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
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.

参考文献

[1] Lygeros J, Tomlin C, Sastry S.Hybrid Systems: Modeling, Analysis and Control [R]. Berkeley, CA 94720, USA: EECS Department, University of California, 2008.
[2] 赖镇洲, 张淼, 王佳伟, 等. 基于混杂系统描述的卫星姿态控制系统研究[C]// 第32届中国控制会议论文集. 西安. USA: IEEE Computer Society, 2013: 4452-4457.
[3] 王雷, 周理, 蒋新华. 合金热挤压中基于混杂模型的突变预测与仿真[J]. 系统仿真学报, 2012, 24(12): 2587-2592.
[4] Taylor J H, Zhang J.Rigorous Hybrid Systems simulation with continuous-time discontinuities and discrete-time components[C]// Proceeding of 2007 Mediterranean Conference on Control and Automation. Athens, Greece: Inst. of Elec. and Elec. Eng. Computer Society, 2007.
[5] Paul C.A. H. The Treatment of Derivative Discontinuities in Differential Equations [R]. Manchester, UK: Manchester Centre for Computational Mathematics, 1999.
[6] 张博, 董领逊, 窦丽华. 一类综合控制系统的MLD建模与仿真研究[J]. 系统仿真学报, 2009, 21(2): 500-502.
[7] Esposito J M, Kumar V, Pappas G J.Accurate Event Detection for Simulating Hybrid Systems[J]. Lecture Notes in Computer Science (S0302-9743), 2001, 2034(2001): 204-217.
[8] Shampine L F, Gladwell I, Brankin R W.Reliable Solution of Special Event Location Problems for ODEs[J]. ACM transactions on Mathematical Software (S0098-3500), 1987, 17(1): 11-25.
[9] Park T, Barton P I.State Event Location in Differential-Algebraic Models[J]. ACM Trans. Model. Comput. Simul.(S1049-3301), 1996, 6(2): 137-165.
[10] Esposito J M, Kumar V.A state event detection algorithm for numerically simulating hybrid systems with model singularities[J]. ACM Transactions on Modeling and Computer Simulation (S1049-3301), 2007, 17(1): 1-26.
[11] Hong-Shan Zhao, Yan-bin Hu. Algorithm of Event Detection for Hybrid Power System Simulation[C]// Proceeding of DPRT 2008. Piscataway, USA: Inst. of Elec. and Elec. Eng. Computer Society, 2008: 990-994.
[12] 郅跃茹, 诸静, 左光华. 混合动态系统状态事件的精确定位方法[J]. 浙江大学学报(工学版), 2005, 39(9): 41-45.
[13] Griffiths D F, Higham D J.Numerical Methods for Ordinary Differential Equations (Initial Value Problems)[M]. 1st ed. London, UK: Springer, 2010.
[14] Navarro-López E M. Hybrid-automaton models for simulating systems with sliding motion: still a challenge[C]// Proceeding of the 3rd IFAC Conference on Analysis and Design of Hybrid System. Zaragoza, Spain: IFAC Secretariat, 2009: 322-327.
[15] M Berry M.A Variable-Step Double-Integration Multi-Step Integrator [D]. Blacksburg, VA, USA: Virginia Polytechnic Institute and State University, 2004.
[16] Gwaltney C R, Lin Y, Simoni L D, et al. Interval methods for nonlinear equation solving applications [K]. Pedrycz W, Skowron A, Kreinovich V. Handbook of Granular Computing. USA: John Wiley & Sons, 2008: 81-96.
[17] Moore R E, Kearfott R B, Cloud M J.Introduction to Interval Analysis[M]. 1st ed. Philadelphia, USA: Society for Industrial and Applied Mathematics, 2009.

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

PDF (PC)

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	李智杰, 石昊琦, 李昌华, 张颉. 基于改进遗传算法的影像中心布局优化方法[J]. 系统仿真学报, 2022, 34(6): 1173-1184.
[2]	陈斌, 刘悦, 杨亚磊. 基于STN的机场航班过站保障时间协同规划建模[J]. 系统仿真学报, 2022, 34(6): 1196-1207.
[3]	杨凯, 陈纯毅, 胡小娟, 于海洋. 蒙卡渲染画面多特征非局部均值滤波降噪算法[J]. 系统仿真学报, 2022, 34(6): 1259-1266.
[4]	陈麒, 崔昊杨. 基于改进鸽群层级的无人机集群视觉巡检模型[J]. 系统仿真学报, 2022, 34(6): 1275-1285.
[5]	王沐晴, 张磊, 范秀敏, 骆晓萌, 朱文敏. VR外设驱动的虚拟人姿态优化仿真方法[J]. 系统仿真学报, 2022, 34(6): 1296-1303.
[6]	陆承, 靳学胜. 基于Steam VR的交互仿真水枪灭火训练系统设计[J]. 系统仿真学报, 2022, 34(6): 1312-1319.
[7]	高宏鼐, 付丽疆, 夏倩, 郭亚. 可观测度在光合作用模型性能评估中的应用[J]. 系统仿真学报, 2022, 34(6): 1330-1342.
[8]	倪凌佳, 黄晓霞, 李红旮, 张子博. 基于协作式深度强化学习的火灾应急疏散仿真研究[J]. 系统仿真学报, 2022, 34(6): 1353-1366.
[9]	蒙盾, 胡卓, 张华军. 基于改进A^*算法的多层邮轮疏散系统仿真[J]. 系统仿真学报, 2022, 34(6): 1375-1382.
[10]	郭宇飞, 赵康, 海永清. 面向有限元分析的三角网格布尔运算方法[J]. 系统仿真学报, 2022, 34(5): 1003-1014.
[11]	吴桐, 王清辉, 徐志佳. 三周期极小曲面多孔材料渗透率尺度特性研究[J]. 系统仿真学报, 2022, 34(5): 1015-1024.
[12]	蒋阳升, 王思琛, 高宽, 刘梦, 姚志洪. 混入智能网联车队的混合交通流元胞自动机模型[J]. 系统仿真学报, 2022, 34(5): 1025-1032.
[13]	梁江涛, 王慧琴. 基于改进蚁群算法的建筑火灾疏散路径规划研究[J]. 系统仿真学报, 2022, 34(5): 1044-1053.
[14]	张其文, 张斌. 基于教学优化算法求解置换流水车间调度问题[J]. 系统仿真学报, 2022, 34(5): 1054-1063.
[15]	邢根上, 鲁芳, 李书山, 罗定提. 基于产品体验性的供应链交货模型与仿真研究[J]. 系统仿真学报, 2022, 34(5): 1064-1075.