基于区间牛顿法的混杂系统状态事件探测算法

系统仿真学报 ›› 2015, Vol. 27 ›› Issue (4): 738-746.

• 仿真建模与仿真算法及数值仿真 • 上一篇下一篇

基于区间牛顿法的混杂系统状态事件探测算法

王海燕, 胡以怀

上海海事大学商船学院, 上海 201306

收稿日期:2014-08-20 修回日期:2014-10-21 发布日期:2020-08-20
第一作者简介:王海燕(1976-),男,河北平山人,博士,副教授,研究方向为轮机自动化与仿真;胡以怀(1964-),男,江苏高邮人,博士,教授,研究方向为船舶动力装置及仿真技术。
基金资助:
上海市一流学科建设项目(船舶与海洋工程)

State Event Detecting Algorithm for Hybrid System Based on Interval Newton's Method

Wang Haiyan, Hu Yihuai

Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China

Received:2014-08-20 Revised:2014-10-21 Published:2020-08-20

摘要/Abstract

摘要： 准确的探测状态事件对混杂系统仿真至关重要,特别是求解有奇点或有重根的模型。提出一个基于可变步长显式多步法的插值多项式来预测事件函数的值,并使用扩展的区间牛顿法求解事件方程的根,从而使状态事件能够被可靠地发现。插值多项式不需使用下一步的状态变量估计值,可用于有奇点系统中。区间牛顿算法可求解具有多重根的方程,并将根的不存在性探测和求根过程结合在一起。仿真实例表明本算法对混杂系统有效,在几种严苛情况下都能探测到状态事件,及时避开模型奇点,避免仿真失败。

关键词: 混杂系统, 状态事件探测, 变步长多步法, 事件函数预测, 区间牛顿法

Abstract: Accurately detecting of state events is critical for hybrid dynamic systems,especially for systems with singularities or event functions with multiple roots. A carefully constructed extrapolation polynomial among state value of past time points was applied to predict values of event functions. The polynomial was derived from a variable-step multi-step integration method. The extended interval Newton's method was employed to find all roots in a certain time interval. Due to no using of values of future time points, the polynomial can be employed to determine the integration step size by checking potential events in systems with model singularities. The procedure of root existence test and root finding was combined into one procedure by using of non-existence test of roots. Simulation results show the algorithm is effective for hybrid dynamic systems with several different critical situations. By this algorithm, model singularities are found on time and simulation failures are avoided.

Key words: hybrid system, state event detecting, vary step multi-step method, state event function predicting, interval Newton's method

中图分类号:

王海燕,胡以怀 . 基于区间牛顿法的混杂系统状态事件探测算法[J]. 系统仿真学报, 2015, 27(4): 738-746.

Wang Haiyan,Hu Yihuai . State Event Detecting Algorithm for Hybrid System Based on Interval Newton's Method[J]. Journal of System Simulation, 2015, 27(4): 738-746.

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基于区间牛顿法的混杂系统状态事件探测算法

State Event Detecting Algorithm for Hybrid System Based on Interval Newton's Method

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