Decentralized uniform finite-time stabilization of large-scale nonlinear networks by small-gain theorems

We solve the problem of decentralized uniform finite-time stabilization for a large-scale network of nonlinear systems in triangular form which are not feedback linearizable and whose input–output maps are not invertible. For this, we provide a new recursive design to satisfy the conditions of a certain modification of the small-gain theorems for the case of the uniform finite-time stability of large-scale networks. In the general case, we consider the general triangular form systems whose input–output links are surjections only. In addition, we consider the special case of the triangular form systems with polynomial integrators, which is also needed as the first step of the proof of our main result. In the latter case, the design becomes constructive, the decentralized stabilizers can be designed explicitly, and this is demonstrated by examples.     

运用栅栏函数验证连续系统的有界时间安全性

栅栏函数在连续系统验证方面有着广泛的应用.其主要想法在于: 在可达集和非安全集之间寻找一个栅栏,从初始区域出发的路径不会越过这个栅栏,而非安全区域在栅栏的另外一端.这样就可以通过寻找栅栏函数来验证一个系统的安全性.近年来,已有一些工作讨论连续系统在无界时间情况下的栅栏函数生成.但是对于有些系统,人们可能只关心其在有界时间内的安全性.因为在无界时间内不安全并不能说明在给定时间内也是不安全的,所以对于这类问题无界时间栅栏函数方法并不适用.受无界时间栅栏函数方法的启发,本文针对有界时间的情况,给出有界时间栅栏函数生成方法.首先给出有界时间栅栏函数的一些充分条件.对于多项式系统,将多项式非负的条件做平方和松弛后利用平方和规划工具求解这些充分条件得到栅栏函数;对于初等系统(包含一些初等函数),先将该初等系统转化为一个多项式系统,然后求解对应多项式系统的栅栏函数.对一些无界时间不安全的实例,演示了我们的方法在验证有界时间安性问题上的有效性.     

混合自动机的多项式phase-portrait近似

抽象近似是验证混合系统安全性的主要方法,模型转换是构造一个可判定的(或半判定的)混合自动机来近似原混合自动机.本文将线性phase-portrait近似推广到多项式phase-portrait近似,叙述了如何自动构造多项式phase-portrait近似自动机及如何精化近似模型.     

Generalized State Scaling and Applications to Feedback, Feedforward, and Nontriangular Nonlinear Systems

We propose a global high-gain scaling-based state-feedback controller for a general class of nonlinear systems containing uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high gain scaling involving appropriate powers of a high gain scaling parameter which is a dynamic signal driven by the state. The design is applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) systems, and also to nontriangular systems as long as a set of linear inequalities involving powers of the polynomial bounds on the ratios of uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov inequalities     

Global stabilization of nonlinear cascade systems

We present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems. These are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section. For polynomial systems, in particular, the stabilizing feedback is given explicitly.     

基于PXI总线的导弹通用计量检定平台设计

为了克服我军现役导弹计量设备体积过大、通用性差、测试资源浪费严重、机动性不强等缺点，在对某型导弹计量设备及测试参数研究的基础上，采用了PXI总线系统和新一代自动测试系统的模块化设计的要求，设计了导弹通用计量检定系统;实现了导弹计量检定设备的通用性和低成本,使导弹计量设备的便携性成为可能;大量工程实践证明，此系统解决了传统计量设备所不能解决的诸多问题，并大大提高了系统的计量效率和精度，因此具有很强的实用性。     

Constructing triangular patch by basic approximation operator plus additional interpolation operator

~~Constructing triangular patch by basic approximation operator plus additional interpolation operator1. Barahill, R. E., Birkhoff, G., Gordon, W. J., Smooth interpolation in triangles, J. Approx. Theory, 1973, 8: 114-128. 2. Gregory, J. A., Smooth interpolation without twist constraints, in Computer Aided Geometric Design (eds. Barn-hill, R. E., Riesenfeld, R. R), New York: Academic Press, 1974, 71-88. 3. Charrot, P., Gregory, J. A., A pentagonal surface patch for comput…     

带形状参数的Bernstein-Bézier曲面

虽然三角域上的曲面造型方法能有效解决不规则产品的几何造型问题, 在实际工程中有着广泛的应用, 但由于其结构的特殊性和复杂性, 目前对三角域曲面的扩展研究并不多。为了丰富三角域曲面的理论, 针对如何增强三角域曲面形状表示的灵活性进行了专门的研究。首先构造了一组三角域上含一个参数的四次多项式基函数, 它是三角域上二次Bernstein基函数的扩展。然后用递推的方式定义了三角域上含一个参数的n+2次多项式基函数, 它是三角域上n次Bernstein基函数的扩展。基于新的n+2次多项式基函数, 定义了相应的n阶三角域曲面。分析了基函数和曲面的性质, 新曲面不仅具备三角域上Bernstein Bézier曲面的基本性质, 而且还可以在不改变控制顶点的情况下, 通过改变参数的值来自由调整曲面的形状。     

Some algebraic methods for solving multiobjective polynomial integer programs

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.     

Global robust servomechanism problem of lower triangular systems in the general case

The global robust servomechanism problem (alternatively, global robust output regulation problem) for lower triangular systems has been studied for two special cases. The first case assumes that the systems only contain polynomial nonlinearities, and the second case limits the exogenous signals and the unknown parameters to be within a known bounded set. This paper presents the solvability conditions of the global robust servomechanism problem for the lower triangular systems for the most general case where neither of the above two assumptions is needed. Our approach consists of two steps. In the first step, we convert the problem into a global adaptive regulation problem for lower triangular systems subject to both dynamic and static uncertainties. In the second step, we derive the solvability conditions of the problem by appealing to the recent result on the solvability of the global adaptive regulation problem for lower triangular systems with both dynamic and static uncertainties.     

