机械系统的拉格朗日法建模与仿真

针时拉格朗日法对复杂系统建模比较方便,但仿真比较困难的问题,通过具体实例,介绍了在拉格朗日法建模的基础上进行仿真的一种新方法,该方法通过将所建立的数学模型,先进行解耦后分别仿真,再应用叠加原理求得系统的仿真结果。     

Bessel function of the first kind with complex argument

A new method of computing integral order Bessel functions of the first kind J_n(z) when either the absolute value of the real part or the imaginary part of the argument z = x + iy is small, is described. This method is based on computing the Bessel functions from asymptotic expressions when x∼ 0 (or y ∼ 0). These expansions are derived from the integral definition of Bessel functions. This method is necessary because some existing algorithms and methods fail to give correct results for small x small y. In addition, our overall method of computing Bessel functions of any order and argument is discussed and the logarithmic derivative is used in computing these functions. The starting point of the backward recurrence relations needed to evaluate the Bessel function and their logarithmic derivatives are investigated in order to obtain accurate numerical results. Our numerical method, together with established techniques of computing the Bessel functions, is easy to implement, efficient, and produces reliable results for all z.     

Automatic h-Scaling for the Efficient Time Integration of Stiff Mechanical Systems

When solving stiff mechanical systems, implicit time integrators overestimate the error and tend to use small stepsizes due to the order reduction phenomenon. This article introduces an algorithm for the detection of stiff components that allows automatic scaling of the stepsize h in the error estimation. It is based on an investigation of the local error and applies existing embedded formulas of implicit Runge–Kutta methods. Thus, implementation and calculation effort are low. Three examples are integrated with the code RADAU5, a linear DAE in two different formulations and a slider crank mechanism.     

线性定常系统仿真的两种新算法

本文提出了两种适合于对线性定常系统进行仿真的新算法,它们不仅保持了改进转移矩阵法和拟Adams法的A-稳定性、计算量较小和精度较高等优点,而且弥补了这两种方法在理论上的不严密性和截断误差较大等缺陷,因而具有更好的数值特性,仿真结果表明,文中提出的算法是有效可行的。     

线性定常系统离散相似法仿真的快速算法

考虑线性定常系统的数字仿真，状态变量的计算步长为Ｔ，而系统输出的计算间隔常常为ＮＴ。本文通过以多项式插值函数逼近系统输入，利用增广矩阵法的结果，给出了基于离散相似法的一类仿真算法。当Ｎ较大时，与一般同类算法相比，本文算法使计算量显著减小。     

Parallel Implementation of a Least-Squares Spectral Element Solver for Incompressible Flow Problems

Least-squares spectral element methods (LSQSEM) are based on two important and successful numerical methods: spectral/hp element methods and least-squares finite element methods. Least-squares methods lead to symmetric and positive definite algebraic systems which circumvent the Ladyzhenskaya–Babuka–Brezzi (LBB) stability condition and consequently allow the use of equal order interpolation polynomials for all variables. In this paper, we present results obtained with a parallel implementation of the least-squares spectral element solver on a distributed memory machine (Cray T3E) and on a virtual shared memory machine (SGI Origin 3800).     

<Emphasis Type="BoldItalic">H</Emphasis><Subscript>2</Subscript>-Control and the Separation Principle for Discrete-Time Markovian Jump Linear Systems

In this paper we consider the H₂-control problem of discrete-time Markovian jump linear systems. We assume that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system is mean square stable and minimizes the H₂-norm of the system. As in the case with no jumps, we show that an optimal controller can be obtained from two sets of coupled algebraic Riccati equations, one associated with the optimal control problem when the state variable is available, and the other associated with the optimal filtering problem. This is the principle of separation for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the H₂-control of discrete-time linear systems. Date received: June 1, 2001. Date revised: October 13, 2003.     

On the strict logic foundation of fuzzy reasoning

This paper focuses on the logic foundation of fuzzy reasoning. At first, a new complete first-order fuzzy predicate calculus system K^* corresponding to the formal system L^* is built. Based on the many-sort system K_ms^* corresponding to K^*, the triple I methods of FMP and FMT for fuzzy reasoning and their consistency are formalized, thus fuzzy reasoning is put completely and rigorously into the logic framework of fuzzy logic.The author is indebted to anonymous referee for his useful comments which have helped to improve the paper.     

