Extensions of ValEncIA‐IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization
Extensions of ValEncIA‐IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization
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ValEnciA-IVP 的扩展，用于减少高估、微分代数系统的模拟以及动态优化
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
E. Hofer
中科院分区：
文献类型：
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作者：
A. Rauh;E. Auer;J. Minisini;E. Hofer
仿真技术通常用于分析初始条件和系统参数的不确定性对动力系统状态变量轨迹的影响。在这种情况下，区间算术方法很有趣。如果已知上述不确定性的最坏情况边界，它们就能够确定所有可达状态的保证边界。此外，尽管在计算机上执行浮点运算时不可避免地会出现舍入误差，但区间算法仍可确保数值结果的正确性。然而，区间算法的简单实现常常会导致高估，即过于保守的范围，这可能会使结果毫无意义。
Simulation techniques are commonly used to analyze the influence of uncertainties of initial conditions and systemparameters on the trajectories of the state variables of dynamical systems. In this context, interval arithmetic approaches are of interest. They are capable of determining guaranteed bounds of all reachable states if worst‐case bounds of the above‐mentioned uncertainties are known. Furthermore, interval algorithms ensure the correctness of numerical results in spite of rounding errors which inevitably arise if floating point operations are carried out on a computer. However, naive implementations of interval algorithms often lead to overestimation, i.e., too conservative enclosures which can make the results meaningless.