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题名	集员辨识-算法、收敛性和鲁棒性
作者	孙先仿
学位类别	工学博士
答辩日期	1994-06-01
授予单位	中国科学院自动化研究所
授予地点	中国科学院自动化研究所
导师	张志方
关键词	集员辨识 算法 收敛性 鲁棒性
学位专业	控制理论与控制工程
中文摘要	随着系统科学和控制理论不断地向纵深方向发展，人们对系统模型的 有效性和精确性提出了越来越高的要求，因而也给系统辨识领域的研究者 提出了越来越多、越来越复杂的研究课题。系统鲁棒辨识和面向控制的系 统辨识正是目前摆在系统辨识研究者面前的两个极富挑战性的课题，而集 员辨识则是这两个课题的基本研究内容。因此，对集员辨识算法的开发及 其性质的研究是极其重要的。 本文在对集员辨识研究现状综合分析的基础上，针对参数线性模型提 出了一些新的集员辨识算法，并且对算法的收敛性和鲁棒性进行了理论分 析。 对集员辨识的椭球外界算法，本文引入了优化的初始椭球，从而提高了 辨识精度。本文提出的对重复递推椭球外界算法的改进，使我们有可能用 较少的重复次数获得与原算法相同的辨识精度。本文给出的内界椭球公式 计算简单，而且接近最优，因而是对外界椭球描述的一个很好的紧性指标。 此外，本文给出了修正Fogel—Huang算法与扩展Khachiyan算法数学等价的 严格证明，由此纠正了最近一篇文献中的错误。 基于本文提出的求解线性规划问题的递推单纯形法，我们给出了集员 辨识的一种递推盒子外界算法．这一算法的提出为集员辨识结果的在线应 用提供了一条新的有效途径。与批处理盒子外界算法相比，它在运算速度 及处理问题规模(参数个数及数据量)方面都具有绝对的优势．而且问题规 模越大，其优势越明显。一般说来，它可处理比批处理算法多几倍的数据。 仿真研究表明，对4参数模型，当数据量达到l00左右时，其运算速度有时 超过了批处理算法的100倍。 我们补充了用Walter—Piet—Lahanier精确描述算法处理退化多面锥体的 情况，由此完善了这一算法。 本文给出了集员辨识算法收敛性和鲁棒性的明确定义。我们将算法的 收敛性划分为集收敛和点收敛两类，将算法(相对于误差界低估)的鲁棒性 划分为可检测和不可检测非鲁棒性。对本文所介绍的几种集员辨识算法， 我们改正了现有文献中有关收敛性结论的某些错误，并给出了一些新的结 论。文中的一个重要工作是对几种算法鲁棒性所进行地系统分析。特别地， 对椭球外界算法鲁棒性的分析为我们利用这些算法消除了一切疑虑，并为 获得更紧的椭球外界，乃至于精确参数值提供了一个指导性的原则和依 据。 对静态变量中有界误差(UBB—EV)模型，我们给出了一种次优递推椭 球外界算法，这种算法所得椭球外界比Clement—Gentil算法所得的更紧。对 动态
英文摘要	Along with the development of systems science and control theory, the requirement for validity and precision of system models is becoming higher and higher, and more and more complex research projects are presented to the researchers in the area of system identification. Robust identification of systems and system identification for control are two challenging projects for the researchers, and set membership identification is the basic substance of the two projects. Hence, it ks very important to develop new algorithms of set membership identification and to study the properties of the algorithms. On the basis of synthetic analyses to the status quo of research on set membership identification, some new algorithms of set membership identification for models linear in the parameters are provided, and convergence and robustness of some algorithms are analyzed in the dissertation. In this dissertation, optimal initial ellipsoids are introduced into the elUpsoidal outer- bounding algorithms, so as to improve the precision of identification. An improved reprocessin8 method of recursive ellipsoidal outer-bounding algorithm is given, which makes it possible to obtain the same precision of identification as the original method can provide, but use less reprocessin8 steps. A simple formula is given to compute the inner- bounding ellipsoid which is approximate to the optimal one. In addition, we give the strict proof of mathematical equivalence of the modified Fogel-Huang algorithm and extended Khachiyan algorithms, thereby correct a mistake in a recent paper. Based on the recursive simplex method for linear programming introduced in the dissertation, a recursive box-type outer-bounding algorithm is provided, which gives us an efficient way for on-line use of the results of set membership identification. This algorithm has absolute advantage over the batch box-type outer-bounding algorithm in the computational speed and the problem scale (the number of parameters and that of data records) being treated. And the larger is the problem scale, the greater is the advantage. In general, it can treat more than a few times of data records than the batch algorithm can do. Simulations show that for a 4 parameters model, when the number of data records reaches 100, its computational speed is sometimes more than one hundred times faster than that of batch algorithm. The Walter-Piet-Lahanier exact description algorithm is complemented by adding the algorithm for the case of degenerate polyhedral cone. The explicit definitions of convergence and robustness are given. Convergence is classified as convergence in set and convergence in point, and robustness is classified as detectable and undetectable nonrobustness. Mistakes in some recent papers about the convergence results of the algorithms introduced in the dissertation are corrected, and more new results are given. One piece of the important work in the dissertation
语种	中文
其他标识符	301
内容类型	学位论文
源URL	[http://ir.ia.ac.cn/handle/173211/5643]
专题	毕业生_博士学位论文
推荐引用方式 GB/T 7714	孙先仿. 集员辨识-算法、收敛性和鲁棒性[D]. 中国科学院自动化研究所. 中国科学院自动化研究所. 1994.

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