A new scheme for the deterministic simulation of PRAMs in VLSI

A deterministic scheme for the simulation of (n, m)-PRAM computation is devised. Each PRAM step is simulated on a bounded degree network consisting of a mesh-of-trees (MT) of siden. The memory is subdivided inn modules, each local to a PRAM processor. The roots of the MT contain these processors and the memory modules, while the otherO(n ²) nodes have the mere capabilities of packet switchers and one-bit comparators. The simulation algorithm makes a crucial use of pipelining on the MT, and attains a time complexity ofO(log² n/log logn). The best previous time bound wasO(log² n) on a different interconnection network withn processors. While the previous simulation schemes use an intermediate MPC model, which is in turn simulated on a bounded degree network, our method performs the simulation directly with a simple algorithm.This work has been supported in part by Ministero della Pubblica Istruzione of Italy under a research grant.     

Convergence and convergence rate of the balanced realization truncations for infinite-dimensional discrete-time systems

In this paper, we study approximation via balanced realizations for a large class of infinite-dimensional discrete-time linear systems. We give properties of the truncated system and prove that the approximation is L₂-convergent. In the case of nuclear systems, we prove convergence in nuclear norm and give an estimation of the L_∞-convergence rate.     

Impulse invariance-based method for the computation of fractional integral of order

This paper presents a simple and efficient method for the design of recursive digital fractional order integrator when the order of integration is a real number between 0 and 1. The proposed method is based on the impulse invariance method. First the initial value theorem is used for the selection of the initial value of the impulse response and then any of the well-established signal modeling techniques can be employed for the parameterization of the discrete impulse response by pole-zero models. For a given model order, the approximation accuracy greatly depends on the initial value selected. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed method.     

Exact computation of infimum for a class of continuous-time H∞ optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output

A noniterative method for the computation of infimum for a class of continuous-time H_∞ optimal control problem is considered in this paper. The problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems. The method is applicable to systems where (i) the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible, and (ii) the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible. The result presented in this paper is a continuation of the previous work of the author and his co-workers (Chen et al., 1992), in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero.     

Chaos synchronization for a class of discrete dynamical systems on the N-dimensional torus

In this paper, a class of dynamical systems on (the N-dimensional torus) is investigated. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that the sequences produced are equidistributed for almost every initial data. The above results are then extended to switched affine transformations of . Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup.     

Computation of the ∞ norm for nonlinear systems A convergence result

In this paper we show that _∞ norm for a class of nonlinear continuous-time systems is the limit of the _∞ norm for approximating discrete-time systems. The convergence result is proved by means of a characterization of the _∞ norm in terms of the value for an ergodic control problem.     

A novel extended precise integration method based on Fourier series expansion for the H2-norm of linear time-varying periodic systems

A new reliable algorithm for computing the H₂-norm of linear time-varying periodic (LTP) systems via the periodic Lyapunov differential equation (PLDE) is proposed. By taking full advantage of the periodicity, the transition matrix of the underlying LTP system associated with the PLDE is effectively computed by developing a novel extended precise integration method based on Fourier series expansion, where the time-consuming work for the computation of the matrix exponential and its related integrals in every sub-interval is avoided. Then, a highly accurate and efficient algorithm for the PLDE is derived using the block form of the transition matrix. Thus, the H₂-norm is evaluated by solving a simple first-order ordinary differential equation. Finally, two numerical examples are presented and compared with other algorithms to verify the numerical accuracy and efficiency of the proposed algorithm.     

Stability of iterative processes with errors for a system of nonlinear -accretive variational inclusions in Banach spaces

In this paper, by using the concept of (A,η)-accretive mappings and the new resolvent operator technique associated with (A,η)-accretive mappings, we introduce and study a system of general mixed quasivariational inclusions involving (A,η)-accretive mappings in Banach spaces, and construct a new perturbed iterative algorithm with mixed errors for this system of nonlinear (A,η)-accretive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.