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Alternative TitleRobust Stability and Non-Linear Programming
Thesis Advisor郑应平
Degree Grantor中国科学院自动化研究所
Place of Conferral中国科学院自动化研究所
Degree Discipline控制理论与控制工程
Keyword鲁棒稳定性 非线性规划 Kuhn—tucker条件 Robust Stability Non-linear Programming Kuhn-tucker Condition
Abstract鲁棒稳定性分析是线性系统性能分析中最重要和最基本的问题之一。具 有创意的Kharitonov定理无疑激发了人们研究多项式族鲁棒稳定性问题的热 情。期望着得到类似的简洁定理,人们尝试着进一步拓广Kharitonov定理:研 究与其对偶的菱形多项式族;将复平面上的左半开平面改为单位圆,乃至拓展到 任意D域;将多项式族的系数从区间关系拓展至系数是仿射依赖,乃至系数是 多仿射依赖的情形, 本文运用非线性规划理论及其Kuhn-Tucker条件,凭借值集分析方法及 其排零原则,尝试着统一历史上已有的一系列结论。诸如棱边定理的新证明;构 造形式的菱形多项式族的鲁棒稳定性分析;长方盒多项式族的任意D域的鲁棒 稳定性分析;以及当系数是非线性依赖于长方盒参数空间时,任意D域的鲁棒 稳定性分析所用的主点概念。 本文还研究了带固定补偿器的菱形对象族的镇定问题,固定补偿器的分 子多项式和分母多项式采用奇次多项式或偶次多项式的形式。利用二次规划的 Kuhn-Tucker条件,证明了当补偿器的分子多项式和分母多项式均取偶次多项式 或奇次多项式时,仅需镇定16个顶点对象即可判定全族对象的镇定问题。当分 子多项式和分母多项式的系数正负交错时,还可减少到检验8个顶点对象。 当 分子多项式是奇次多项式而分母多项式是偶次多项式时,或反之,则需要检验32 条棱边对象族。
Other AbstractRobust Stability Analysis is one of the most important and fundamental problems in analyzing linear systems. Motivated by Kharitonov's (1978) seminal theorem on robust stability for a class of polynomials, a lot of papers have tried to extend the result for such neat results. Some concentrated on the so-called dual problem for a diamond of polynomials. Some study the arbitrary D-domain in complex plane, e.g. the unit disc for discrete linear systems. Some consider the coefficients affinely dependent on parameter space, and even multi-affinely. In this paper, a series of historical results are unified by the non-linear mathematical programming approach with its Kuhn-Tucker conditions via value set analysis and zero exclusion principle. These results include: the famous Edge Theorem, the robust stability of diamond families, the robust stability of box polynomials for arbitrary D-domain, and the principal points concept for the robust stability of multi- affinely dependent coefficients for arbitrary D-domain This paper studies the stabilization of diamond plants with the fixed compensator whose numerator and denominator are chosen from even or odd polynomials. By the quadratic programming approach, it is proved that the necessary and sufficient conditions for the compensator to robustly stabilize the diamond plants is that it simultaneously stabilizes 16 vertex plants when both of the numerator and denominator are even or odd, and 8 vertex plants if the coefficients of the odd or even numerator and denominator of the fixed compensator positively and negatively interlaced. When numerator is even but denominator odd, or the reverse, it is suffices to check 32 specially selected edges.
Other Identifier387
Document Type学位论文
Recommended Citation
GB/T 7714
赵相一. 鲁棒稳定性与非线性规划[D]. 中国科学院自动化研究所. 中国科学院自动化研究所,1996.
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