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首页> 外文会议>17th Anniversary of the International Simulatros Conference, Apr 16-20, 2000, Washington, D.C. >FUZZY CALCULUS APPROACH TO COMPUTER SIMULATION: AN APPLICATION TO CONTROL PROBLEMS
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FUZZY CALCULUS APPROACH TO COMPUTER SIMULATION: AN APPLICATION TO CONTROL PROBLEMS

机译：计算机计算的模糊计算方法：控制问题的一种应用

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摘要

The use of digital computers to perform calculations necessary to simulate or solve dynamical systems is inherently flawed. This flaw is the use of finite number of binary digits to represent real numbers, which can be classified as round-off error. The set of real numbers is mapped to a discrete spectrum of finite precision numbers that can be generated by a digital computer, which implies that every real number used in a digital computer is an approximation. This mapping is lacking since numbers that are small in magnitude may be represented by the value 0 and numbers of very large magnitude can not be represented at all or cause an overflow exception to occur. Therefore, algorithms developed utilizing real numbers may not yield correct or consistent numerical results. In this paper, a fuzzy calculus approach based on neoclassical analysis is used to give a description for the mathematical behavior of numerical algorithms subject to finite precision representation of real numbers. Finite precision mathematics, under the formalism of fuzzy calculus is illustrated using infinite series. Many differential equations utilize infinite series as a means to obtain a solution, for example optimal control problems; therefore the material presented here is of useful for understanding the numerical solutions.
机译：使用数字计算机执行模拟或求解动力学系统所需的计算具有固有的缺陷。此缺陷是使用有限数量的二进制数字表示实数，可以将其分类为舍入误差。实数集映射到可由数字计算机生成的有限精度数字的离散频谱，这意味着数字计算机中使用的每个实数都是近似值。缺少此映射，因为量级较小的数字可能由值0表示，而量级非常大的数字根本无法表示或导致发生溢出异常。因此，利用实数开发的算法可能不会产生正确或一致的数值结果。在本文中，基于新古典分析的模糊演算方法被用来描述数值算法的实数有限精度表示的数学行为。使用无限级数，说明了模糊演算形式化下的有限精度数学。许多微分方程利用无限级数作为获得解的手段，例如最优控制问题。因此，这里介绍的材料对于理解数值解很有用。

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