Computational Methods for Verification of Stochastic Hybrid Systems

Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is challenging because of the interaction between the discrete and the continuous stochastic dynamics. In this paper, we propose a probabilistic method for verification of SHSs based on discrete approximations focusing on reachability and safety problems. We show that reachability and safety can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. We present a numerical algorithm for computing the solution based on discrete approximations that are derived using finite-difference methods. An advantage of the method is that the solution converges to the one for the original system as the discretization becomes finer. We also prove that the algorithm is polynomial in the number of states of the discrete approximation. Finally, we illustrate the approach with two benchmarks: a navigation and a room heater example, which have been proposed for hybrid system verification.     

三角域上带形状参数的三次Bézier曲面

张量积Bézier曲面被成功地应用于商业CAD系统中,然而实际工程中的某些外形却无法依靠张量积形式实现.因此在CAGD中,三角Bézier曲面成为外部形状设计的主要工具之一.为了更加灵活地控制三角曲面的形状,构造了一组带形状参数的三次多项式基函数,它们是三角域上三次Bernstein基的扩展.利用该组基函数定义了三角域上带形状参数的多项式曲面.基函数和曲面分别具有Bernstein基和Bézier曲面的性质.在形状参数的取值范围内,三次Bézier三角曲面是它的特例.由于含有可调的形状参数,该曲面在形状修改与变形中具有更大的灵活性.形状参数具有明确的几何意义,参数越大曲面越逼近控制网格.实例表明,通过改变形状参数的取值可以调整曲面的形状,在CAGD中该方法是有效的.     

Solution of systems of Boolean equations via the integer domain

This paper presents a new method for solving systems of Boolean equations. The method is based on converting the equations so that we operate in the integer domain. In the integer domain better and more efficient methodologies for solving equations are available. The conversion leads us to a system of polynomial equations obeying certain characteristics. A method is proposed for solving these equations. The most computationally demanding step is the repeated multiplication of polynomials. We develop a method for this problem that is significantly faster than the standard approach. We also introduce another variant of the method, the so-called hybrid approach, that leads to reduced memory requirements. Theoretical and experimental results indicate the superior performance of the proposed method and its variant compared to the competing methods. The proposed method is also validated by applying it to the problem of hardware verification.     

FIOWHM operator and its application to multiple attribute group decision making

To study the problem of multiple attribute decision making in which the decision making information values are triangular fuzzy number, a new group decision making method is proposed. Then the calculation steps to solve it are given. As the key step, a new operator called fuzzy induced ordered weighted harmonic mean (FIOWHM) operator is proposed and a method based on the fuzzy weighted harmonic mean (FWHM) operator and FIOWHM operators for fuzzy MAGDM is presented. The priority based on possibility degree for the fuzzy multiple attribute decision making problem is proposed. At last, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.     

Solutions of linear dynamic systems by generalized orthogonal polynomials

Generalized orthogonal polynomials that represent all types of orthogonal polynomial are introduced in this paper. Using the idea of orthogonal polynomial functions that can be expressed by power series, and vice versa, the operational matrix for integration of a generalized orthogonal polynomial is first derived and then applied to solve the equations of linear dynamic systems. The characteristics of each kind of orthogonal polynomial in relation to solving linear dynamic systems is demonstrated. The computational strategy for finding the expansion coefficients of the state variables is very simple, straightforward and easy. The operational matrix is simpler than those of conventional orthogonal polynomials. Hence the expansion coefficients are more easily calculated from the proposed recursive formula when compared with those obtained from conventional orthogonal polynomial approximations.     

三角域上生成三角多项式曲面的实用方法

提出一种三角域上带三个形状参数的三角多项式基函数,基于此基函数可以生成一种三角域上的三角多项式曲面。该曲面可以构建边界为椭圆弧、抛物线弧以及圆弧的曲面。在不改变控制网格的情况下,所提出的曲面可以使用形状参数对曲面进行可预测的灵活调整。为了能够高效稳定地计算该三角多项式曲面,提出一种实用的de Casteljau-type算法。此外,还给出了连接两个三角多项式曲面的[G1]连续条件。     

Fundamental theory of the semi-radial singularity mapping with applications to fracture mechanics

Fundamental theory of the semi-radial singularity mapping is presented, which yields the necessary singularities in the stress and strain with bounded strain energy. In particular the quadrilateral semi-radial singularity mapping as well as the triangular one with collapse are described explicitly. With some verification example in linear fracture mechanics, the trial function spaces due to the conventional polynomial interpolations with these peculiar mappings are examined in detail.     

Verification of clocked and hybrid systems

This paper presents a new computational model for real-time systems, called the clocked transition system (CTS) model. The CTS model is a development of our previous timed transition model, where some of the changes are inspired by the model of timed automata. The new model leads to a simpler style of temporal specification and verification, requiring no extension of the temporal language. We present verification rules for proving safety a nd liveness properties of clocked transition systems. All rules are associated with verification diagrams. The verification of response properties requires adjustments of the proof rules developed for untimed systems, reflecting the fact that progress in the real time systems is ensured by the progress of time and not by fairness. The style of the verification rules is very close to the verification style of untimed systems which allows the (re)use of verification methods and tools, developed for u ntimed reactive systems, for proving all interesting properties of real-time systems. We conclude with the presentation of a branching-time based approach for verifying that an arbitrary given CTS isnon-zeno. Finally, we present an extension of the model and the invariance proof rule for hybrid systems. Received: 23 September 1998 / 7 June 1999