引用本文:柴伟, 孙先仿.改进的全对称多胞形集员状态估计算法[J].控制理论与应用,2008,25(2):273~277.[点击复制]
CHAI Wei, SUN Xian-fang.An improved estimation algorithm for set membership states by zonotopes[J].Control Theory and Technology,2008,25(2):273~277.[点击复制]
改进的全对称多胞形集员状态估计算法
An improved estimation algorithm for set membership states by zonotopes
摘要点击 1957  全文点击 1438  投稿时间：2006-05-28  修订日期：2006-11-29
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DOI编号  10.7641/j.issn.1000-8152.2008.2.018
  2008,25(2):273-277
中文关键词  非线性系统  不确定系统  状态估计  集员  全对称多胞形
英文关键词  nonlinear systems  uncertain systems  state estimation  set membership  zonotopes
基金项目  国家自然科学基金资助项目(60234010, 60674030); 北京市自然科学基金资助项目(4032014).
作者单位
柴伟, 孙先仿 北京航空航天大学自动化科学与电气工程学院, 北京100083 
中文摘要
      针对带有有界的噪声和参数的非线性离散时间系统, 提出了一种改进的全对称多胞形集员状态估计算法.在算法的时间更新过程中, 采用区间算术的方法计算一个包含系统轨迹的全对称多胞形.在算法的量测更新过程中, 则要首先在状态空间中给出一个集合作为与量测输出相一致的区域的外界描述, 然后计算一个具有最小容积的全对称多胞形作为时间更新全对称多胞形与此集合的交集的外界描述.由于此集合可表示为多个带的交集, 所以需要研究全对称多胞形与带的交集的外界描述方法.在提出改进的外界描述方法之前, 指出了原始外界描述方法的保守性.改进的外界描述方法给出了新的包含二者交集的全对称多胞形族, 然后找到具有最小容积的全对称多胞形作为二者交集的外界描述. 此后证明了改进外界描述方法得到的全对称多胞形不会比原始方法大. 最后, 采用仿真实验来检验不同噪声分布对算法性能的影响.仿真结果表明了改进算法得到的状态估计的均方误差和全对称多胞形的容积比原始算法小, 而且当存在重尾分布噪声时此优势更加明显.
英文摘要
      An improved estimation algorithm for set membership states by zonotopes is proposed for nonlinear discretetime systems with a bounded description of noise and parameters. This algorithm requires computation of a zonotope bounding the uncertain trajectory of the system using interval arithmetic in time updating. The observation update first determines a set bounding the region of the state space which is consistent with the measured output, and then computes a minimal-volume zonotope bounding the intersection of the time-updated zonotope and this set. Since this set is obtained as the intersection of strips, it is necessary to compute an outer bound of the intersection of the zonotope and the strips. The conservatism of the original outer bound computation of the intersection is pointed out before improving. The improved outer bound computation gives a new family of zonotopes containing the intersection and selects the minimal-volume one as the outer bound. It can be proved that the improved computation gives smaller zonotopes than the original one. Simulation experiments are performed to examine the influence of noise distributions on the performance of the algorithms. The results show that the improved algorithm has better performance than the original one in terms of mean-square errors and zonotope volumes especially in the presence of uniformly heavy-tailed noise.