Stability Region Analysis Using Simulations and Sum-of-Squares Programming
Stability Region Analysis Using Simulations and Sum-of-Squares Programming
复制标题
使用模拟和平方和编程进行稳定性区域分析
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
T. Wheeler
中科院分区：
文献类型：
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作者：
U. Topcu;A. Packard;P. Seiler;T. Wheeler
研究了多项式向量场系统吸引域的界的计算问题。吸引域的不变集被刻画为李雅普诺夫函数的子级集。李雅普诺夫函数的有限维多项式参数化。提出了一种利用仿真信息生成满足双线性约束必要条件的候选李雅普诺夫函数的方法。李雅普诺夫函数候选人的适用性进行评估，解决线性平方和优化问题。合格的候选人被用来计算可证明不变的吸引区域的子集，并初始化各种双线性搜索策略，以进一步优化。我们说明了从文献中得出的几个小例子的方法。
The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant sets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for the Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of the Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute provably invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on several small examples drawn from the literature.