以有效地消除矢量地图中的非线性误差,理论上也有所深入。实验中将该算法应用于合肥、成都等城市的矢量地图校正中,取得了良好的校正效果。应用校正算法得到的交通矢量地图将为交通管理或监控导航系统提供准确的资料信息和更好的智能决策服务,从而给人们生活带来极大的便利。     

An algebraic approach to supervisory control

Supervisory control problems are formulated in terms of a process model where the mechanism of control is expressed in terms of an algebraic operator with the plant and supervision processes as its arguments. The solution subspaces for supervisory processes restrict the observation and the control capability of supervision. The main result corresponds to decentralized marked supervision under partial observations, and specific cases are derived from this result in a unified, algebraic way. The result and its derivation demonstrate the relative simplicity of the algebraic process formulation.     

Discrete generalized algebraic Riccati equations and polynomial matrix factorization

This paper presents an algorithm for solving discrete generalized algebraic Riccati equations with the help of an orthogonal projector. A generalization of the procedure of forming and correcting the orthogonal projector is considered and also that of correcting the proper solution by the Newton-Raphson scheme. The possibility to use the discrete generalized Riccati equations for polynomial matrix factorization with respect to the unit circle is demonstrated. A numerical example is given.     

A class of marked invariant subspaces with an application to algebraic Riccati equations

Invariant subspaces of a matrix A are considered which are obtained by truncation of a Jordan basis of a generalized eigenspace of A. We characterize those subspaces which are independent of the choice of the Jordan basis. An application to Hamilton matrices and algebraic Riccati equations is given.     

Isolated nonnegative solutions of infinite-dimensional algebraic Riccati equations

For an infinite-dimensional continuous (or discrete)-time linear system, based on the study of the representation of nonnegative solutions of the algebraic Riccati equation (ARE), we get some sufficient and necessary conditions for a nonnegative solution of (ARE) to be isolated in the set of all nonnegative solution of (ARE) with respect to the norm topology, the strong operator topology and weak operator topology, respectively.     

A conservative discrete ordinate method for model Boltzmann equations

A class of conservative discrete ordinate method (C-DOM) for the Bhatnagar–Gross–Krook (BGK) model Boltzmann equation is presented. The C-DOM is the extension of the discrete ordinate method in my previous study (Yang and Huang, 1995 [3]). In the C-DOM, a conservative molecular collision process is employed and thus the conservation properties of the collision integral are maintained at the molecular level. For a broad range of Knudsen number, several test problems, including unsteady shock-tube problem and supersonic/hypersonic flows over circular cylinder, are utilized to demonstrate the performance and validity of the DOM and C-DOM. Results show that the C-DOM can greatly reduce the computer time and memory requirements in hypersonic rarefied gas flow computations.     

离散混沌系统类随机性的符号熵分析法

采用符号熵分析法,分析和讨论了经典的Logistic映射和Henon映射的类随机性强弱.先将离散混沌系统产生的实数序列转化为二进制序列,然后进行编码,计算其符号熵,绘制其符号熵图,并深入讨论了系统参数和初始值对符号熵的影响.数值仿真分析表明,符号熵法能定量区别不同离散混沌系统类随机性的强弱.同时作为随机源,Logistic映射比Henon映射好.